Pricing Perpetual American Lookback Options Under Stochastic Volatility

In this paper, we study the lookback option of the American style suggested in Dai (Journal of Computational Finance 4(2):63–68, 2000 ), and Dai and Kwok (SIAM Journal on Applied Mathematics 66(1):206–227, 2005 ) under stochastic volatility. By the asymptotic analysis introduced in Fouque et al. (De...

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Bibliographic Details
Published inComputational economics Vol. 53; no. 3; pp. 1265 - 1277
Main Author Lee, Min-Ku
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2019
Springer Nature B.V
Subjects
Applications of mathematics
Behavioral/Experimental Economics
Computation
Computer Appl. in Social and Behavioral Sciences
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Finance
Markets
Math Applications in Computer Science
Mathematics
Maturity
Operations Research/Decision Theory
Political economy
Volatility
Stochastic volatility
Lookback option
Option pricing
Perpetual American option
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Summary:In this paper, we study the lookback option of the American style suggested in Dai (Journal of Computational Finance 4(2):63–68, 2000 ), and Dai and Kwok (SIAM Journal on Applied Mathematics 66(1):206–227, 2005 ) under stochastic volatility. By the asymptotic analysis introduced in Fouque et al. (Derivatives in financial markets with stochastic volatility, Cambridge University Press, Cambridge, 2000 ), we derive the explicit formula for the price and the optimal exercise value of the option with infinity maturity whose volatility follows the Ornstein–Uhlenbeck process. Especially, we investigate the effects of the stochastic volatility on the perpetual American lookback option in comparison with the constant volatility [cf. (Black and Scholes in The Journal of Political Economy 81(3):637–654, 1973 ] by using the results of the computational experiment.
ISSN:0927-7099
1572-9974
DOI:10.1007/s10614-017-9782-5