February 1999
Anurag Gupta, Marti G. Subrahmanyam
ABSTRACT
This paper examines the convexity bias introduced by pricing interest rate swaps off the Eurocurrency futures curve
and the market's adjustment of this bias in prices over time. The convexity bias arises because of the difference
between a futures contract and a forward contract on interest rates, since the payoff to the latter is non-linear
in interest rates. Using daily data from 1987-1996, the differences between market swap rates and the swap rates
implied from Eurocurrency futures prices are studied for the four major interest rate swap markets - $, £,
DM and ¥. The evidence suggests that swaps were being priced off the futures curve (i.e. by ignoring the convexity
adjustment) during the earlier years of the study, after which the market swap rates drifted below the rates implied
by futures prices. The empirical analysis shows that this spread between the market and futures-implied swap
rates cannot be explained by default risk differences, liquidity differences or information asymmetries between
the swap and the futures markets. Using alternative term structure models (one-factor Vasicek, Cox-Ingersoll and
Ross, Hull and White, Black and Karasinski, and the two-factor Heath, Jarrow and Morton), the theoretical value
of the convexity bias is found to be related to the empirically observed swap-futures differential. We interpret
these results as evidence of mispricing of swap contracts during the earlier years of the study, with a gradual
elimination of that mispricing by incorporation of a convexity adjustment in swap pricing over time.
Anurag Gupta: (212) 998-0326 agupta0@stern.nyu.edu
Marti G. Subrahmanyam: (212) 998-0348 msubrahm@stern.nyu.edu
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