We propose a way to compute the hedging Delta using the Malliavin weight method. Our approach, which we name the l-method, generally outperforms the standard Monte Carlo finite difference method, especially for discontinuous payoffs. Furthermore, our approach is nonparametric, as we only assume...

We present in a Monte Carlo simulation framework a novel approach for the evaluation of hybrid local volatility (Dupire 1994, Derman and Kani 1998) models. In particular, we consider the stochastic local volatility model - see e.g. Lipton et al. (2014), Piterbarg (2007), Tataru and Fisher...

Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed by direct Monte Carlo methods. Least...

This paper investigates the pricing of single-asset autocallable barrier reverse convertibles in the Heston local-stochastic volatility (LSV) model. Despite their complexity, autocallable structured notes are the most traded equity-linked exotic derivatives. The autocallable payoff embeds an...

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...

Local volatility models are widely used to manage many exotic options in a way consistent with available market prices of vanilla options. Once calibrated, a local volatility grid can be used in numerical methods such as PDE or Monte Carlo to price and hedge exotic options consistently with...

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...

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...