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
AbstractThis 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 InfoPaper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 07-11.
Length: 22 pages
Date of creation: Aug 2006
Date of revision:
Stochastic volatility models; incomplete markets; Delta hedging; locally R-minimizing hedging strategies Malliavin calculus;
Find related papers by 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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