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INTER EST RATE OPTIONS DEAL ERS' HEDGING IN THE US DOLL AR
FIXED INCOME MARKET
JohnKambhu
Federal Reserve Bank of New York
Research Paper No. 9719
May 1997
This paper is being circulated for purposes of discussion and commen t only.
The contents should be regarded as preliminary and not for citation or quotation without
rily
permission of the author. The views expressed are those of the author and do not necessa
reflect those of the Federal Reserve Bank of New York of the Federal Reserve System.
Single copies are available on request to:
Public Information Department
Federal Reserve Bank of New York
New York, NY 10045
Interest Rate Options Dealers' Hedging
in the US Dollar Fixed Income Market
John Kambhu
Federal Reserve Bank of New York
May 22, 1997
Abstract
asset
The potential for the dynamic hedging of written options to lead to positive feedback in
Using
price dynamics has received repeated attention in the literature on financial derivatives.
paper
data on OTC interest rate options from a recent survey of global derivatives markets, this
With
addresses the question whether that potential for positive feedback is likely to be realized.
in
volume
ion
transact
,
the possible exception of the medium term segment of the term structure
available hedging instruments is sufficiently large to absorb the demands resulting from the
shocks.
dynamic hedging of US dollar interest rate options even in response to large interest rate
and
I an1 grateful for helpful comments and suggestions of Young Ho Eom, James Mahoney,
Bank
participants in worksho ps at the Bank for International Settlements and the Federal Reserve
reflect
ily
necessar
of New York. The views expressed in this paper are the authors' and do not
the position of the Federal Reserve Bank of New York or the Federal Reserve System.
May 22, 1997
t
Interest Rate Options Dealers' Hedging in the US Dollar Fixed Income Marke
John Kambhu
beyond
has gone
With the growth of derivatives markets the scope of financial intermediation
s allow
the traditional realm of credit intermediation. The instruments in these market
ers by unbundling
derivatives dealers to intermediate the risk management needs of their custom
a custom er can trade
customer risks and reallocating them through the derivatives markets. Thus
one example of such
or hedge away unwanted risks while retaining other exposures. Options are
prices in one direction
unbundling as they allow the buyer to acquire exposure to a change in asset
without exposure to a move of asset prices in the opposite direction.
by
In addition to advances in technology, the growth of these markets have been driven
intermediate
the two-sided nature of custom er demands. Hence, dealers have been able to
t themselves
customer demands, passing exposures from some customers to others withou
1
exposures, the
assuming all the risks shed by their customers. Without such ability to lay off
by their customers.
markets' growth would be limited by dealers' ability to absorb the risks shed
, some residual risks
Nevertheless, in the over-th e-coun ter US dollar interest rate options market
they have purchased,
are concen trated among dealers. First, dealers have sold more options than
. Sold options
and additionally, the bought and sold options may have different characteristics
A2), and sold
exceed bought options by 30% in terms of notional amount (see Annex Table
dealer portfolio has
options also have lower degrees of moneyness. Hence, while the aggreg ate
the aggregated
positive value (to dealers as a group), large changes in interest rates would cause
dealer portfolio val~e to turn negative.
1
/
For additional discussion, see Kambhu, Keane, and Benado n (1996).
2
Dealers' hedging transactions in underlying fixed income markets required for the
management of the price risks of their options' business raises two questions. First, might dealers'
hedging demands be so large as to disrupt the markets in the available hedging products? Second,
is the dynamic hedging of dealers' residual exposures sufficiently large to justify a concern about
positive feedback in price dynamics in the fixed income market?
The potential for dynamic hedging of written options positions to introduce positive
feedback in asset price dynamics has received repeated attention in the literature on financial
derivatives. A short and incomplete list would include, Grossman (1988), Gennotte and Leland
(1990), Fernald, Keane and Mosser (1994), Bank for International Settlements (1995), and
Pritsker (1997). Using data on OTC US dollar interest rate options from a survey of global
derivatives markets, this paper assesses the likelihood of such positive feedback caused by
dynamic hedging of options.
The estimates in this paper suggest that, with the possible exception of the medium term
segment of the term structure, transaction volume in available hedging instruments is large enough
to absorb dealers' dynamic hedging of US dollar interest rate options. While a definitive answer
to the positive feedback question would require data on investors' demands in addition to dealers'
hedging demands (see Pritsker 1997), comparing potential hedging demand with transaction
volume in typical hedging instruments might give a provisional assessment of the likelihood of
positive feedback.
1. Introduction
The analysis in thi5 paper is based on global market data for US Dollar OTC interest rate
options from the April 1995 Central Bank Survey of Derivatives Markets (Bank for International
Settlements, 1996). The options were option contracts on US dollar interest rates, most of which
were probably LIBOR related rates.2 Using data on the options' notional amounts and market
2/
The Survey also included data for over-the-counter options on traded interest rate
securities (bond options). These options were not included in the analysis in this
3
al dynamic hedging
values, strike prices of the options were estimated and used to analyze potenti
and maturity data
volume in response to interest rate shocks. In particular, given notional amount
ed of the
(from the Survey) and market growth data (from ISDA'), estimates were generat
on historical
notional amount of options by maturity and origination date. Strike prices, based
time, such that the
interest rate data, were then assigned to the options originated at each point in
strike prices produced option values equal to those observed in the survey.
would
With the estimated strike prices and a postulated interest rate shock, we ask what
of a hedged option
be the change in dealers' hedge positions that would restore the net delta
net demand of
portfolio to its initial level? This hedge adjustment is the estimated incremental
ed demand for
dealers for hedge instruments, given the assumed interest rate shock. The estimat
k effects
hedge instruments might give some indication of the potential for positive feedbac
attributable to derivatives dealers' hedging of their OTC options portfolios.
Options
2. Price Sensitivity of the Global Dealer Portfolio of US Dollar Interest Rate
on data
Figure 1 shows the estimated price sensitivity of the global dealers' portfolio based
t reported in the
at the end of March 1995. The value at the prevailing forward rates is the amoun
values. While
Survey, and the values at the indicated changes in interest rates are estimated
rates the
dealers have sold more options than they have purchased, at the prevailing forward
portfolio was
bought options had higher market values and the net value to dealers of the global
l amounts and
positive (see Annex Tables Al and A2). This relationship between the notiona
ers had a lower
market values of bought and sold options implies that the options sold to custom
strike prices are
degree of "moneyness" than options purchased from customers. The estimated
were found
consistent with this relationship, as relative to swap rates at origination, sold options
ed to be in-theto be out-of-the money while options purchased from customers were estimat
moncy.
paper. They amounted to less than 8% of options related to interest rates.
3
/
International Swaps and Derivatives Association.
4
Since dealers were net sellers of options, large interest rate shocks that drive the sold
options into-the-money will cause the value of the sold options to exceed the bought options'
value. Hence, the aggregate dealers' portfolio value becomes negative if interest rate rise by more
than I 00 basis points. Figure I shows, however, that if the portfolio is hedged (but the hedge not
dynamically adjusted) the value of the hedged portfolio would tum negative only after an
extremely large interest rate shock. A rise of interest rates of almost 200 basis points would be
required before the hedged portfolio value turns negative. Dynamically adjusting the hedge
position as interest rates change would make such an adverse outcome even less likely.
The curverture of the option value function implies that the hedge position must be
adjusted after an interest rate shock because the option values decrease at an increasing rate as
interest rates rise. Without the hedge adjustment, the gain in value of the initial hedge position
would no longer be sufficient to compensate for the declining option values. This need to
dynamically adjust the hedge position as interest rates change introduces a potential for positive
feedback. Since the required hedge is a short position in fixed income securities, the hedge
adjustment would introduce additional sales into the market on top of the initial selling pressure
that accompanied the initial interest rate shock.
Another feature of the aggregate dealer position is its exposure to rising interest rates: the
negative slope of the option value curve at the prevailing forward rates in Figure 1. The
conventional view of financial institutions' interest rate risk profile holds that these firms have a
structural long position in the fixed income market. Namely, exposure to rising rates. Thus figure
1 implies that, in the aggregate, dealers as a group can not hedge their net option exposures with
offsetting structural exposures from other business lines. While some dealers may have offsetting
exposures elsewhere in their firms that hedge their options position, Figure 1 suggests that not all
dealers can fully hedge internally.
3. Dynamic Hedging Volume
The market for US dollar interest rate products is ·sufficiently large and diverse that
5
options dealers can choose from a wide range of hedging instruments, such as futures contracts ,
FRAs, interest rate swaps, and Treasury securities. While these instruments are not perfect
substitutes because of differences in credit risks, transactions costs, and liquidity, dealers
intermediate risks and provide risk management services to the markets by taking on and
managing these risks. If dealers have sufficient time to hedge a position or replace a hedge with a
cheaper alternative, they are unlikely to encounte r difficulty meeting their hedging needs. For
immediate hedge adjustmen ts in large volume, however, their alternatives may be be more limited.
Across the range of maturities that need to be hedged, the most liquid instruments available are
Eurodolla r futures, Treasury securities, and Treasury futures.
Eurodollar futures:
The Eurodolla r futures market appears to have transaction volume sufficiently large to
accommo date the estimated hedge adjustments for small interest rate shocks. At shorter
maturities, the Eurodolla r futures market is more than large enough to accommo date dealers'
hedging demands, even for large interest rate shocks. For hedging of longer maturity exposures,
however, the Eurodolla r futures market appears to be able to accommo date only the hedging of
residual exposures (after the use of other hedging instruments) and marginal adjustmen ts to hedge
positions.
The largest daily turnover volume of Eurodollar futures contracts exceeds the estimated
hedge adjustments: out to 10 year maturities, for a 10 basis point change in forward rates; out to
4 to 5 years, and also between 8 and 10 year maturities for a 25 basis point change in forward
rates (Table 1); and, out to only 2 year maturities, for a 75 bp change in forward rates (Table 2).
To put these figures in perspective, a 25 basis point change is slightly less than the largest daily
change, and a 75 basis point change is slightly less than the largest two-week change, in forward
rates in the 4 to 7 year segment of the yield curve (during the period 1991 to 1995).
The estimated hedge adjustments are smaller than the stock of outstandi ng futures
contracts. Even in the case of hedge adjustments to a 75 basis point change in forward rates, the
6
estimated hedge adjustment in most cases is much less than half of outstanding futures contracts
(Table 3.)
With respect to the estimated hedge position, rather than adjustments to the hedge
position, for longer maturity exposures the Eurodollar futures market is not large enough to
accommodate the entire hedge demands that would be generated by a fully delta neutral hedging
strategy, especially for exposures beyond 4 or 5 years (Table 3.)
Treasury securities:
To hedge exposures to forward rates between 5 and 10 years maturity, a possible hedge
position in Treasury securities consists of a short position (sale of a borrowed security) in the I 0
year note, and a long position in the 5 year note. With this hedging method, dealers' estimated
hedge adjustments would be less than the daily turnover volume of on-the-run securities (Table 4,
Panel A). For an extremely large shock to forward interest rates, however, such as a 75 basis
point shock to forward rates beyond 5 years out, the estimated hedge adjustment in the 5 and 10
year note would be as large as half of average daily turnover.
With regard to the hedge position, the on-the-run issue volume appears to be too small to
accommodate hedging demand if a fully delta neutral hedging strategy were attempted exclusively
in the cash market in Treasury securities. For example, if dealers fully hedged their exposures
beyond 5 years with 5 and 10 year on-the-run issues, the required hedge position would be
approximately equal to the outstanding amount of the on-the-run 5 and IO year notes (Table 4,
Panel A).
Two means by which the Treasury market may accommodate this hedging demand exist.
First, the existence of a large repo (collateralized security lending) market in Treasury securities
allows a fixed stock of on-the-run Treasury securities to meet trading demands that exceed the
size of the on-the-run issue. Through the repo market, a trader that establishes a short position
enables another trader to establish a long position in the security. Hence, the size of market
7
participants' long position in the security can be larger than the outstanding stock of the security.
Second, off-the-run issues when available can also be used, further enlarging the pool of available
ately
hedging instruments. Heming (1997) reports that off-the-run securities account for approxim
24% of daily turnover.
Futures on Treasury securities:
In addition to the cash market in Treasury securities, dealers can also hedge exposures
B of
between 5 and 10 year maturities with futures contracts on Treasuries. As seen in Panel
d
Table 4, open interest and turnover volume in the Treasury futures market exceeds estimate
of the
dealers' hedging demand. Nevertheless, that demand could be significant relative to the size
large as
market. For example, the estimated hedge adjustment to a 75 basis point shock could be
the
25% of the combined average daily turnover in the Treasury cash and futures markets, while
(see
estimated hedge position could be as large as a third of total outstandings in both markets
Table 4, Panels A and B).
Interest rate term structure models and hedging:
If dealers are willing to accept model risk (correlation risk), they could also hedge
of
exposures beyond 5 years by spreading their hedging demands across a wider maturity range
factor
securities than only the 5 and 10 year notes. For example, with the use of a two (or more)
5 and
interest rate term structure model, a dealer could construct a hedge of exposures between
the
10 years using a position in one year bills and 30 year bonds that replicate the exposure to
,
term structure factors that drive forward rates between 5 and 10 years. Such hedges, however
for.
would be vulnerable to atypical price shocks that the term structure model does not account
Conclusions:
The estimated size of dealers' hedge positions of longer maturity exposures, suggests that
of
dealers' hedges, especially of exposures beyond 4 years maturity, are distributed over a range
than
fixed income instruments. While outstanding Eurodollar futures contract volume is smaller
the estimated size of the hedge position beyond 5 years, the large size of the US dollar fixed
8
income market suggests that the hedge positions can still be absorbed by the markets in other
fixed income instruments. With regard
to
an immediate dynamic hedge adjustments to an interest
rate shock, however, the ideal hedging instrument is one that is liquid and has low transactions
costs, such as Eurodollar futures, on-the-run Treasury securities, or Treasury futures.
Impact on transaction volume.
The Eurodollar futures, on-the-run Treasury securities, and Treasury futures markets
together can easily absorb hedge adjustments to shocks to the forward curve as large as 25 basis
points along the entire term structure (Tables I and 4). For example, the estimated hedge
adjustment for 5 to 10 year exposures to a 25 basis point shock is approximately 10% of the
combined turnover in the Treasury on-the-run cash and futures markets.
For an extremely large interest rate shock, however, such as a 75 basis point shock
to
forward rates, dealers' dynamic hedge adjustments would generate significant demand relative to
turnover in these hedging instruments: on the order of 25% of combined turnover (see Tables 2
and 4). In this case, by bearing the price risk of a partially hedged position and spreading the
hedge adjustment over more than one day, the hedge adjustment could be broken into pieces that
would be small relative to daily turnover. The terms of this tradeoff between price risk and the
cost of immediacy or liquidity of course would depend on the volatility of interest rates, and
volatility may rise at the same time that liquidity is most impaired.
These results suggest that dealers' intermediation of price risks through market making in
interest rate options is supported by liquidity in underlying markets that allow them to manage
their residual price risks. Transaction volume in the standard hedging instruments appear to be
large enough to accommodate dealers' dynamic hedging in all but the most extreme periods of
interest rate volatility.
Price impact.
With regard to the price impact of dynamic hedging our results are less clear. For a
9
definite answer an analysis of demands of other market participants would be required (see
be
Pritsker, 1997). For example, investors whose demands are driven by "fundamentals" could
flows if
expected to undertake transactions in the opposite direction of dealer's dynamic hedging
s
those transactions drove interest rates to levels that appeared unreasonable. If these investor
and
constitute a sufficiently large part of the market, then their transactions would stabilize prices
only
keep positive feedback dynamics in check. However, such stabilizing investors are not the
trends
other market participants. Other participants include traders who follow short term market
to be
either because of "technical trading" strategies or because they interpret short term changes
impact
driven by transactions of better informed investors. These traders could amplify the price
depend
of dealers dynamic hedging. Thus, the ultimate impact of dealers' dynamic hedging would
on the relative sizes of these types of market participants, as described in Pritsker ( 1997).
At shorter maturities, transaction volume and open interest of the most liquid trading
driven
instruments are so much larger than dealers' dynamic hedging flows that positive feedback
r,
by dealers' dynamic hedging seems unlikely, even with very large interest rate shocks. Howeve
large
at longer maturities, around 5 to 10 years, dynamic hedging in response to an extremely
open
interest rate shock could be of significant volume relative to total transaction volume and
the
interest in the most liquid trading instruments. Hence, at this segment of the yield curve,
d.
positive feedback hypotheses in the case of a very large interest rate shock can not be dismisse
be large
The dynamic hedging volume in response to an unusually large interest rate shock could
y
enough to have a significant impact on order flows. Such order flows might have a transitor
impact on this medium term segment of the yield curve.
4. Volatility Shocks
The results in Section 3 were estimated under the assumption that the volatility of interest
rates are
rates remained constant while interest rates changed. However, large changes in interest
typically associated with higher implied volatilities in options prices. For this reason, hedge
(Table
adjustments were also estimated assuming simultaneous volatility and interest rate shocks
was
5). Forward rates were assumed to increase by 75 basis points, while interest rate volatility
10
assumed to increase by 25% relative to initial volatility levels at the shortest maturity and by 8%
at IO-years (one-third of the change at the short end). While the estimated hedge adjustment is
larger, the difference does not appreciably change the conclusions in Section 3.
While exposure of interest rate option values to interest rate changes can be hedged with a
wide range of instruments, exposure to changes in the volatility of interest rates is not easily
hedged. Given that dealers as a group are net writers of options, their exposure to volatility
probably remains largely unhedged as the volatility risk of an option can be fully hedged only with
another option. Figure 2 shows the estimated volatility risk of the global dealer portfolio. An
increase in volatility of approximately 40% would cause the portfolio value to tum negative.
Since most customer options in the over-the-counter market are probably held to maturity,
changes in volatility would affect dealers through changes in their hedging costs and the
mismatches between the option and hedge positions over the life of an option. A rise in volatility
would raise these hedging costs, as it amplifies the costs of adjusting hedge ratios. The increase
in these costs over the life of an option equals the change in the option's value. Figure 2 shows an
estimate of these costs.
5. The Data and Estimation
Options market data:
The data are from the 1995 Central Bank Survey of Derivatives Markets (Bank for
International Settlements, 1996). This data, reported by derivatives dealers world wide, are
global market totals of outstanding derivatives contracts at end of March 1995. The options data
in the survey included notional amounts, market values, and maturity data, broken down by
bought and sold options, as shown in Annex Tables Al, A2, and A3. The options data had three
counterparty types: interdealer options, options bought from customers, and options sold to
customers. Since reporters in the Survey were derivatives dealers, interdealer transactions appear
as both bought and sold options because an option bought by one dealer would also be reported
as an option sold by another dealer. The discrepancy between interdealer amounts in the bought
11
and sold columns is reporting error in the survey.
Maturity distribution:
The maturity data in Table A3 and market growth rates from ISDA's surveys were used to
estimate a more refined maturity distribution. This distribution was based on an assumption that
the options had maturities up to 10 years, with origination dates up to 10 years earlier, both in 6
month increments. The maturity distribution of options originated at any date is described by a
quadratic function, and the notional amount of options with t periods remaining maturity,
originated p periods in the past is
p
(Ilg.)(a + b(t+p) + c(t+p)2)
=
n(t,p)
(I)
j•O J
and, n(t,p) = 0, for t+p < 1 year,
,
where tis remaining maturity, t < 10 years; pis the origination date (periods earlier), p < IO
years; t+p is the original maturity, t+p < 10 years; gi is the market growth term at period j. The
restriction in (I) forces caps and floors to have maturities of at least one-year when originated.
(Regardless of this restriction, the first caplet (option) in any cap or floor has a maturity of 3
months (the midpoint of the first 6-month time band). Estimates without this restriction are
shown in Section 6.
The maturity distribution is found by solving for the parameters (a,b,c) of the quadratic
function (1) in the following system of equations,
I: I: n<r.p)
=
N,
(2a)
I: I: n<r,p)
lyr<ts:5yrs
=
Ns
(2b)
I: I: n(t,pl
5yr<ts:
=
N,o
(2c)
ts:1yr p
p
IOyrs
p
12
where Nm are notional amounts in the survey's three maturity categories (see Annex Table A3).
Separate maturity distributions were estimated for interdealer options, options purchased
from customers, and options sold to customers. The maturity data, however, were available only
for all sold options and all bought options, where interdealer options were included in the maturity
data of both bought and sold options. The maturity distribution of interdealer options was
assumed to be the average of the bought and sold options' maturity distributions.
Figures Al and A2 show the estimated distribution of outstanding contracts over
remaining maturity and origination dates. In these charts, contracts along the diagonal from left
to right are contracts that were ten-year contracts at origination, where the left most point is a 10year contract originated within 6-months of the survey date. The growth of the market is
apparent along this diagonal. Most outstanding contracts were of less than five years remaining
maturity and were originated within three years of the survey date. The estimated distribution has
a trough along the diagonal for caps of greater than 5 and less than 10 years maturity (at
origination). This feature of the distribution suggests that long maturity caps are clustered at
discrete maturities, and at the 10 year maturity in particular.
Option price function:
All options are assumed to be caps and floors on 6-month interest rates, whose values are
estimated using Black's forward contract option model (see Hull, 1993). The value of the period
t payoff of a cap and floor with strike rate x and notional amount n is
-,,
1
C(n,t,x)
=
e ' [f, N(Dl(t,x)) - x N(D2(t,x))]-- n
F(n,t.r)
=
e-','[x N(-D2(t,x)) - J,N(-Dl(t,x))]
1 +
.
I
}..J,
}..
+
}..J,
n
2
a, t
where,
DI (t;>:)
2
=
a, {t
D2(t,x)
=
Dl(t,x) -
o, {t ,
13
is the
and A is the length of the period for which the reference interest rate applies (6-months),f,
. The
period t interest rate, a, is its volatility, and N(.) is the standard normal distribution function
value of a cap (floor) with maturity rn is,
v '(n,rn,x)
L C(n,t,x),
=
t<m
v 1(n,rn,x)
L F(n,t,x).
=
l<m
The valuation used the term structure of forward rates and the term structure of implied
volatilities coinciding with the option value data (end-of-March 1995).4 Section 6 presents
estimates using alternative implied volatility structures.
Strike prices:
Strike prices were derived from historical yield curves. Because separate market values
was
were not available for caps and floors, a relationship between the strikes of caps and floors
of
required in the estimation. The structure was chosen on the assumption that buyers (sellers)
of
caps and floors had similar preferences regarding their options' moneyness. Thus, if buyers
caps desired out-of-the money options because of their cheaper premia, then buyers of floors
would also. This structure regarding the options' moneyness was implemented in three different
ways. These implementations gave similar results as shown in Table 6.
First, a proportional displacement of the strike price from the swap rate. The strikes of
caps and floors are,
x"P(t,p,A)
4
/
=
h(t+p,p) A
(3. la)
The data are from Derivatives Week (1996). The Derivatives Week data on
forward rates and implied volatility data are consistent with those implied by
Eurodollar futures prices and Eurodollar futures options prices.
14
:,!1' (t,p,A)
=
h(t+p,p)
A
(3.lb)
where, tis the remaining maturity of the cap, p is the origination period (periods earlier), t+p is
the cap's original maturity, h(m,p) is the historical swap rate of p periods earlier for am period
maturity swap, and A is a scaling factor. 5
Second, a cap and floor are assumed to have equal premia at origination,
v"•(n, t, h(t,p )A"")
=
v"'(n, t, h(t,p)A"'),
(3.2a)
where the option values are evaluated at the term structures prevailing at origination, the strikes
are defined as,
x"•(t,p,A) = h(t,p )A"•, and, x"(t,p,A) = h(t,p )A"',
(3.2b)
and A"" and A"' are separate scaling factors for caps and floors.
Third, a cap and floor are assumed to have equal deltas at origination,
LI v"•(n, t, h(t,p)A"")
=
I LI v"'(n, t, h(t,p)A"') I,
(3.3)
where LI v"• and LI v"' are the deltas of a cap and floor (evaluated at the term structures prevailing
at origination), and the strikes are defined as in (3.2b).
The scaling factors (A) are chosen so that the option values at the resulting strike prices
5
/
A complete 10 year time series for swap rates could not be found (data were
available only from 1988). To complete the time series, the missing values were
assumed to equal the corresponding Treasury rate plus the last available swap
spread.
15
equal the observed market values in the Survey. In each of the above specifications, the
(A) for
restrictions are applied to bought and sold options separately, with different scaling factors
y when
bought and sold options. In these strike price specifications, a cap will be out-of-the-mone
6.
a floor is out-of-the-money. These specifications produced similar results, as seen in Table
Other strike price specifications are presented in Section 6.
Estimated strike prices and option values:
Given the strike prices defined in (3), total values for bought and sold customer options,
and interdealer options can be defined as functions ofthe scaling factors (A),
(4a)
=
p
I
=
V (A')
·'
LL v'(S '(t,p),t,x '(t,p,A '))
p
I
p
I
+
LL vf(Sf(t,p),t,xf(t,p,A '))
(4b)
p
I
=
I
p
I
p
amount
where Band Sare notional amounts for bought and sold customer options, Dis notional
maturity
of interdealer options; and v(n,t,x) is the value of a cap (floor) with notional amount n,
on
t, and strike price x. The index t represents remaining maturity, the index p is the originati
date, where t+p < 10 years, and the superscripts c and f denote caps and floors.
On the basis ofISDA data we assume that caps amount to 73% of the options with the
yearremainder being floors. A small proportion of interest rate options are swaptions (19% at
or
end 1994 in the ISDA data). However, for simplicity, we treat all options as either caps
floors.6
6
/
This assumption is not likely to alter the paper's conclusions. For example, if a one
year option on a five year swap were reported as a one year option, then the
swaptions would appear as shorter maturity options in the data. Hence, the true
exposures of shorter maturity would be less than assumed in the estimation, with
the result that hedging demand for shorter maturity instruments would be smaller
16
The value of each group of options in (4) is determined by the scaling factors in the strike
rates -- the parameter A in the strike price equations (3) and the value equations (4). The
estimation is to find values of Ab, A', and Av, such that:
(Sa)
(Sb)
subject to the restriction in (3.1, 3.2, or 3.3), where v• (and v,) is the observed market value of
US dollar options bought (and sold) by dealers including interdealer options.
Given the value of interdealer options (see below), in the case of the strike price structure
(3.1), the estimation for bought options consists of solving for the single parameter A• in equation
(Sa). In the strike price structure (3.2), however, the estimation for bought options consists of
solving for the two parameters A ,ap, Afl' in the two equations (3.2a) and (Sa).
lnterdealer options:
Separate market values of interdealer US dollar options were not collected in the Survey.
(The interdealer market values was available only in aggregate across all currencies, see Annex
Table Al). For that reason, the solution to the equations in (5) is calculated using four alternative
assumptions: (1) inter-dealer options have strikes equal to the reference rate, Av=l, in (3.1), (atthe-money strikes, relative to the swap term structure); (2) inter-dealer options have the same
than estimated. This effect would only strengthen the conclusion that shorter
maturity hedging volumes are small relative to transaction volume in Eurodollar
futures. On the other hand, however, the swaptions would add to the estimated
hedging demand at longer maturities. Nevertheless, since swaptions are only 19%
of the market, the net increment to estimated hedging demand would not
significantly change the conclusions. The effect would be to strengthen the
conclusion that longer maturity hedging demand could be significant relative to
order flows in longer maturity hedge instruments, but not so much larger as to
overwhelm the market.
17
strikes as options bought from customers, AD=Ab; (3) inter-dealer options have the same strikes
as options sold to customers, AD=A', and; (4) estimate the value of US Dollar interdealer
options from the data in Annex Tables Al and A2. The la.st estimation method (4) distributes the
market value of interdealer options in Annex Table Al between US dollar and other currencies so
as to minimize the error in the ratios of market value to notional amounts relative to the margin
ratios of the totals in Annex Tables Al and A2.
The first and la.st alternatives produce comparable values for interdealer options. The atthe-money assumption (1) produces a value of interdealer options of$ I 1.3 billion, while the
estimation in (4) results in a value ofinterde aler options of$10.9 billion. Table 8 shows the
comparability of the hedge estimates with assumptions (1) and (4). Results using the other
assumptions (2 and 3) were also similar to those in (1) and (4). The results reported in Sections 2
3, and 4 were derived using assumption (4).
An implication of the comparability of methods (1) and (4) is that interdealer options have
strikes closer to at-the-money than customer options. This result is plausible, since dealers who
use the interdealer market to hedge their short volatility and negative gamma position would
obtain more hedging benefit from at-the-money options since such options have larger gamma and
provide the most hedging benefit relative to their premia.
Customer options:
For options sold to customers, estimated strikes consistent with observed market values
were predominantly deep out-of-the money (relative to swap rates of comparable maturity) at
origination. This result is plausible, as customers buying options to hedge could acquire cheap
protection against large -interest rate shocks with deep out-of-the money options. For caps sold to
customers, the estimated strike rates were 18% higher than swap rates of the same maturity at
origination. The figure of 18% is comparable to the standard deviation of annual changes in
interest rates, or two standard deviations of quarterly interest rate changes (6-month LIBOR rates
during the period 1991 to 1995).
18
For options bought from customers, strike prices consistent with the observed market
values were predominantly in-the-money (relative to swap rates of comparable maturity) at
origination. This relationship is the opposite of the relationship found for options sold to
customers. While this result might appear counterintuitive and could point to a problem in the
estimation, it is consistent with market commentary in the early 1990s. Customers looking for
"yield-enhancement" during the low-interest rate regime of the early '90s, acquired higher premia
by selling interest rate caps with a higher degree of moneyness. While this "higher yield" is the
market price or compensation for the expected payout of the option, investors speculating on the
path of interest rates would obtain higher investment returns (or losses) per option by selling inthe-money options. In addition, investors who believed that the forward curve was an
overestimate of the future path of spot rates would sell options that were in-the-money relative to
the forward curve. In retrospect, for positions that were not leveraged, the risks appear to have
been moderate.
Assumptions regarding hedging:
The analysis of dealers' hedging behavior relies on the following assumptions.
(al)
Customers do not hedge their options positions.
Customers who have sold or bought options are assumed not to hedge, because doing so
would negate what ever hedging or investment objective the options were used for. Customers
who have sold options to dealers presumably did so for speculative "yield enhancement" or
intertemporal income shifting. In which case, the costs of delta hedging the options would negate
that investment objective. On the other hand, customers who have bought options from dealers
for hedging purposes would not hedge the option since doing so would expose the underlying
position the option was hedging.
If customers were to hedge their options, perhaps due to a reassessment of risks, then the
market impact of dealers hedge adjustments would be smaller because they would be offset by
customers' hedging. Since the predominance of our results support the claim that the market
19
(al)
impact of dealers' hedging is small relative to the size of the market, dropping assumption
would only strengthen the results.
(a2)
Dealers restore the net delta of their position after an interest rate shock to its initial level.
Regardless of whatever hedge ratio they had initially, subsequent to an interest rate shock
back to its
dealers are assumed to adjust their hedge position to bring the net delta of the portfolio
initial level. Dealers may or may not fully hedge the initial delta of the options book, and
positions
whatever hedging is initially done may be accomplished either internally with offsetting
internal
in the firm or with external hedging transactions. These initial offsetting positions, either
or external, are assumed to have small gamma so that a change in the options' delta requires
additional hedging transactions to return the portfolio's net delta to its original level.
(a3)
has
An option exposur e to a period t interest rate is hedged with an instrument that also
exposure to the period t interest rate -- no basis risk in hedged positions.
e.
With this assumption, a separate hedge ratio was calculated for each maturity's exposur
Estimated hedge:
The delta and the change in delta of the global dealers' portfolio was calculated given the
notional amounts (from equation (2)) and estimated strike prices (from equation (5)). The
in delta
estimated delta is the hedge position of all dealers' (if they fully hedged) and the change
to
given an assumed interest rate shock is the change in the dealers' hedge position. In response
their
an interest rate shock, if dealers are assumed to restore the net delta of their portfolios to
for
initial levels, then the change in delta of the global portfolio is the incremental dealer demand
ents
hedge instruments. If hedging is executed with futures contracts, the estimated hedge adjustm
) is shown in
are shown in Tables 1 and 2, and the hedge position (assuming complete hedging
year
Table 3. Table 4 shows the hedge adjustment and hedge position, if hedging of 5 to 10
described
exposures is done with Treasur y securities and futures on treasuries. These results are
in Section 3.
20
6. How robust are the results?
The results shown in Tables 1 to 4 are the results with the basic assumptions described
above with the strike price specification (3.1). To explore whether these results were sensitive to
the assumptions, estimates were also performed using a variety of assumptions regarding the
structure of strike prices, implied volatility, and other restrictions. The estimated hedge position
and its change due to interest rate shocks were comparable across these different specifications
and do not alter the conclusions. The results with these alternative assumptions are shown in
Tables 6 through 8. The first column in these tables is the result under the basic assumptions,
and the other columns are the results with the alternative assumptions.
Strike price variations:
Distribution of strike prices. Options uniformly distributed over two different strike prices, with
the larger strike 22% higher than the smaller (10% above and below the reference rate).
Maturity variation in strike prices. For options bought from customers, the options' "moneyness"
was assumed to vary with original maturity. In the first variation, the deviation of the strike from
the swap reference rate decreased with maturity, and in the second the deviation increased with
maturity.
Identical strike prices for caps and floors. Estimation of the value of bought options with the
restriction that caps and floors have identical strikes. This estimation produced in-the-money caps
and out-of-the money floors. Applying a similar restriction for sold options was not meaningful,
as it produced estimated option values that exceeded the observed values. This result supports
the use of equation (3) for sold options.
Implied voJati1ity variations:
Cap and floor implied volatilities. Option values estimated with different volatilities for caps and
floors. Caps were estimated using the Derivatives Week implied volatility data as in the base
case, but volatilities for floors were adjustment upwards to conform with the difference between
21
cap and floor implied volatility in DRI data. (The DRI implied volatility data are available only
from January, 1996; while the Derivatives Week implied volatility data are derived from caps).
Volatility smile. AI, an alternative to a common implied volatility across all degrees of
"moneyness," results were also estimated using a volatility smile. A volatility smile over degrees
of moneyness consistent with Eurodollar futures options prices was constructed, and extrapolated
across all maturities using the base volatility term structure as the at-the-money volatility.
Other variations:
Options on 3-month interest rates. Instead of assuming that all options were on the 6-month
interest rate, results were derived on the assumption that the options were 3-month interest rate
options.
Growth rate assumption in maturity distribution. The ISDA market size data for interest rate
options contained a number of anomalous growth rates between certain dates. On the possibility
that these growth rates were due to survey problems at those dates, alternative smoothed growth
rates were derived by ignoring the anomalous market volumes. The notional amounts from the
Central Bank Survey were then distributed across maturities and origination dates using these
alternative growth rates in equations (1) and (2).
Unrestricted maturity distribution. The distribution of notional amounts across maturities and
origination dates in (I) and (2) was estimated without the restriction that all caps (floors) have a
maturity of at least one year when originated.
22
References
Bank for International Settlements. Issues of Measurement Related to Market Size and
Macroprudential Risks in Derivatives Markets. February, 1995.
___ . Central Bank Survey ofForeiw Exchan~e and Derivatives Market Activity. May, 1996.
Derivatives Week. April 1, 1996.
Fernald, Julia, Frank Keane, and Patricia Mosser. "Mortgage Security Hedging and the Yield
Curve." Federal Reserve Bank of New York Quarterly Review, 19, #2, 1994.
Fleming, Michael. "The Round-the-Clock Market for U.S. Treasury Securities." Federal Reserve
Bank of New York Economic Policy Review. Forthcoming, 1997.
Gennotte, Gerard, and Hayne Leland. "Market Liquidity, Hedging, and Crashes." American
Economic Review, 80, #5, 1990.
Grossman, Sanford. "An Analysis of the Implications for Stock and Futures Price Volatility of
Program Hedging and Dynamic Hedging Strategies." Journal of Business, 61, 1988.
Hull, John. Options. Futures and other Derivative Securities, 2nd edition. Prentice Hall,
Englewood Cliffs, NJ, 1993.
Kambhu. John, Frank Keane. and Catherine Benadon. "Price Risk Intermediation in the Over-theCounter Derivatives Markets: Interpretation of a Global Survey." Federal Reserve Bank of New
York Economic Policy Review, 2, #2, 1996.
Pritsker, Matt. "Liquidity Risk and Positive Feedback." Working Paper. Federal Reserve Board,
March, 1997.
23
Annex: Data
Table Al
Market Values of OTC Interest Rate Options
Billions of USD
USD
Bought
Other
Total
USD
Total
21.6
14.6
22.4
15.2
Dealer
Customer
Total
Sold
Other
37.6
16.7
20.9
16.8
19.4
36.2
Table A2
Notional Amounts of OTC Interest Rate Options
Billions of USD
USD
Bought
Other
Total
Dealer
Customer
529.4
432.7
726.5
340.6
1255.9
772.2
Total
961.1
1067.1
2028.1
Sold
Other
USD
681.9
398.1
1258.1
1088.4
1080.0
2346.5
576.1
690.4
1266.5
Total
Table A3
Maturity Distribution of USO Interest Rate Options
Bought Options
Up to one year
Over one and up to five years
Over five years
295
573
116
Total
984
(30%)
(58%)
(12%)
Sold Options
357
697
189
(28%)
(56%)
(15%)
1,243
Note: With adjustment for reporting error in interdealer bought and sold options.
Figure Al
Bought Options
Origination
Date
Remaining
Maturity
Nb
Figure A2
Sold options
Origination
Date
Remainin
Maturity
Ns
Note: The period numbers on the axis are in six month increments (20 periods= 10 years), and the origination
date is the number of periods ealier.
Figure 1
Net Options and Hedge Values(-)
2,---- ,----,- --.,--- ---,--- .----r- ---,--- ,
0
Option values
V_Opt
Value of Hedge
-v_Hg
9
(with sign reversed)
-0.04
-0.03
-0.02
--0.01
0.01
0.02
0.03
0.04
Notes:
( 1) Vertical axis is market value in billions, and horizontal axis is interest rate change in percentage points
(0.01 is lOObp).
(2) The solid curve is the options value, and the dotted line is the mirror image of a hedge portfolio
that delta hedges the options at the initial interest rate. The hedged portfolio has positive
value when the solid curve (the options value) is above the dotted line (the hedge).
Figure 2
Option Values As a Function of Changes in Volatility
3
2
0
-1'-----'----'-----'---'-----'-----'-----'-----'
-0.6
----0.45
-0.3
----0.15
0.15
0.3
0.45
0.6
Note:
Vertical axis is market value in billions, and horizontal axis is volatility change in percentage points
(0.5 is a 50 percent increase in volatility).
Table 1
Change in required hedge position
compared to daily volume of Eurodollar futures
25 BP change in forward curve
Largest volume
Mtrtv (vcs)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Notes;
Change in
Hdg Pstn
-6.3
-9.2
-7.7
-5.7
-4.6
-3.7
-3.1
-2.6
-2.1
-1.9
-1.6
-1.4
-1.2
-1.0
-0.9
-0.6
-0.4
-0.3
-0.1
vol of
1st con tr
374.0
260.9
55.1
26.9
9.2
7.3
3.9
2.7
2.4
2.0
1.3
1.3
1.0
3.3
0.6
0.8
1.2
1.2
1.0
1.2
vol of
2nd contr
334.1
135.2
39.7
18.9
7.5
4.5
2.6
3.3
2.3
1.4
2.4
1.3
1.2
0.7
1.2
3.7
J.2
1.7
0.7
1.0
Average volume
vol of
vol of
2nd contr
1st contr
148.36
115.73
35.81
92.05
14.00
19.99
5.96
9.40
3.26
4.02
1.94
2.69
1.32
1.52
1.09
1.20
0.79
0.89
0.46
0.75
0.23
0.20
0.20
0.22
015
0.17
0.12
0.20
0.09
0.07
0.11
0.07
0.09
0.11
0.08
0.08
0.06
0.07
0.04
0.06
(1) Billions of USD. Hedge estimates based on data at end of March 1995.
(2) The second coluumn is the change in hedged position by maturity of exposure.
(3) The middle columns are the largest daily volumn of futures contracts (by maturity of contract)
in the first half of 1995.
(4) The right most columns are the average daily volume (by maturity) in the first half of 1995.
(5) The first and second futures contracts in the futures volumn columns represent the two back
to back contracts on 3-month interest rates required to hedge a six month exposure.
(6) Bold indicates contract volume in excess of change in hedge position.
(7) Negative values indicate an increase in a short position.
Table 2
Change in required hedge position
compared to daily volwne of Eurodollar futures
75 BP change in forward curve
Mtrtv (vrsl
0.5
l
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9:5
10
Change in
Hd• Pstn
-31.9
-31.2
-23.7
-17.2
-13.6
-11.0
-9.0
-7.6
-6.2
-5.5
-4.7
-4.l
-3.5
-3.0
-2.4
-1.9
-1.3
-0.7
-0.3
Largest volume
vol of
vol of
1st con tr
2nd contr
374.0
260.9
55.1
26.9
9.2
7.3
3.9
2.7
2.4
2.0
1.3
1.3
1.0
3.3
0.6
0.8
1.2
1.2
1.0
l.2
334.1
135.2
39.7
18.9
7.5
4.5
2.6
3.3
2.3
.1.4
2.4
1.3
1.2
0.7
1.2
3.7
1.2
1.7
0.7
1.0
Average volume
vol of
vol of
1st contr
2nd contr
115.73
92.05
19.99
9.40
4.02
2.69
1.52
1.20
0.89
0.75
0.20
0.22
0.17
0.20
0.07
0.07
0.11
0.08
0.07
0.06
148.36
35.81
14.00
5.96
3.26
l.94
1.32
1.09
0.79
0.46
0.23
0.20
0.15
0.12
0.09
0.11
0.09
0.08
0.06
0.04
Notes:
{l) Billions of USD. Hedge estimates based on data at end of March 1995.
(2) The second coluumn is the change in hedged position by maturity of exposure.
(3) The middle columns are the largest daily volumn of futures contracts (by maturity of contract)
in the first haifof 1995.
(4) The right most columns are the average daily volume (by maturity) in the first half of 1995.
(5) The first and second futures contracts in the futures volumn columns represent the two back
to back contracts on 3-month interest rates required to hedge a six month exposure.
(6} Bold indicates contract volume in excess of change in hedge position.
(7) Negative values indicate an increase in a short position.
Table 3
Requ.ired hedge position in eurodollar futures contracts
Compared to contracts outstanding
Mtrtv Ives)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Hdg Pstn
38.3
23.9
2.8
-4.0
-9.8
-13.4
-16.4
-17.9
-20.2
-18.9
-18.8
-18.4
-17.5
-15.1
-12.6
-9.6
-6.2
-3.4
-1.4
Open Int
1st contr
561.9
279.7
174.0
114.2
84.9
60.3
49.5
34.4
22.6
12.9
7.5
6.2
6.7
6.8
3.8
1.6
1.8
1.7
0.8
0.8
Open Int
2nd contr
366.4
222.0
145.4
96.3
68.6
54.8
38.8
27.2
14.5
9.5
7.7
5.9
6.8
4.5
2.5
2.2
1.8
2.0
0.9
0.0
Chg in Hd
!75 BP Ch•
-31.9
-31.2
-23.7
-17.2
-13.6
-11.0
-9.0
-7.6
-6.2
-5.5
-4.7
-4.1
-3.5
-3.0
-2.4
-1.9
-1.3
-0.7
-0.3
Notes:
(1) Billions of USO. Hedge estimates and open interest at end of March 1995.
(2) The second coluumn is the hedge position by maturity of exposure.
(3) The middle columns are the outstanding volumn of futures contracts at end of March 1995.
(4) The first and second futures contracts in the futures volumn columns represent the two back
to back contracts on 3-month interest rates required to hedge a six month exposure.
(5) Bold indicates contract volume in excess of hedge position.
(6) Negative values indicate a short position or an increase in a short position.
Table4
Hedge Position In Bonds
Using 5 and 10 Year Securities
Panel A: Treasurv Securities
Hedg,
Chg Hdg
Positior
(10 BP)
5 yea,
13.0
0.4
10 vea1
-13.0
-0.4
Pane!B: Treasurv Futures
Hedg,
Positior
5 yeai
13.0
10 ve,
-13.0
Chg Hdg
(10 BP)
0.4
-0.4
Chg Hdg
(25 BP)
1.0
-I.I
Chg Hd~
(75 BP
2.9
-3.3
On-the-run Treasury
Outstnd Dailv Vol
13.2
6.0
13.8
4.0
Chg Hdg
/25 BPl
1.0
Chg Hd1
(75 BP
2.9
-3.3
"'-en Intr Lr• Div Vol Av Div Vo
19.7
12.3
5.1
25.8
24.4
9.2
-I.I
Treasury Futures
Notes:
(I) Billions of USD. Hedge estimates based on data at end of March 1995.
(2) Treasuries outstanding at end of March 1995; daily volume is from GovPX only (Fleming, 1997).
(3) Trea.s:ury futures are the 5 and 10 year note contracts, Open interest at of
end of March 1995, and volume is over first half of 1995.
(4) Negative values indicate a short position or an increase in a short position.
TableS
Change in required hedge position
due to simultaneous volatility and forward rate shocks
Mtrtv (vrs)
Change in futures hedge
0.5
1.5
2
2.5
3
3.5
4
4.5
Change in Bond hedge
5 year
10 vear
I.R. anc
LR. Shock Volt. Shock
Onlv Volt. Shocl
Onlv
-31.9
-31.2
-23.7
-17.2
-13.6
-11.0
-9.0
-7.6
-6.2
-6.0
-9.7
-8.7
-7.7
-6.2
-4.9
-3.9
-3.0
-2.2
-40.7
-38.7
-29.4
-22.6
-17.9
-14.4
-11.6
-9.5
-7.5
2.9
-3.3
0.8
-0.8
3.4
-3.8
Notes:
(I) Billions of USD. Hedge estimates based on data at end of March 1995.
(2) Forward rates increase by 75 basis points, and volatility increases
by 25% relative to initial volatility levels at short maturities,
and by 8% at 10 years.
(3) Negative values indicate an increase in a short position.
Table6
Strike Price Variations
Change In required hedge position
due to 75 bp change in forward curve
Mtrty !vrs)
Base
Change in futures hedge
-31.9
0.5
-31.2
I
-23.7
1.5
-17.2
2
-13.6
2.5
-11.0
3
-9.0
3.5
-7.6
4
-6.2
4.5
Change in Bond hedge
5 year
2.9
10 year
-3.3
Equal
Premia
Equal
Delta
Strike
Distr.
-38.3
-32.9
-24.2
-17.3
-13.6
-10.9
-8.9
-7.5
-6.2
-33.3
-30.5
-22.8
-16.6
-13.2
-10.7
-8.8
-7.4
-6.1
-34.9
-27.1
-21.3
-15.9
-12.7
-10.4
-8.6
-7.2
-6.0
-38.5
-33.3
-24.3
-17.4
-13.6
-10.9
-8.9
-7.5
-6.2
-24.8
-29.6
-23.4
-17.2
-13.7
-I I.I
-9.2
-7.7
-6.4
-55.8
-42.2
-29.3
-20.1
-15.4
-12.1
-9.8
-8. 1
-6.6
2.9
-3.2
2.9
-3.2
2.8
-3.2
2.9
-3.2
3.0
-3.3
3.1
-3.4
Maturity
Vrtn I
Notes:
(I) Billions of USD. Hedge estimates based on data at end of March 1995.
(2) Column headings indicate the assumption as described in the text.
(3) Negative values indicate an increase in a short position.
Maturity
Vrtn 2
Identical
Caps/floor,
Table7
Volatility Variations
Change in required hedge position
due to 75 bp change in forward curve
Base
Mtrtv (vrs)
Change in futures hedge
-31.9
0.5
-31.2
I
-23.7
1.5
-17.2
2
-13.6
2.5
-11.0
3
-9.0
3.5
-7.6
4
-6.2
4.5
!Change in Bond hedge
2.9
5 year
-3.3
JO year
Notes:
Cap/Floor
Volatility
Volatility
Smile
Cap/Fioo,
and Smil<
-31.5
-31.2
-23.7
-17.2
-13.6
-10.9
-9.0
-7.5
-6.2
-27.2
-27.8
-21.1
-14.6
-11.4
-9.J
-7.4
-6.2
-5.3
-26.8
>27.7
-21.0
-14.5
-11.3
-9.0
-7.4
-6.2
-5.3
2.9
-3.3
2.6
-2.9
2.6
-2.9
(I) Billions of USD. Hedge estimates based on data at end of March 1995.
(2) Column headings indicate the assumption as described in the text.
(3) Negative values indicate an increase in a short position.
Table 8
Other Variations
Change in required hedge position
due to 75 bp change in forward curve
Base
Mtrtv (vrs)
Change in futures hedge
0.5
-31.9
-31.2
I
-23.7
1.5
-17.2
2
I
-13.6
2.5
-I 1.0
3
-9.0
3.5
-7.6
4
-6.2
4.5
Change in Bond hedge
5 year
2.9
-3.3
10 vear
Dlr optn
at-the-rn
-25.2
-28.6
-22.6
-16.6
-13.2
-10.7
-8.9
-7.5
Options on
3-mth rate
Growth
Rate
Unrest,
MtrvDst
-6.2
-32.5
-30.4
-23.4
-17.0
-13.5
-10.9
-9.0
-7.5
-6.2
-38.6
-32.2
-25.5
-19.2
-15.4
-12.5
-10.2
-8.3
-6.6
-35.9
-30.9
-24.4
-18.1
-14.5
-11.7
-9.6
-7.9
-6.4
2.9
-3.3
2.9
-3.3
2.4
-2.7
2.8
-3.1
Notes
(I) Billions of USD. Hedge estimates based on data at end of March 1995.
(2) Column headings indicate the assumption as described in the text.
(3) Negative values indicate an increase in a short position.
FEDERAL RESERVE BANK OF NEW YORK
RESEARCH PAPERS
1997
The following papers were written by economists at the Federal Reserve Bank of
New York either alone or in collaboration with outside economists. Single copies of up
to six papers are available upon request from the Public Information Department,
Federal Reserve Bank of New York, 33 Liberty Street, New York, NY 10045-0001
(212) 720-6134.
9701. Chakravarty, Sugato, and Asani Sarkar. "Traders' Broker Choice, Market Liquidity, and
Market Structure." January I 997.
9702. Park, Sangkyun. "Option Value of Credit Lines as an Explanation of High Credit Card
Rates." February 1997.
9703. Antzoulatos, Angelos. "On the Determinants and Resilience of Bond Flows to LDCs,
1990 - 1995: Evidence from Argentina, Brazil, and Mexico." February 1997.
9704. Higgins, Matthew, and Carol Osler. "Asset Market Hangovers and Economic Growth."
February 1997.
9705. Chakravarty, Sugato, and Asani Sarkar. "Can Competition between Brokers Mitigate
Agency Conflicts with Their Customers?" February 1997.
9706. Fleming, Michael, and Eli Remolona. "What Moves the Bond Market?" February 1997.
9707. Laubach, Thomas, and Adam Posen. "Disciplined Discretion: The German and Swiss
Monetary Targeting Frameworks in Operation." March 1997.
9708. Bram, Jason, and Sydney Ludvigson. "Does Consumer Confidence Forecast Household
Expenditure: A Sentiment.Index Horse.Race. " .. March 1997.
9709. Demsetz, Rebecca, Marc Saidenberg, and Philip Strahan. "Agency Problems and Risk
Taking at Banks." March 1997.
9710. Lopez, Jose. "Regulatory Evaluation of Value-at-Risk Models." March 1997.
9711. Cantor, Richard, Frank Packer, and Kevin Cole. "Split Ratings and the Pricing of Credit
Risk." March 1997.
9712. Ludvigson, Sydney, and Christina Paxson. "Approximation Bias in Linearized Euler
Equations." March 1997.
9713. Chakravarty, Sugato, Sarkar, Asani, and Lifan Wu. "Estimating the Adverse Selection
Cost in Markets with Multiple Informed Traders." April 1997.
9714. Laubach, Thomas, and Adam Posen. "Some Comparative Evidence on the Effectiveness
oflnflation Targeting." April 1997.
9715. Chakravarty, Sugato, and Asani Sarkar. "A General Model of Brokers' Trading, with
Applications to Order Flow Internalization, Insider Trading and Off-Exchange Block
Sales." May 1997.
9716. Estrella, Arturo. "A New Measure of Fit for Equations with Dichotomous Dependent
Variables." May 1997.
9717. Estrella, Arturo. "Why Do Interest Rates Predict Macro Outcomes? A Unified Theory of
Inflation, Output, Interest and Policy." May 1997.
9718. Ishii Jun, and Kei-Mu Yi. "The Growth of World Trade." May 1997.
To obtain more information about the Bank's Research Papers series and other
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