Pricing perpetual timer option under the stochastic volatility model of Hull–White

Jichao Zhang, Xiaoping Lu, Yuecai Han


The valuation of perpetual timer options under the Hull–White stochastic volatility model is discussed here. By exploring the connection between the Hull–White model and the Bessel process and using time-change techniques, the triple joint distribution for the instantaneous volatility, the cumulative reciprocal volatility and the cumulative realized variance is obtained. An explicit analytical solution for the price of perpetual timer call options is derived as a Black–Scholes–Merton-type formula.



timer option, stochastic volatility, Bessel process.


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.