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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

Author

Listed:
  • 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.

Suggested Citation

  • Christian-Olivier Ewald & Klaus Reiner Schenk-Hoppe & Zhaojun Yang, 2007. "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," Swiss Finance Institute Research Paper Series 07-11, Swiss Finance Institute.
  • Handle: RePEc:chf:rpseri:rp0711
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    Keywords

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

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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