A stochastic-local volatility model with Levy jumps for pricing derivatives

We introduce a new mixed model unifying local volatility, pure stochastic volatility, and L e ' vy type of jumps in this paper. Our model framework allows the pure stochastic volatil-ity and the jump intensity to be functions of fast (and slowly) varying stochastic processes and the local volatility to be given in a constant elasticity of variance type of parametric form. We use asymptotic analysis to derive a system of partial integro-differential equa-tions for the prices of European derivatives and use Fourier analysis to obtain an explicit formula for the prices. Our result is an extension of a stochastic-local volatility model from no jumps to L e ' vy jumps and an extension of a multiscale stochastic volatility model with L e ' vy jumps from the zero elasticity of variance to the non-zero elasticity of variance. We find that our model outperforms two benchmark models in view of fitting performance when the time-to-maturities of European options are relatively short and outperforms one benchmark model in terms of pricing time cost.(c) 2023 Elsevier Inc. All rights reserved.