长记忆随机波动率模型下标的资产价格带跳的欧式期权定价

发布时间：2018-07-09 13:33

本文选题：期权定价 + 跳-扩散过程　；参考：《华南理工大学》2013年硕士论文

【摘要】：经典的Black-Scholes期权定价公式是建立在理想假设之上的，这就使得该定价公式在实际应用中得出的结果与现实不符。大量的研究发现金融时间序列都具有长期依赖性。因此，近年来许多学者开始运用具有这种性质的分数Brown运动研究股票价格波动率运动规律及进行相应的期权定价。经典的Black-Scholes模型假设波动率为常数，但实证分析显示，股票价格波动率随着时间变化而变化，，而且具有长记忆性，其中波动率驱使噪声是分数布朗运动，因此研究波动率的长记忆性及相应的期权定价，具有重要的理论及现实意义。在本学位论文中致力于数学金融学中的期权定价问题研究,我们假定股票价格St满足：其中μ,θ与σ为常数；过程W=(Wt)0ζtζT与B=(Bt)0ζtζT为(Ft)适应的、互不相关的标准布朗运动；过程R=(Rt)0ζtζT为(Ft)适应的复合Poisson过程，和过程W、B相互独立,其中过程N=(Nt)0ζtζT与过程W、B相互独立,并为(Ft)适应，具有强度参数λ的普通Poisson过程，`ξnβ用来刻划第n次突发事件对风险资产报酬的影响。
[Abstract]:The classical Black-Scholes option pricing formula is based on the ideal hypothesis, which makes the result of the formula in practice inconsistent with the reality. A large number of studies have found that financial time series have long-term dependence. Therefore, in recent years, many scholars have begun to use fractional Brownian motion with this property to study the law of stock price volatility and carry out the corresponding option pricing. The classical Black-Scholes model assumes that volatility is constant, but empirical analysis shows that the volatility of stock price changes with time and has long memory, in which volatility drives noise is fractional Brownian motion. Therefore, it is of great theoretical and practical significance to study the long memory of volatility and the corresponding option pricing. In this dissertation, we study the problem of option pricing in mathematics and finance. We assume that the stock price St is satisfied, where 渭, 胃 and 蟽 are constant, the process W = (Wt) 0 味 t 味 T and B = (BT) 0 味 t 味 T are adaptive and independent standard Brownian motions. Process R = (RT) 0 味 t 味 T is a compound Poisson process adapted to (Ft), and process WNB is independent of process WNT, where process N = (NT) 0 味 t 味 T and process WNB are independent and (Ft) adaptive. In the ordinary Poisson process with intensity parameter 位, `尉 n 尾 is used to describe the influence of the nth emergency on the return of risky assets.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.91;O211.6

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