Option pricing using the fast Fourier transform under the double exponential jump model with stochastic volatility and stochastic intensity

Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

“…It is remarkable that when the stochastic intensity process is a constant (κ λ = θ λ = σ λ =0), the MGF can be found in [28] under this special case. When the jump diffusion of variance process is removed, the MGF can be found in [19] under this special condition. Moreover, if the stochastic intensity process is a constant and the jump diffusion of variance process is removed, the MGF can be gotten in [30].…”

“…With the rapid growth of trading of variance/volatility swaps in the past twenty years, researchers in this field attempt to construct more practical models and find more feasible methods for pricing variance/volatility swaps. Incorporating jump diffusions into models of pricing and hedging variance swaps, Carr et al [8] and Huang et al [19] studied the existence of many small jumps that cannot be adequately modelled by using finite-activity compound Poisson processes. Cont and Kokholm [13] presented a model for the joint dynamics of a set of forward variance swap rates along with the underlying index; they used Lévy processes as building blocks and provided the tractable pricing framework for variance swaps, VIX futures, and vanilla call/put options.…”

“…Santa-Clata and Yan [23] found the components of the jump intensity risk after calibrating the S&P 500 index option prices from the beginning of 1996 to the end of 2002. Huang et al [19] studied the valuation of the option when the underlying asset follows the double exponential jump process with the stochastic volatility and stochastic intensity, in which the model captures the stock prices, volatility and stochastic intensity. However, as pointed out by Chang et al [11], it is necessary to make the additional extension work to incorporate both the varying continuous volatility and stochastic intensity to model the characteristic of the asset price in the financial market.…”

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

“…(3) expresses the evolution of activity rate process and can be simulated in various discretization schemes. Certainly, J t can be specified as other distributional forms, for example, in [25][26][27], it is assumed to follow the double exponential distribution, generating double exponential jump diffusion stochastic volatility process. W t and B t respectively denote independent Wiener processes driven by different factors.…”

An IMEX‐BDF2 compact scheme for pricing options under regime‐switching jump‐diffusion models

“…The celebrated Black-Scholes model 1,2 is based on assumption that the price of the underlying asset behaves like a geometric Brownian motion with a drift and a constant volatility, which cannot explain the market prices of options with various strike prices and maturities. To explain this behavior, a number of alternative models has appeared in the financial literatures, for example, nonlinear models, [3][4][5][6][7][8] stochastic volatility models, [9][10][11][12] jump-diffusion models, [13][14][15][16] regime-switching models, 17,18 and regime-switching jump-diffusion models, 19,20 which are given by coupled partial integro-differential equations (PIDEs). However, these models are more difficult to handle numerically in contrast to the celebrated Black-Scholes model.…”