基于MATLAB的欧式期权定价的敏感性分析

本文以Black-Scholes-Merton期权定价公式为研究对象,利用MATLAB的求导功能求得了Black-Scholes-Merton期权定价敏感性指标的计算公式。在Notebook环境下调用金融衍生产品工具箱中相关命令编写了一个"Black-Scholes-Merton模型欧式期权敏感性指标通用计算模板",在Word中实现了欧式期权敏感性指标的快捷计算。绘制了敏感性四维网面图生动地展现了欧式期权敏感性指标随时间、股票价格、期权价格的动态过程。     

基于Lévy过程带模糊参数的欧式期权定价

在实际经济行为中，标的资产的价格会受到突发事件（如自然灾害、疾病等）的影响而产生跳跃，为了描述这个跳跃，文章以标的资产价格服从几何Lévy过程为基本模型研究欧式期权的定价问题。给出了欧式期权在0时刻和t (0 t T<≤时刻的定价公式。由于实际中我们不能精确地确定模型参数，需要将模型参数做模糊化处理，进而)可以得到参数是模糊数情形下的欧式期权定价公式。     

几何双分式布朗运动下欧式期权的定价

为了体现金融资产的长记忆性,采用几何双分式布朗运动刻画欧式期权标的资产价格变化的行为模式。建立了双分式布朗运动环境下的欧式期权价值所满足的偏微分方程,并通过边界条件和变量代换得到该偏微分方程的解,即欧式期权的定价公式。     

美式期权的二叉树定价模型

美式期权不同于欧式期权,可以在到期日以前任意时间操作.一般而言,美式期权定价的解析解是很上得到的,二叉树模型是目前金融界最基本的期权定价方法之一,是比较好的数值计算方法,收敛于Black2Schoes期权定价公式的价格本文对二叉树模型进行介绍,并用其来研究美式期权的定价问题.     

基于无套利对冲原理的信用风险期权定价

文章拓展了Klein假设中关于固定违约门槛的假设,构造可变违约门槛,根据无套利对冲原理,通过偏微分方程这种数学工具,推导出含信用风险的欧式脆弱期权价格波动的偏微分方程组和期权定价模型,进而求其显示解,得到类似于Black-Scholes公式的定价公式,该公式的推导过程比使用鞅理论推导更加浅显易懂。     

不完全信息下的期权定价

本文讨论了不完全信息下的期权定价问题,采用风险中性估值原理对期权进行定价,将不完全信息引入到模型中去,构造投资者不完全信息集,利用马尔科夫性质、条件期望性质、Fubini定理等结论,给出了在不完全信息集下的欧式期权定价公式。     

股票价格服从纯生跳-扩散过程的期权定价模型

本文假定股票价格的跳过程为比Possion过程更一般的跳过程-纯生跳过程，建立了股票价格的纯生跳-扩散行为模型。在风险中性假设下推导出欧式期权定价公式。     

服从多种形式跳过程的期权定价模型

股票价格过程包含跳跃和扩散两种随机运动，其中跳跃是重大信息到达对股票价格的冲击。本文将引起股票价格跳跃的重大信息按照相对重要程度分为l类，建立了多种形式跳的股票价格过程，运用无风险证券、股票和期权复制其他期权的方法，推导出期权价值方程和欧式期权定价公式，给出了引起股票价格跳跃的不可观测参数的确定方法。     

不确定市场下的期权定价理论综述

由于B-S定价公式是在完全市场条件假设下推导出来的,这与现实存在很大的出入,所以后来的学者就针对市场条件状况,研究了不同市场条件下的期权定价,其中以不确定性市场条件下的期权定价为主,这显然与事实更加吻合。不确定性市场下的期权定价研究主要有欧式期权定价的情形、美式期权定价的情形、二叉树期权定价的情形以及实物期权定价的情形。文章在此基础上,分析总结了在这个市场假设条件下的研究现状,并给出了未来值得深入研究的方向:主要是进一步放松B-S定价模型的假设条件,引入更多的现实因素,深入研究不同市场状况下的期权定价问题。     

差分方法在期权定价中的应用

本文对有限差分方法进行了简单的介绍,并以欧式看涨期权为例说明了差分方法在期权定价过程中的应用。     

Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate (SIR), stochastic volatility (SV), and double exponential jump into the jump-diffusion settings. The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns, rare events, and an SIR. Using the model, we deduce the pricing characteristic function and pricing formula of a European option. Then, we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV. For verification purposes, we conduct time efficiency analysis, goodness of fit analysis, and jump/drift term analysis of the proposed model. In addition, we compare the pricing accuracy of the proposed model with those of the Black–Scholes and the Kou (2002) models. The empirical results show that the proposed option pricing model has high time efficiency, and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.     

Min–max multi-step barrier options and their variants

This paper studies a new type of barrier option, min–max multi-step barrier options with diverse multiple up or down barrier levels placed in the sub-periods of the option’s lifetime. We develop the explicit pricing formula of this type of option under the Black–Scholes model and explore its applications and possible extensions. In particular, the min–max multi-step barrier option pricing formula can be used to approximate double barrier option prices and compute prices of complex barrier options such as discrete geometric Asian barrier options. As a practical example of directly applying the pricing formula, we introduce and evaluate a re-bouncing equity-linked security. The main theorem of this work is capable of handling the general payoff function, from which we obtain the pricing formulas of various min–max multi-step barrier options. The min–max multi-step reflection principle, the boundary-crossing probability of min–max multi-step barriers with icicles, is also derived.     

Pricing European continuous-installment currency options with mean-reversion

In this paper, we consider European continuous-installment currency option under the mean-reversion environment. Specifically, we provide efficient pricing formula of installment currency put option via a partial differential equation (PDE) approach when the exchange rate follows the mean reverting lognormal model. Using the Mellin transform techniques, we derive the integral equation representation for the optimal stopping boundary from the PDE for pricing of the option. To verify the efficiency and accuracy of our approach, we provide computational results with the least square Monte Carlo method proposed by Longstaff and Schwartz (2001). We also present some numerical examples to examine the characteristics of the optimal boundaries and prices.     

基于实物期权法对R&D项目价值评估的研究——对布莱克-舒尔斯定价模型的改进

针对R&D项目投资的特点,探讨了采用布莱克一舒尔斯期权定价模型对R&D项目价值评估可能存在的缺陷,并提出一种改进方法,即将决策树和布莱克一舒尔斯定价模型结合运用,因为决策树能够模拟研发项目的阶段性决策过程,考虑到多个离散型不确定性因素的相关性,模拟并计算出对决策路径依赖的现金流,因此能克服纯粹使用布莱克一舒尔斯公式的不足,在考虑多个不确定性因素的影响下,实现对多阶段R&D项目价值的评估,作出正确的投资决策。     

Probability of multiple crossings and pricing of double barrier options

This paper derives pricing formulas of standard double barrier option, generalized window double barrier option and chained option. Our method is based on probabilitic approach. We derive the probability of multiple crossings of curved barriers for Brownian motion with drift, by repeatedly applying the Girsanov theorem and the reflection principle. The price of a standard double barrier option is presented as an infinite sum that converges very rapidly. Although the price formula of standard double barrier option is the same with Kunitomo and Ikeda (1992), our method gives an intuitive interpretation for each term in the infinite series. From the intuitive interpretation we present the way how to approximate the infinite sum in the pricing formula and an error bound for the given approximation. Guillaume (2003) and Jun and Ku (2013) assumed that barriers are constant to price barrier options. We extend constant barriers of window double barrier option and chained option to curved barriers. By employing multiple crossing probabilities and previous skills we derive closed formula for prices of 16 types of the generalized chained option. Based on our analytic formulas we compute Greeks of chained options directly.     

Lognormal option pricing for arbitrary underlying assets: a synthesis

All European option pricing formulas sharing the assumption of a lognormally distributed terminal price for the underlying asset are formally similar. It is thus natural to seek a single explicit general formula for this class of options. This paper provides such a synthesis. The key insight is recognizing that all option pricing equations depend explicitly on the expected terminal price of the arbitrary underlying asset, which is often obtained through basic financial reasoning. To illustrate the power and pedagogical value of this framework, I obtain several classical option pricing formulas as special cases of the general equation.     

Pricing of vulnerable exchange options with early counterparty credit risk

The exchange option is one of the most popular options in the over-the-counter (OTC) market, which enables the holder of two underlying assets to exchange one with another. In OTC markets, with the increasing apprehension of credit default risk in the case of option pricing since the global financial crisis, it has become necessary to consider the counterparty credit risk while evaluating the option price. In this study, we combine the vulnerable exchange option and early counterparty default risk to obtain the closed-form formula for the vulnerable exchange option with early counterparty credit risk by using the method of dimension reduction, Mellin transform, and the method of images. Moreover, we examine the pricing accuracy of the option value by comparing our closed-form solution with the formula derived by the Monte-Carlo simulation.     

A Gaussian approximation scheme for computation of option prices in stochastic volatility models

We consider European options on a price process that follows the log-linear stochastic volatility model. Two stochastic integrals in the option pricing formula are costly to compute. We derive a central limit theorem to approximate them. At parameter settings appropriate to foreign exchange data our formulas improve computation speed by a factor of 1000 over brute force Monte Carlo making MCMC statistical methods practicable. We provide estimates of model parameters from daily data on the Swiss Franc to Euro and Japanese Yen to Euro over the period 1999–2002.     

An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching

In this paper, an analytical approximation formula for pricing European options is obtained under a newly proposed hybrid model with the volatility of volatility in the Heston model following a Markov chain, the adoption of which is motivated by the empirical evidence of the existence of regime-switching in real markets. We first derive the coupled PDE (partial differential equation) system that governs the European option price, which is solved with the perturbation method. It should be noted that the newly derived formula is fast and easy to implement with only normal distribution function involved, and numerical experiments confirm that our formula could provide quite accurate option prices, especially for relatively short-tenor ones. Finally, empirical studies are carried out to show the superiority of our model based on S&P 500 returns and options with the time to expiry less than one month.