Exact simulation of option greeks under stochastic volatility and jump diffusion models
WSC '04 Proceedings of the 36th conference on Winter simulation
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In this paper we provide a general framework for pricing forward start derivatives, i.e. contingent claims which set their exercise price on a later time than inception. We show that dealing with this kind of options mainly means exposure to future stochastic volatility. In particular, we propose a theoretical comparison between the pricing implications of modeling through Monte Carlo simulations forward start calls or puts as derivatives of two state variables, namely the underlying price process and the stochastic instantaneous volatility, and the same implications arising if the stochastic implied volatility is modeled as well. Therefore, we address the issue on whether it is worthwhile employing the implied volatility as a primitive state variable when pricing derivatives sensitive to volatility risk.