Time-Changed Fast Mean-Reverting Stochastic Volatility Models

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales

Interest rate models with Markov chains

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Optimal Investment Strategies under Stochastic Volatility - Estimation and Applications

This paper studies the impact of stochastic volatility (SV) on optimal investment decisions. We consider three different SV models: an extended Stein/Stein model, the Heston Model and an extended Heston Model with a constant elasticity variance (CEV) process and derive the the long-term optimal investment strategies under each of these processes. Since volatility is not a directly observable quantity, extended Kalman filter techniques are adopted to deal with this partial information problem. Optimal investment strategies based on the CEV volatility model are obtained by adopting the Backward Markov Chain approximation method since analytical solutions are no longer available. We find in the empirical investigation that the Heston model is favored as a more parsimonious model compared with the other two models. All three investment strategies based on the three SV models contain a positive intertemporal hedging term in addition to the static mean-variance portfolio. However, in their details the three investment strategies differ from each other. We also ?nd that the investment strategies are sensitive to the CEV parameter.asset allocation; stochastic volatility; partial information problem; extended Kalman ?lter; the Heston model; CEV process