本文選題：回望期權　切入點：亞式期權　出處：《華中師范大學》2012年碩士論文

【摘要】：期權在國際金融衍生市場上發(fā)展迅速,近年來,出現了大量的奇異期權,強路徑依賴期權就是其中之一。強路徑依賴期權主要包括兩類：回望期權和亞式期權。這類強路徑依賴期權的收益既依賴于標的資產價格,又依賴于期權在整個或者部分期權有效期內的標的資產價格歷程。 本文介紹了基于B-S歐式期權定價模型推廣下的幾種模型：CEV模型、B-P混合驅動模型、CEV下且受B-P混合驅動模型。CEV模型中,標的資產價格的波動率不是常數,而標的資產價格的波動率彈性是常數；對于B-P混合驅動模型,考慮到了標的資產價格在服從幾何布朗運動的同時,也可能會發(fā)生隨機跳躍；CEV下支付紅利且受B-P混合驅動模型,是對標的資產價格綜合考慮了前面兩個模型的情況。這三個模型,使得標的資產價格所遵從的隨機過程更接近現實。 作者在前人的研究基礎上,綜合研究了上述三種推廣模型下的回望期權和亞式期權的定價問題,主要是采用無套利原理和風險中性定價,得到了在這幾種模型下的回望期權和亞式期權的定價模型,并用二叉樹期權定價模型研究了支付離散紅利的算術平均亞式期權的數值解法。這樣可以使我們更好地比較三種推廣模型對期權定價的影響。
[Abstract]:Options have developed rapidly in the international financial derivatives market. In recent years, a large number of exotic options have emerged. Strong path-dependent options are one of them. Strong path-dependent options include two main types: the lookback option and the Asian option. The returns of these options are dependent on the underlying asset price. It also depends on the underlying asset price course of option in the whole or part of the period of validity of the option. This paper introduces several kinds of models based on B-S European option pricing model. The volatility of underlying asset price is not constant under B-P hybrid drive model. The volatility elasticity of the underlying asset price is constant. For the B-P hybrid drive model, it is considered that the underlying asset price may pay dividends under the stochastic jump CEV and be subjected to the B-P hybrid drive model, while the underlying asset price is moving from geometric Brownian motion to the geometric Brownian motion. These three models make the stochastic process of underlying asset price more realistic. On the basis of previous studies, the author synthetically studies the pricing problems of the lookback option and Asian option under the above three generalized models, which are mainly based on the no-arbitrage principle and risk-neutral pricing. The pricing models of the lookback options and Asian options under these models are obtained. The numerical solution of arithmetic average Asian option for discrete dividend payment is studied by using the binomial tree option pricing model, which enables us to better compare the effects of the three generalized models on option pricing.
【學位授予單位】：華中師范大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：F224;F830.9

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本文編號：1656880