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PRICING COUPON‐BOND OPTIONS AND SWAPTIONS IN AFFINE TERM STRUCTURE MODELS
Author(s) -
Singleton Kenneth J.,
Umantsev Len
Publication year - 2002
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2002.tb00132.x
Subject(s) - coupon , affine transformation , affine term structure model , swap (finance) , econometrics , bond , term (time) , valuation of options , computer science , economics , mathematics , yield curve , physics , finance , geometry , quantum mechanics
This paper provides a numerically accurate and computationally fast approximation to the prices of European options on coupon‐bearing instruments that is applicable to the entire family of affine term structure models. Exploiting the typical shapes of the conditional distributions of the risk factors in affine diffusions, we show that one can reliably compute the relevant probabilities needed for pricing options on coupon‐bearing instruments by the same Fourier inversion methods used in the pricing of options on zero‐coupon bonds. We apply our theoretical results to the pricing of options on coupon bonds and swaptions, and the calculation of “expected exposures” on swap books. As an empirical illustration, we compute the expected exposures implied by several affine term structure models fit to historical swap yields.