支付離散紅利的美式看漲期權定價
發(fā)布時間：2018-12-15 21:42
【摘要】：期權是重要的衍生工具之一,期權的核心問題是期權的定價問題.近年來,為了與金融市場實際情況更好的吻合,滿足更多投資者的需求,人們逐步放寬了Black-Scholes模型最初的假設.許多學者考慮了在期權有效期內標的資產有紅利支付的歐式期權的定價公式,但相關的美式期權的定價研究較少.本文考慮當標的資產在期權有效期內有離散紅利支付時,美式看漲期權的定價公式. 首先,為了給出美式看漲期權的解析公式,引入了三種模型.模型1假設凈紅利股票價格,即股票價格減去未來紅利的現值,服從幾何布朗.模型2假設累積紅利股票價格,即股票價格加上己付紅利的現值,服從幾何布朗運動.模型3是利用泰勒展開把離散紅利近似轉化為連續(xù)紅利率,從而使得在到期日的股票價格服從對數正態(tài)分布. 其次,研究利率是常數,且標的資產在期權有效期內有離散紅利支付時,美式看漲期權的價格.利用風險中性測度定價原理得到了價格的解析公式. 最后,討論當利率服從Vasicek模型時,相應的美式期權的定價公式.利用等價鞅測度變換及Girsanov定理得到價格的解析公式.
[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.
【學位授予單位】：河北師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：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.
【學位授予單位】：河北師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F832.5;F224
【參考文獻】
相關期刊論文 前10條
1 蔡華;苗杰;;隨機利率下有紅利支付的跳擴散模型的期權定價[J];昌吉學院學報;2007年03期
2 李莉英,張q，
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