RT Journal Article
SR Electronic
T1 An Approximate Swaption Formula in Heath–Jarrow–Morton Models
JF The Journal of Derivatives
FD Institutional Investor Journals
SP 30
OP 50
DO 10.3905/jod.2020.1.101
VO 27
IS 4
A1 Hideharu Funahashi
YR 2020
UL https://pm-research.com/content/27/4/30.abstract
AB 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.