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In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and calibration of implied volatility is the addition of a few other factors to the volatility process. This paper contemplates two extensions of the Heston stochastic volatility model. Out of which, one considers the addition of jumps to the stock price process (a stochastic volatility jump diffusion model) and another considers an additional stochastic volatility factor varying at a different time scale (a multiscale stochastic volatility model). An empirical analysis is carried out on the market data of options with different strike prices and maturities, to compare the pricing performance of these models and to capture their implied volatility fit. The unknown parameters of these models are calibrated using the non-linear least square optimization. It has been found that the multiscale stochastic volatility model performs better than the Heston stochastic volatility model and the stochastic volatility jump diffusion model for the data set under consideration.
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston characteristic fu
We consider the stochastic volatility model $dS_t = sigma_t S_t dW_t,dsigma_t = omega sigma_t dZ_t$, with $(W_t,Z_t)$ uncorrelated standard Brownian motions. This is a special case of the Hull-White and the $beta=1$ (log-normal) SABR model, which are
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique
The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with simple structur
The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal t