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,...

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...

Implied volatility skew and smile are ubiquitous phenomena in the financial derivative market especially after the Black Monday 1987 crash. Various stochastic volatility models have been proposed to capture volatility skew and smile in derivative pricing and hedging. Almost 30 years after the...

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...

In recent years, Germany has significantly increased its share of electricity produced from renewable sources, which is mainly due to the Renewable Energy Act (EEG). The EEG substantially impacts the dynamics of intra-day electricity prices by increasing the likelihood of negative prices. In...

This paper analyses the attributes and the significance of the roughness of oil market volatility. We employ unspanned stochastic volatility models driven by rough Brownian motions that yield semi-analytical prices for futures options entailing efficient calibration applications. By performing a...

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...