随机波动率模型下欧式回望期权定价

doi:10.16088/j.issn.1001-6600.2015.03.013

Abstract

Abstract: The valuation on European lookback option with floating strike price is considered under the Hull-White stochastic volatility model. Using the Taylor series expansion technique, the approximated explicit formulas for the price and delta value of the European lookback option are obtained. Numerical experiments show that the proposed explicit formula performs accurately and efficiently compared with Monte Carlo simulation, and is easy to implement in practice. Finally, the impacts of the key parameters in the volatility process on both the option price and its delta value are analyzed through numerical examples.

Key words: Hull-White model, lookback options, Taylor series expansion technique, Monte Carlo simulation

CLC Number:

O211.9

XU Lei, DENG Guo-he. Valuation on European Lookback Option under Stochastic Volatility Model[J].Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(3): 79-90.

References

[1] HE Hua, KEIRSTEAD W P, REBBOLZ J. Double lookbacks[J]. Mathematical Finance, 1998, 8(3): 201-228.
[2] LEE H. Pricing equity-indexed annuities with path-dependent options[J]. Insurance: Mathematics and Economics, 2003, 33(3): 677-690.
[3] HYER T, LIPTON-LIFSCHITZ A, PUGACHEVSKY D. Passport to success[J]. Risk, 1997, 10(9):127-131.
[4] GOLDMAN M B, SOSIN H B, GATTO M A. Path dependent options: buy at the low, sell at the high[J]. Journal of Finance, 1979, 34(5): 1111-1127.
[5] CONZE A, VISWANATHAN R. Path dependent options: the case of lookback options[J]. Journal of Finance, 1991, 46(5): 1893-1907.
[6] BLACK F, SCHOLES M. The pricing of options and corporate liabilities[J]. The Journal of Political Economy, 1973, 81(3): 637-654.
[7] DAI Min, WONG H Y, KWOK Y K. Quanto lookback options[J]. Mathematical Finance, 2004, 14(3): 445-467.
[8] WONG H Y, KWOK Y K. Sub-replication and replenishing premium: efficient pricing of multi-state lookbacks[J]. Review of Derivatives Research, 2003, 6(2): 83-106.
[9] HEYNEN R C, KAT H M. Lookback options with discrete and partial monitoring of the underlying price[J]. Appl Math Finance, 1995, 2(4): 273-284.
[10] BUCHEN P, KONSTANDATOS O. A new method of pricing lookback options[J]. Mathematical Finance, 2005, 15(2): 245-259.
[11] LAI T L, LIM T W. Exercise regions and efficient valuation of American lookback options[J]. Mathematical Finance, 2004, 14(2): 249-269.
[12] BAKSHI G, CAO C, CHEN Zhi-wu. Empirical performance of alternative option pricing models[J]. Journal of Finance, 1997, 52(5): 2003-2049.
[13] HULL J, WHITE A. The pricing of options on assets with stochastic volatility[J]. Journal of Finance, 1987, 42(2): 281-300.
[14] HESTON S L. A closed-form solution for options with stochastic volatility with applications to bond and currency options[J]. Reviews of Financial Studies, 1993, 6(2): 327-343.
[15] FORSYTH P A, VETZAL K R, ZVAN R. A finite element approach to the pricing of discrete lookbacks with stochastic volatility[J]. Applied Mathematical Finance, 1999, 6(2): 87-106.
[16] WONG H Y, CHAN C M. Lookback options and dynamic fund protection under multiscale stochastic volatility[J]. Insurance: Mathematics and Economics, 2007, 40(3): 357-385.
[17] PARK S H, KIM J H. A semi-analytic pricing formula for lookback options under a general stochastic volatility model[J]. Statistics and Probability Letters, 2013, 83(11): 2537-2543.
[18] LEUNG K S. An analytic pricing formula for lookback options under stochastic volatility[J]. Applied Mathematics Letters, 2013, 26(1): 145-149.
[19] SABANIS S. Stochastic volatility[J]. International Journal of Theoretical and Applied Finance, 2002, 5(5): 515-530.
[20] 温鲜, 邓国和, 霍海峰. Hull-White随机波动率模型的欧式障碍期权[J]. 广西师范大学学报:自然科学版, 2009, 27(4): 49-52.
[21] DUFFIE D, PAN Jun, SINGLETON K. Transform analysis and asset pricing for affine jump-diffusions[J]. Econometrica, 2000, 68(6): 1343-1376.

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Valuation on European Lookback Option under Stochastic Volatility Model

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