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...

In this article we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a non-parametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by...

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 study I apply forward sensitivity analysis to the dynamical system of nonlinear asset flow differential equations (AFDE). I find that all parameters in AFDE are needed and can be estimated from market prices and net asset values data. Moreover, the market price is the most fluctuating...

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,...

We combine the multilevel Monte Carlo (MLMC) method with the numerical scheme for the Heston model that simulates the variance process exactly or almost exactly and applies the stochastic trapezoidal rule to approximate the time-integrated variance process within the SDE of the logarithmic asset...

We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic...

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...