In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model, by developing efficient transform based pricing methods. This non-affine model gives prices of options on realized variance which allow upward sloping implied...

This paper calculates option portfolio Value at Risk (VaR) using Monte Carlo simulation under a risk neutral stochastic implied volatility model. Compared to benchmark delta-normal method, the model produces more accurate results by taking into account nonlinearity, passage of time,...

I develop a new method for approximating and estimating nonlinear, non-Gaussian state space models. I show that any such model can be well approximated by a discrete-state Markov process and estimated using techniques developed in Hamilton (1989). Through Monte Carlo simulations, I demonstrate...

In this article we suggest a new method for solutions of stochastic integrals where the dynamics of the variables in integrand are given by some stochastic differential equation. We also propose numerical simulation of stochastic differential equations which is based on iterated integrals method...

We propose a hybrid scheme for the simulation of stochastic Volterra equations. The scheme is a mix of the hybrid scheme for Brownian semistationary processes of Bennedsen et al. [Financ. Stoch., 21(4), 931-965, 2017] and then the multifactor approximations of Abi Jaber et al. [SIAM J. Finan....

We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time, small-noise. Specialising the results to the Heston model,...

The Fourier inversion method solves the Heston option pricing formula. However, this method does experience the noteworthy disadvantage of a computationally sedate solution process. As a result, the literature introduces faster approximations with accuracies later improved by the joint...

We present a simple and numerically efficient approach to the calibration of the Heston stochastic volatility model with piecewise constant parameters. Extending the original ansatz for the characteristic function, proposed in the seminal paper by Heston, to the case of piecewise constant...

This paper develops an unbiased Monte Carlo approximation to the transition density of a jump-diffusion process with state-dependent drift, volatility, jump intensity, and jump magnitude. The approximation is used to construct a likelihood estimator of the parameters of a jump-diffusion observed...