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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

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Author Info

  • 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)

Abstract

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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Bibliographic Info

Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 07-11.

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Length: 22 pages
Date of creation: Aug 2006
Date of revision:
Handle: RePEc:chf:rpseri:rp0711

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Web page: http://www.SwissFinanceInstitute.ch
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Related research

Keywords: Stochastic volatility models; incomplete markets; Delta hedging; locally R-minimizing hedging strategies Malliavin calculus;

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