Regime switching~模型下的幂式期权定价

华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (6): 32-39.

Regime switching~模型下的幂式期权定价

苏小囡¹, 王伟², 王文胜³

1. 南京审计学院数学与统计学院, 南京 211815; 2. 宁波大学数学系, 浙江宁波 315211; 3. 杭州师范大学数学系, 杭州 310036

收稿日期:2013-01-01 修回日期:2013-04-01 出版日期:2013-11-25 发布日期:2014-01-13

Valuing power options under a regime-switching model

SU Xiao-nan¹, WANG Wei², WANG Wen-sheng³

1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing 211815, China; 2. Department of Mathematics, Ningbo University, Ningbo Zhejiang 31521, China; 3. Department of Hangzhou Normal University, Hangzhou 310036, China

Received:2013-01-01 Revised:2013-04-01 Online:2013-11-25 Published:2014-01-13

摘要/Abstract

摘要： 研究了标的资产价格过程服从马尔科夫调节的几何布朗运动时的欧式幂型看涨期权的定价问题.
特别是, 市场利率,
标的风险资产的预期收益率与波动率随着马尔科夫链的状态转移而变化.
由于市场不完备, 通过采用 regime switching Esscher
变换得到一个等价鞅测度并给出期权的定价公式. 最后,
考虑了所得结果的数值分析.

关键词: regime switching, 幂式期权, regime switching Esscher 变换, 期权定价, 数值分析

Abstract: The pricing of European style power call options was
considered when the dynamics of the underlying risky asset are
driven by the Markov-modulated Geometric Brownian Motion. In
particular, the market interest rate, the appreciation rate and the
volatility of the underlying risky asset switched over time
according to the sates of the continuous time Markov chain process.
Since the market is incomplete, the regime switching Esscher
transform was employed to determine an equivalent martingale measure
and derive the valuation of the options. Then, the numerical
analysis of our result was given.

Key words: regime switching, power options, regime switching Esscher transform, option pricing, numerical analysis

中图分类号:

O211

苏小囡, 王伟, 王文胜. Regime switching~模型下的幂式期权定价[J]. 华东师范大学学报(自然科学版), 2013, 2013(6): 32-39.

SU Xiao-nan, WANG Wei, WANG Wen-sheng. Valuing power options under a regime-switching model[J]. Journal of East China Normal University(Natural Sc, 2013, 2013(6): 32-39.

参考文献

{1} BLACK F, SCHOELS M. The pricing of options and corporate liability[J]. Journal of Political Economy, 1973, 81(3): 637-659.
{2} MERTON R. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3(1-2): 125-144.
{3} KOU S, WANG H. Option pricing under a double exponential jump diffusion model[J]. Management Science, 2004, 50(9): 1178-1192.
{4} CHAN T. Pricing contingent claims on stocks driven by L\acute{\rm e}vy processes[J]. Annals of Applied Probability, 1999, 9(2): 504-528.
{5} ELLIOTT R, OSAKWE C. Option pricing for pure jump processes with Markov switching compensators[J]. Finance and Stochastics, 2006, 10(2): 250-275.
{6} HARRISON J, KREPS D. Martingales and arbitrage in multiperiod security markets[J]. Journal of Economic Theory, 1979, 20: 381-408.
{7} HARRISON J, PLISKA S. Martingales and stochastic integrals in the theory of continuous trading[J]. Stochastic Processes and Their Applications, 1981, 11: 215-260.
{8} GERBER H, SHIU E. Option pricing by Esscher transforms[J]. Transactions of the Society of Actuaries, 1994, 46: 99-191.
{9} HAMLTON J. A new approach to the economic analysis of nonstationary time series and the business cycle[J]. Econometrica, 1989, 57: 357-384.
{10} ELLIOTT R, CHAN L, Siu T. Option pricing and Esscher transform under regime switching[J]. Annals of Finance, 2005, 1(4): 423-432.
{11} ELLIOTT R, SIU T, CHAN L. Pricing volatility swaps under Heston's stochastic volatility model with regime switching[J]. Applied Mathematical Finance, 2007, 14(1): 41-62.
{12} SIU T, YANG H, LAU J. Pricing currency options under two-factor Markov-modulated stochastic volatility models[J]. Insurance: Mathematics and Economics, 2008, 43(3): 295-302.
{13} GOPAL K B, MRINAL K G, ANINDYA G. Risk minimizing option for a class of exotic options in a Markov-modulated market[J]. Stochastic Analysis and Applications, 2011, 29(2): 259-281.
{14} YOON J, JANG R. An analytic valuation method for multivariate contingent claims with regime-switching volatilities[J]. Operations Research Letters, 2011, 39(3): 180-187.

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