Closed-Form Solutions For European And Digital Calls In The Hull And White Stochastic Volatility Model And Their Relation To Locally R-Minimizing And Delta Hedges
Christian-Olivier Ewald (University of Leeds, School of Mathematics) Klaus Reiner Schenk-Hoppe (University of Leeds, Business School and School of Mathematics) Zhaojun Yang (Human University, School of Economics and Trade, China)
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This paper derives an analytic expression for the distribution of the average volatility ds in the stochastic volatility model of Hull and White. This result answers a longstanding question, posed by Hull and White (Journal of Finance 42, 1987), whether such an analytic form exists. Our findings are applied to obtain closed-form solutions for European and Digital call option prices. The paper also provides an explicit solution for the Delta hedge of a European call. Moreover, it is proved that the Delta hedge under the minimal martingale measure coincides with the locally R-minimizing hedge in the model considered here.
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