Test data sets for calibration of stochastic and fractional stochastic volatility models

AbstractData for calibration and out-of-sample error testing of option pricing models are provided alongside data obtained from optimization procedures in "On calibration of stochastic and fractional stochastic volatility models" [1]. Firstly we describe testing data sets, further calibration data obtained from combined optimizers is visually depicted – interactive 3d bar plots are provided. The data is suitable for a further comparison of other optimization routines and also to benchmark different pricing models

Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memory

In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise.Comment: 21 pages; 2 figure

Option pricing in stochastic volatility models driven by fractional jump-diffusion processes

In this paper, we propose a fractional stochastic volatility jump-diffusion model which extends the Bates (1996) model, where we model the volatility as a fractional process. Extensive empirical studies show that the distributions of the logarithmic returns of financial asset usually exhibit properties of self-similarity and long-range dependence and since the fractional Brownian motion has these two important properties, it has the ability to capture the behavior of underlying asset price. Further incorporating jumps into the stochastic volatility framework gives further freedom to financial mathematicians to fit both the short and long end of the implied volatility surface. We propose a stochastic model which contains both fractional and jump process. Then we price options using Monte Carlo simulations along with a variance reduction technique (antithetic variates). We use market data from the S&P 500 index and we compare our results with the Heston and Bates model using error measures. The results show our model greatly outperforms previous models in terms of estimation accuracy.peer-reviewe