Highly efficient Shannon wavelet-based pricing of power options under the double exponential jump framework with stochastic jump intensity and volatility

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

“…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. It is an extension of the work by Christoffersen et al [10], Kou and Wang [12] and Huang et al [16].…”

“…We choose the appropriate level of resolution m by two error convergence analyses. Firstly, we follow the line of [16] to compute the tail mass that the characteristic function Φ not recovered, which can be approximated by…”

“…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.…”

“…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.…”

A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier

“…Fourier transform methods are widely used in many applications including signal processing [1] [2], spectroscopy [3] [4] and computational finance [5] [6] [7].…”