标的股票服从跳—扩散过程的复合期权定价模型

董翠玲; 师恪

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标的股票服从跳—扩散过程的复合期权定价模型

更新时间：2026-01-21

- 标的股票服从跳—扩散过程的复合期权定价模型
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Issue 1, (2005)
- 作者机构：
  
  新疆大学数学与系统科学学院,新疆大学数学与系统科学学院新疆乌鲁木齐 830046,新疆,乌鲁木齐,830046
- 作者简介：
- 基金信息：
- DOI：
  CLC： F224
- Published：2005
- 稿件说明：
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[1]董翠玲,师恪.标的股票服从跳—扩散过程的复合期权定价模型[J].新疆大学学报(自然科学版),2005(01):26-30.

董翠玲, 师恪. 标的股票服从跳—扩散过程的复合期权定价模型[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2005, (1).
[1]董翠玲,师恪.标的股票服从跳—扩散过程的复合期权定价模型[J].新疆大学学报(自然科学版),2005(01):26-30. DOI：

董翠玲, 师恪. 标的股票服从跳—扩散过程的复合期权定价模型[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2005, (1). DOI：

摘要

当公司以债券和股票来融资时

股票可以看作基于该公司价值的看涨期权

则基于该公司股票的期权可看作是基于公司价值的期权的期权

既复合期.R.Geske(1979)建立了当公司价值服从"标准几何Brown运动"的复合期权的定价模型

并给出了定价公式.C.R.Gukhal(2004)给出了当标的股票服从跳-扩散过程的一种特殊情形--跳跃的相对高度的期望k=E(Y-1)=0的复合期权的定价公式.本文在建立了标的股票服从跳-扩散过程且跳跃的高度随机变量Y服从对数正态分布时的复合期权定价模型

并给出了定价公式

推广了Geske和Gukhal的结论.

Abstract

When firm are financed with a combination of debt and equity

the equity in the firm can be interpreted as a call option on the firm

then the stock option is an option on a call option on the firm

that is

a compound option. R. Geske (1979) derived an analytical volution formula for compound option when the firm value followed a geometric Brownian Motion. C.R. Gukhal (2004) derived analytical volution formula for compound option when underlying asset followed a special case of jump-diffusion process

that is

the expectation of percentage change in underlying asset price k = ∈ (Y - 1) = 0 . In this paper

we derive analytical volution formula for compound option when underlying asset follows jump-diffusion and the random variable Y has a log-normal distribution. this formula extends both Geske and Gukhal's conclusions.

关键词

Keywords

references

Geske R. The Valuation of Compound Option [J]. Journal of Financial Economics,1979,7:63-81.

Gukhal C R. The Compound Option Approach to American OPtions on jump-diffusions [J]. Journal of Economics Dynamics and Control,2004, 28:2055-2074.

约翰·赫尔.期权期贷和其他衍生产品.第三版[M].张陶伟译.北京:华夏出版社,2000.418-419.

Merton R C. Option Pricing When Underlying Stock Returns Are Discontinuous [J]. Journal of Financial Economics, 1976,3:125-144.

Scott L O. Pricing Stock Options In a Jump-diffusion Modle with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods [J]. Mathematical Finance,1997,(4):413-426.

Amin K I. Jump Diffusion Option Valuation in Discrete Time [J]. Journal of Finance,1993,(5):1833-1863.

Aase K K. Contigent Claims Valuation When the Security Price Is a Combination of ITOProcess and a Random Point Process [J]. Journal of StochasticProcess and Their Application, 1988,28:185-220.

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