Numerical pricing of European options under the double exponential jump-diffusion model with stochastic volatility

• Main Authors: Hozman, J., Tichý, T.
• Format: Conference Proceeding
• Language: English
• Subjects: Differential equations; Operators (mathematics); Pricing; Stochastic models; Volatility
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0163421

Stochastic volatility models with jumps generalize the classical Black–Scholes framework to capture more properly the real world features of option contracts. The extension is performed by incorporating jumps and a stochastic nature of volatility of asset returns into the dynamics of underlying asset prices. In this paper, we focus on pricing of European-style options under the model that combines the Heston stochastic volatility model with the Kou-type double exponential jumps in the underlying prices. As a result, the pricing function is governed by a partial-integro differential equation having the price of the underlying asset and its variance as spatial variables. Moreover, a presence of the non-local operator arising from jumps increases the complexity of the problem. Therefore, to improve the numerical pricing process we solve the relevant pricing equation by a discontinuous Galerkin approach with a semi-implicit time stepping scheme, where the differential operator is treated implicitly while the integral one explicitly by a composite trapezoidal rule. Finally, the numerical results demonstrate the capability of the numerical approach presented within the simple experiments.