Pricing of the Quanto Game Option with Asian Feature
Journal of Finance and Accounting
Volume 8, Issue 3, May 2020, Pages: 143-147
Received: Jun. 7, 2020; Published: Jun. 8, 2020
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Author
Guo Peidong, School of Management, Shanghai University of Engineering Science, Shanghai, China
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Abstract
The game option, which is also known as Israel option, is a new type of American option to give the option writer the right to cancel the contract before the maturity. This article studies the pricing behaviors of the quanto game option with Asian features based on partial differential equation and the stochastic analysis. The Asian feature in an option model refers to the payoff of the option depends on both the average asset price over the life of the option. The quanto options (currency-translated foreign equity options) are contingent claims where the payoff depends on exchange rate level at the option exercise time. The Asian quanto game options can be regarded as double-barrier European options for the features that both the holder and the writer can exercises the options contract at any time over the life of the option. We derive the pricing equation and provide the integral expression of pricing formula for the option. The option price is decomposed into the corresponding European option price and the penalty paid by the option writer for an early callable and the penalty paid by the option holder for early exercise of the option. In addition, we discuss optimal exercise strategies and continuation regions of the option.
Keywords
American Option, Quanto Game Option, Asian Feature, Callable Strategy
To cite this article
Guo Peidong, Pricing of the Quanto Game Option with Asian Feature, Journal of Finance and Accounting. Vol. 8, No. 3, 2020, pp. 143-147. doi: 10.11648/j.jfa.20200803.15
References
[1]
Kifer, Y. Game options [J]. Finance and Stochastic, 2000, 4: 443-463.
[2]
Kwok, Y. K., L. X. Wu. Effects of Callable Feature on Early Exercise Policy [J]. Review of Derivatives Research, 2000, 4: 189-211.
[3]
Dai, M. A Closed Form Solution to Perpetual American Floating Strike Lookback Option [J]. Journal of Computational Finance, 2001, 4: 63-68.
[4]
Kyprianou, A. E. Some Calculations for Israeli Options [J]. Finance and Stochastics, 2004, 8: 73-86.
[5]
Baurdoux E J, Kyprianou A E. Further calculations for Israeli options [J]. Stochastics and Sto-chastics Reports, 2004, 76 (6): 549-569.
[6]
Hernandez U, Luis G. Pricing of Game Options in a market with stochastic interest rates [D]. America: School of mathematics of Georgia institute of technology, 2005.
[7]
Ekström, E. (2006). Properties of game options. Mathematical Methods of Operations Research, 63, 221–238.
[8]
Kuhn, C. and A. E. Kyprianou. Callable as Composite Exotic Options [J]. Mathematical Finance, 2007, 17: 487-502.
[9]
Dolinsky Y, Kifer Y. Hedging with risk for game options in discrete time [J]. Stochastics An International Journal of Probability and Stochastic Processes, 2007, 79 (1-2): 169-195.
[10]
Peidong Guo, Qihong Chen, Xicai Guo, Yue Fang. Path-dependent game options: a lookback case [J] Rev Deriv Res, 2014, 17: 113–124.
[11]
Yam S C P, Yung S P, Zhou W. Game call options revisited [J]. Mathematical Finance, 2014, 24 (1): 173-206.
[12]
Park K, Jeon J. A simple and fast method for valuing American knock-out options with rebates [J]. Chaos Solitons Fractals, 2017, 103: 364–70.
[13]
Le N, Dang D. Pricing American-style Parisian down-and-out call options [J]. Appl Math Comput, 2017, 305: 330–47.
[14]
Balajewicz M, Toivanen J. Reduced order models for pricing European and American options under stochastic volatility and jump-diffusion models [J]. J Comput Sci, 2017, 20: 198–204.
[15]
Gong X, Zhuang X. American option valuation under time changed tempered stable Lévy processes [J]. Phys. A, 2017, 466: 57–68.
[16]
Kang M, Jeon J, Han H, Lee S. Analytic solution for American strangle options using Laplace–Carson transforms [J]. Commun Nonlinear Sci NumerSimul, 2017, 47: 292–307.
[17]
Zhao H, Yang H. Semismooth Newton methods with domain decomposition for American options [J]. Journal of Computational and Applied Mathematics, 2018, 337: 37–50.
[18]
Chen W, Du K, Qiu X. Analytic properties of American option prices under a modified Black–Scholes equation with spatial fractional derivatives [J]. Phys A, 2018; 491: 37–44.
[19]
Madi S, Bouras M, Haiour M, Stahel A. Pricing of American options, using the Brennan-Schwartz algorithm based on finite elements [J]. Applied Mathe-matics and Computation, 2018, 339: 846–52.
[20]
Soleymani F, Barfeie M, Haghani F. Inverse multi-quadric RBF for computing the weights of FD method: application to American options [J]. Commun Nonlinear Sci NumerSimul, 2018, 64: 74–88.
[21]
Chen C, Wang Z, Yang Y. A new operator splitting method for American options under fractional Black-Scholes models [J]. Computers & Mathematics with Applications, 2019, 77 (8): 2130–44.
[22]
Zaevski T. A new form of the early exercise premium for American type derivatives [J]. Chaos Solitons Fractals, 2019, 123: 338–40.
[23]
Gao Y, Song H, Wang X, Zhang K. Primal-dual active set method for pricing American better-of option on two assets [J]. Communications in Nonlinear Science and Numerical Simulation, 2020, 80: 104976.
[24]
Tsvetelin S. Zaevski. Discounted perpetual game call options [J]. Chaos Solitons Fractals, 2020, 131: 109503.
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