Vanilla Option Pricing on Stochastic Volatility market models
We want to discuss the option pricing on stochastic volatility market models, in which we are going to consider a generic function β (νt ) for the drift of volatility process. It is our intention choose any equivalent martingale measure, so that the drift of volatility process, respect at the new measure, is zero. This technique is possible when the Girsanov theorem is satisﬁed, since the stochastic volatility models are uncomplete markets, thus one has to choice an arbitrary risk price of volatility. In all this cases we are able to compute the price of Vanilla options in a closed form. To name a few, we can think to the popular Heston’s model, in which the solution is known in literature, unless of an inverse Fourier transform.
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- John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005.
"A Theory Of The Term Structure Of Interest Rates,"
World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164
World Scientific Publishing Co. Pte. Ltd..
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- Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
- Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536. Full references (including those not matched with items on IDEAS)
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