Fourier Transform Methods for Regime-Switching Jump-Diffusions and the Pricing of Forward Starting Options
AbstractIn this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1105.4567.
Date of creation: May 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-05-30 (All new papers)
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- Giuseppe Di Graziano & L. C. G. Rogers, 2009. "Equity with Markov-modulated dividends," Quantitative Finance, Taylor and Francis Journals, vol. 9(1), pages 19-26.
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