A uniform asymptotic expansion for stochastic volatility model in pricing multi‐asset European options

In this paper, we consider a stochastic volatility model for pricing multi‐asset European options that are widely used in the real world, under the assumption that the volatilities are driven by different OU processes. Using the singular perturbation method for multi‐parameter and the boundary layer theory, we derive a uniform asymptotic expansion for the option prices, as well as the uniform error estimates. Copyright © 2011 John Wiley & Sons, Ltd.     

负债代理冲突下企业投融资互动行为的实物期权分析

准确分析企业投融资之间的互动关系,实现两种决策的协同,有助于提高企业决策效率和项目价值.通过把项目融资政策内生到投资决策的实物期权模型中,构建基于股东价值最大化和企业价值最大化的投融资决策互动模型,得到两种情形下的投融资决策临界点和期权价值,并借助数值分析负债代理冲突对企业投融资行为的影响.研究结果表明,负债融资既可能引发过度投资问题,也可能抑制投资.这种非效率投资将相应地提高负债融资的成本,对企业的负债融资产生抑制作用.     

随机利率下服从分数跳-扩散模型的重置期权定价

假设利率服从扩展的Vasicek模型,标的资产价格服从分数跳-扩散过程,利用无套利理论与多元正态分布,导出了规定时间的重置期权的定价公式.     

A note on first-passage times of continuously time-changed Brownian motion

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, for example, for the pricing of single-barrier and double-barrier options in a Black-Scholes framework. One popular possibility to generalize the Black-Scholes model is to introduce a stochastic time scale. This equips the modelled returns with desirable stylized facts such as volatility clusters and jumps. For continuous time transformations, independent of the Brownian motion, we show that analytical results for the double-barrier problem can be obtained via the Laplace transform of the time change. The result is a very efficient power series representation for the resulting exit probabilities. We discuss possible specifications of the time change based on integrated intensities of shot-noise type and of basic affine process type.     

A comprehensive mathematical approach to exotic option pricing

This work illustrates how several new pricing expressions for exotic options can be derived within a Lévy framework by employing a unique pricing expression. To the purpose, a unifying formula is obtained by solving some nested Cauchy problem for pseudodifferential equations generalizing Black–Scholes PDE. The main result extends (Agliardi R. The quintessential option pricing formula under Lévy processes. Applied Mathematics Letters 2009; 22:1626‐1631) and is a powerful tool for generating new valuation expressions. Several examples of pricing formulas under the Lévy processes are provided to illustrate the flexibility of the method. Some of them are new in the financial literature. Finally, many existing pricing formulas of the traditional Gaussian model are easily obtained as a by‐product. Copyright © 2012 John Wiley & Sons, Ltd.     

基于近似对冲跳跃风险的美式看跌期权定价及数值解法研究

考虑了基于近似对冲跳跃风险的美式看跌期权定价问题。首先,运用近似对冲跳跃风险、广义It 公式及无套利原理,得到了跳-扩散过程下的期权定价模型及期权价格所满足的偏微分方程。然后建立了美式看跌期权定价模型的隐式差分近似格式,并且证明了该差分格式具有的相容性、适定性、稳定性和收敛性。最后,数值实验表明,用本文方法为跳-扩散模型中的美式期权定价是可行的和有效的。     

马尔可夫调制的跳扩散过程下幂式期权的定价

假定市场经济状态由两状态连续时间马尔可夫链描述,风险资产满足马尔可夫调制的跳扩散过程,研究了马尔可夫调制模型下幂式期权的定价问题.通过测度变换和Girsanov定理,得出幂式看涨期权定价公式,并利用看涨、看跌的平价关系得到了幂式看跌期权的定价公式.此外,还利用蒙特卡洛方法给出了幂式看涨期权价值的数值结果.     

光滑树图期权定价模型的叉熵分析法

为了克服CRR模型收敛的波动性,以及强调历史信息的预测作用的情况,提出了一个新奇的光滑收敛的树图模型.新模型基于历史信息,运用最小叉熵原理
来推导树图的关键参数p,u,d, 然后使用倒推法推断期权的价格.显然,新模型所得的期权的价格隐含着历史信息.由于最小叉熵原理是一个凸规划问题,能求得唯一的最优解,所以,新模型也适用于不完全金融市场期权定价.最后,数值算例表明,相比于CRR模型,新模型收敛光滑平稳且有更高的计算精度;对上涨(下跌)的二元期权、欧式期权,新模型都能光滑收敛于B-S公式.     

布朗运动和泊松过程共同驱动下的欧式期权定价

针对布朗运动和泊松过程共同驱动下股票价格的随机微分方程,利用It0公式和随机积分的方法,得到了该形式下欧式期权定价的模型,并给出了模型的求解.     

有交易费和连续红利时的期权定价公式

期权定价模型为期权等金融衍生工具定价问题的研究带来了创新,但是该模型的一些基本假设与现实情况不符,使得由此计算出来的期权价格和实际金融市场上的期权价格有较大出入.作者通过改变无交易成本和无红利支付这2个条件改进了B-S模型,使其更具有现实意义,并利用偏微分方程基本解的方法,获得了修正后B-S模型的看涨-看跌期权的定价公式.