Highly Efficient Option Valuation Under the Double Jump Framework with Stochastic Volatility and Jump Intensity Based on Shannon Wavelet Inverse Fourier Technique

A Shannon Wavelet Method for Pricing Forward Starting Options under the Double Exponential Jump Framework with Two-Factor Stochastic Volatilities

“…Kou and Wang [12] has proposed another model assuming that the jump size follows an asymmetric double exponential distribution, it can explain extreme movements in asset price and capture the leptokurtic feature as well. Moreover, prior empirical research [13] revealed a low level of correlation between stock volatility and jump intensity; then, Huang et al [14][15][16] assumed in their work that the stochastic volatility and jump intensity are governed by separate processes. erefore, in this paper, we consider combining double stochastic volatilities, asymmetric double exponential jump with stochastic intensity in the modeling framework to valuate forward starting options.…”

“…While the above stochastic structures work well in effectively capturing various market features and obtaining more accurate option prices as a result, how to find a closedform solution under these complicated models becomes a demanding task. e numerical pricing methods for models with stochastic volatility can be classified into three main groups [14,17]: the Monte Carlo simulation, numerical integration methods, and partial (integro-) differential equation methods. In general, the price of European-style options is determined by the discounted expectation of payoff function.…”

“…Zhang and Geng [20] applied the COS method to price forward starting options under the double Heston model. In this paper, we choose the SWIFT method to valuate forward starting options, due to the established accuracy and robustness of Shannon wavelets in option pricing, as demonstrated in a wealth of existing literature [14,16,24,25]. Secondly, this paper proposes a more realistic model that incorporates two-factor stochastic volatilities, asymmetric double exponential jump with stochastic jump intensity to capture various features observed in financial markets.…”