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PRICING PERPETUAL TIMER OPTION UNDER THE STOCHASTIC VOLATILITY MODEL OF HULL–WHITE

Part of: Integral transforms, operational calculus Mathematical finance

Published online by Cambridge University Press:  16 May 2017

JICHAO ZHANG Open the ORCID record for JICHAO ZHANG [Opens in a new window] ,
XIAOPING LU Open the ORCID record for XIAOPING LU [Opens in a new window]  and
YUECAI HAN Open the ORCID record for YUECAI HAN [Opens in a new window]
JICHAO ZHANG
Affiliation:
School of Mathematics, Jilin University, Changchun, Jilin 130012, China email zhangjc13@mails.jlu.edu.cn, hanyc@jlu.edu.cn
XIAOPING LU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, WollongongNSW 2522, Australia email xplu@uow.edu.au
YUECAI HAN*
Affiliation:
School of Mathematics, Jilin University, Changchun, Jilin 130012, China email zhangjc13@mails.jlu.edu.cn, hanyc@jlu.edu.cn
*
✉hanyc@jlu.edu.cn
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Abstract

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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.

Keywords

timer optionstochastic volatilityBessel process

MSC classification

Primary: 91G20: Derivative securities
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 44A10: Laplace transform
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 406 - 416
Copyright
© 2017 Australian Mathematical Society 

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