支付离散红利的美式看涨期权定价
发布时间：2018-12-15 21:42
【摘要】：期权是重要的衍生工具之一,期权的核心问题是期权的定价问题.近年来,为了与金融市场实际情况更好的吻合,满足更多投资者的需求,人们逐步放宽了Black-Scholes模型最初的假设.许多学者考虑了在期权有效期内标的资产有红利支付的欧式期权的定价公式,但相关的美式期权的定价研究较少.本文考虑当标的资产在期权有效期内有离散红利支付时,美式看涨期权的定价公式. 首先,为了给出美式看涨期权的解析公式,引入了三种模型.模型1假设净红利股票价格,即股票价格减去未来红利的现值,服从几何布朗.模型2假设累积红利股票价格,即股票价格加上己付红利的现值,服从几何布朗运动.模型3是利用泰勒展开把离散红利近似转化为连续红利率,从而使得在到期日的股票价格服从对数正态分布. 其次,研究利率是常数,且标的资产在期权有效期内有离散红利支付时,美式看涨期权的价格.利用风险中性测度定价原理得到了价格的解析公式. 最后,讨论当利率服从Vasicek模型时,相应的美式期权的定价公式.利用等价鞅测度变换及Girsanov定理得到价格的解析公式.
[Abstract]:Option is one of the important derivatives, the core problem of option is option pricing. In recent years, in order to better match the actual situation of financial markets and meet the needs of more investors, people have gradually relaxed the initial assumptions of the Black-Scholes model. Many scholars have considered the pricing formula of European option with dividend payment of the underlying asset during the term of validity of the option, but there is little research on the pricing of the American option. This paper considers the pricing formula of American call option when the underlying asset has discrete dividend payment during the period of validity of the option. Firstly, in order to give the analytic formula of American call option, three models are introduced. Model 1 assumes the net dividend stock price, that is, the stock price minus the present value of the future dividend, from geometric Brown. Model 2 assumes that the cumulative dividend stock price, that is, the stock price plus the present value of the pay-as-you-go dividend, is governed by geometric Brownian motion. Model 3 uses Taylor expansion to approximate the discrete dividend to a continuous red interest rate, so that the stock price at maturity date from the logarithmic normal distribution. Secondly, we study the price of American call option when interest rate is constant and the underlying asset has discrete dividend payment during the term of option. The analytical formula of price is obtained by using the pricing principle of risk neutral measure. Finally, the pricing formula of American option is discussed when interest rate is based on Vasicek model. By means of equivalent martingale measure transformation and Girsanov theorem, the analytical formula of price is obtained.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.5;F224
[Abstract]:Option is one of the important derivatives, the core problem of option is option pricing. In recent years, in order to better match the actual situation of financial markets and meet the needs of more investors, people have gradually relaxed the initial assumptions of the Black-Scholes model. Many scholars have considered the pricing formula of European option with dividend payment of the underlying asset during the term of validity of the option, but there is little research on the pricing of the American option. This paper considers the pricing formula of American call option when the underlying asset has discrete dividend payment during the period of validity of the option. Firstly, in order to give the analytic formula of American call option, three models are introduced. Model 1 assumes the net dividend stock price, that is, the stock price minus the present value of the future dividend, from geometric Brown. Model 2 assumes that the cumulative dividend stock price, that is, the stock price plus the present value of the pay-as-you-go dividend, is governed by geometric Brownian motion. Model 3 uses Taylor expansion to approximate the discrete dividend to a continuous red interest rate, so that the stock price at maturity date from the logarithmic normal distribution. Secondly, we study the price of American call option when interest rate is constant and the underlying asset has discrete dividend payment during the term of option. The analytical formula of price is obtained by using the pricing principle of risk neutral measure. Finally, the pricing formula of American option is discussed when interest rate is based on Vasicek model. By means of equivalent martingale measure transformation and Girsanov theorem, the analytical formula of price is obtained.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.5;F224
【参考文献】
相关期刊论文 前10条
1 蔡华;苗杰;;随机利率下有红利支付的跳扩散模型的期权定价[J];昌吉学院学报;2007年03期
2 李莉英,张q，
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