TY - JOUR
T1 - An Approximate Swaption Formula in Heath–Jarrow–Morton Models
JF - The Journal of Derivatives
SP - 30
LP - 50
DO - 10.3905/jod.2020.1.101
VL - 27
IS - 4
AU - Funahashi, Hideharu
Y1 - 2020/05/31
UR - http://jod.pm-research.com/content/27/4/30.abstract
N2 - This article provides an analytical approximation formula for a swaption price when the instantaneous forward rate follows a Heath–Jarrow–Morton (HJM) model. The author’s approximation strategy, based on the chaos expansion approximation, is to replicate the probability density function of the complex quasi-Gaussian process from a simpler one, which has a semi-closed form solution. It is not restricted to the linear approximation, as is the technique proposed by the existing literature, but can be extended to higher order approximations. Moreover, computation of the approximation is fast; hence, it is suitable for calibration purposes. The author illustrates results through numerical implementation and calibration done using market data.TOPICS: Options, interest-rate and currency swaps, derivativesKey Findings• The authors approximation strategy, based on the chaos expansion approximation, is to replicate the probability density function of the complex quasi-Gaussian process from a simpler one, which has a semi-closed form solution.• It is not restricted to the liner approximation, as is the technique proposed by the existing literature, but can be extended to higher-order approximations.• Computation of the approximation is fast; hence, it is suitable for calibration purposes.
ER -