期刊文献+

对数正态随机波动率期权局部风险最小定价与风险对冲

THE LOCAL R-MINIMIZED PRICING AND HEDGING OF OPTION UNDER THE LOG-NORMAL STOCHASTIC VOLATILITY
下载PDF
导出
摘要 随机波动率模型是著名的Black-Scholes模型的推广,该模型描述的市场是不完备的,相应期权的定价与保值和投资者的风险态度有关.本文假设标的资产波动率为对数正态过程,根据局部风险最小准则,运用梯度算子方法,得到了欧式看涨期权的局部风险最小定价及套期保值策略的显式解. Stochastic volatility models are the generalization of the well-known Black-Scholes model, and the markets described by them are incomplete. Therefore, the pricing and hedging of the option depend on the attitude of the investors. Generally speaking, it is extremely difficult for one to obtain an explicit solution to the pricing or hedging. In this paper, we assuming the volatility follows a log-normal stochastic process, this paper derived the ex- plicit solutions to the local R-minimized pricing and hedging of European option by means of the gradient operator method.
作者 杨招军
出处 《经济数学》 北大核心 2009年第2期16-22,共7页 Journal of Quantitative Economics
基金 国家社科基金资助项目(06BJL022)
关键词 随机波动率 期权定价与保值 局部风险最小化 显式解 stochastic volatility option pricing and hedging local R-minimality explicit solutions
  • 引文网络
  • 相关文献

参考文献10

  • 1BLACK F, SCHOLES M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81 : 637 - 659.
  • 2DAS S R, SUNDARAM R K. Of smiles and smirks: a term structure perspective[J]. Journal of Financial and Quantitative Analysis, 1999, 34:211-239.
  • 3FOLLMER H, SCHWEIZER M. Hedging of contingent claims under incomplete information[ C]//Davis M H A, Elliott R J eds, Applied Stochastic Analysis. London: Gordon and Breach, 1990.
  • 4FOLLMER H, SONDERMANN D. Hedging of non-redundant contingent claims[M]//Hildenbrand W, Mas-Colell A eds. Contributions to Mathematical Economics, 1986: 205- 223.
  • 5YANG Z J, HUANG L H. One property of a gradient operator and its application to option hedging[ C]//Proceedings of 2003 International Conference on Management Science & Engineering. Harbin:Harbin Polytechnical University Press, 2003.
  • 6YANGZhaojun,HUANGLihong,MAChaoaun.EXPLICIT EXPRESSIONS FOR THE VALUATION AND HEDGING OF THE ARITHMETIC ASIAN OPTION[J].Journal of Systems Science & Complexity,2003,16(4):557-561. 被引量:9
  • 7SCHWEIZER M. Option hedging for semimartingales[J]. Stochastic Processes and their Applications, 1991, 37:339 - 363.
  • 8SCHWEIZER M. Hedging of options in a general semimartingale model[D]. Diss ETHZ No 8615, Zurich, 1988.
  • 9YOR M. On Some exponential functionals of brownian motion[J ]. Adv Appl Prob, 1992, 24:509 - 531.
  • 10OCONE D L, Karatzas I. A generalized clark representation formula, with application to optimal portfolios[J]. Stochastics and Stochastic Reports, 1991, 34: 187-220.

二级参考文献8

  • 1A G Z. Kemna and A C F Vorst. A pricing method for options based on average asset values,Journal of Banking and Finance, 1990, 14: 113-129.
  • 2S M Turnbull and L M Wakeman. A quick algorithm for pricing European average options,Journal of Financial and Quantitative Analysis, 1991, 26: 377-389.
  • 3L C G Rogers and Z Shi. The value of an Asian option, Journal of Applied Probability, 1995,32: 1077-1088.
  • 4S Simon, M J Goovaerts, and J Dhaene. An easy computable upper bound for the price of an arithmetic Asian option, Insurance: Mathematics and Economics, 2000, 26: 175-183.
  • 5H Geman and M Yor. Bessel processes, Asian options and perpetuities, Mathematical Finance,1993, 4: 345-371.
  • 6H Geman and M Yor. The valuation of double-barrier: A probabilitic approach, Working paper,1995.
  • 7M Yor. On some exponential functionals of Brownian Motion, Adv Appl Prob, 1992, 24: 509-531.
  • 8J A Yan. Introduction to martingal methods in option pricing, LN in Math 4, Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong(1998).

共引文献8

相关主题

;
使用帮助 返回顶部