An empirical study on asymmetric jump diffusion for option and annuity pricing

Abstract

In this paper, we present a method to estimate the market parameters modelled by an asymmetric jump diffusion process. The method proposed is based on Kou’s jump diffusion model while the market parameters refer to the market drift, the market volatility, the jump intensity on market price, and the rate of jump occurrence in a consistent manner throughout the entire paper. The model captures the asymmetric nature of the price fluctuation during up trend markets and down trend markets. The results are compared to conventional options to observe the impact of jump effects. The results from simulation show that the asymmetric jump diffusion model can estimate the fair prices of European call options and annuity better than the Black-Scholes model and the symmetric jump diffusion model proposed by Kou and Merton.

Upside and downside correlated jump risk premia of currency options and expected returns

“…Frame and Ramezani ( 2014 ) used the affine jump-diffusion model to assess the asymmetric features of the S&P 500 index, the NASDAQ index, and selected stocks from 2007 to 2010, discovering that parameter estimates differ significantly under different economic conditions. Lau et al ( 2019 ) utilized Gibbs sampling to estimate the asymmetric jump-diffusion process on five indexes (the DJIA, NASDAQ, FTSE 100, S&P 500, and NYSE ARCA Oil & Gas Index) from 2005 to 2014, indicating that the asymmetric jump-diffusion model is more accurate than the symmetric models in estimating fair prices of European call options. Alexeev et al ( 2019 ) analyzed high-frequency data for the S&P 500 index from 2003 to 2017, finding that downside jumps significantly impact portfolio returns more than upside jumps, especially during extreme events.…”

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

“…Chang and Wang (2020) presented option pricing driven by double stochastic volatility model in conjunction with stochastic interest rate model and double exponential jumps and stochastic intensity. Lau et al (2019) presented an approach to estimate market parameters modelled using a certain jump-diffusion model. Novat et al (2019) discussed Merton's jump-diffusion model in stock markets of three East African countries.…”