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Assing, Sigurd; Jacka, Saul; Ocejo, Adriana (2014)
Publisher: The Institute of Mathematical Statistics
Languages: English
Types: Article
Subjects: QA, Optimal stopping, Mathematics - Optimization and Control, coupling, American option, 91G20, Mathematics - Probability, time-change, 60G40, stochastic volatility model
Identifiers:doi:10.1214/13-AAP956
We consider a pair $(X,Y)$ of stochastic processes satisfying the equation $dX=a(X)Y\,dB$ driven by a Brownian motion and study the monotonicity and continuity in $y$ of the value function $v(x,y)=\sup_{\tau}E_{x,y}[e^{-q\tau}g(X_{\tau})]$, where the supremum is taken over stopping times with respect to the filtration generated by $(X,Y)$. Our results can successfully be applied to pricing American options where $X$ is the discounted price of an asset while $Y$ is given by a stochastic volatility model such as those proposed by Heston or Hull and White. The main method of proof is based on time-change and coupling.

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