Title: Stock Price Models with Stochastic Volatility
Abstract: Stock price models with stochastic volatility have been developed in the last decades to improve the performance of the celebrated Black-Scholes model. The volatility of the stock in such a model is described by a nonnegative stochastic process. For instance, in the Hull-White model, a geometric Brownian motion plays the role of stochastic volatility, in the Stein-Stein model, the volatility is represented by an Ornstein-Uhlenbeck process, or by the absolute value of this process, while in the Heston model, the volatility process is the square root of a CIR-process. Chapter 2 focuses on stochastic volatility models. In addition, it presents Girsanov’s theorem, risk-neutral measures, and market prices of risk. It is explained in Chap. 2 how to use Girsanov’s theorem to find risk-neutral measures in uncorrelated stochastic volatility models, and how to overcome complications, arising in the case of a non-zero correlation between the stock price and the volatility. The chapter presents results of C. Sin, concerning risk-neutral measures in the correlated Hull-White model. Sin’s results show that the existence of such measures is determined by the possibility of explosions in finite time for solutions of certain auxiliary stochastic differential equations.
Publication Year: 2012
Publication Date: 2012-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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