金融工程中资产收益的连续时间模型评述

总结了在过去30年中金融资产收益连续时间模型的发展及主要成果,讨论了迄今连续时间模型参数估计的主要方法,其中特别讨论了MCMC方法;最后指出了现在和未来该领域研究所面临的主要课题。     

多维汇率联动期权跳——扩散模型及其定价

在资产价格服从跳——扩散模型,汇率服从不同跳跃幅度的不连续模型的基础上,考虑用无套利分析方法得到了期权应满足的随机微分方程,并由Feynman-Kac公式,得到了多种欧式汇率联动期权的计算公式;当汇率联动期权具有随机寿命时,进一步研究了多种欧式汇率联动期权的价格。     

Pricing power options with a generalized jump diffusion

In this article, the valuation of power option is investigated when the dynamic of the stock price is governed by a generalized jump-diffusion Markov-modulated model. The systematic risk is characterized by the diffusion part, and the non systematic risk is characterized by the pure jump process. The jumps are described by a generalized renewal process with generalized jump amplitude. By introducing NASDAQ Index Model, their risk premium is identified respectively. A risk-neutral measure is identified by employing Esscher transform with two families of parameters, which represent the two parts risk premium. In this article, the non systematic risk premium is considered, based on which the price of power option is studied under the generalized jump-diffusion Markov-modulated model. In the case of a special renewal process with log double exponential jump amplitude, the accurate expressions for the Esscher parameters and the pricing formula are provided. By numerical simulation, the influence of the non systematic risk’s price and the index of the power options on the price of the option is depicted.     

Static Hedging of Geometric Average Asian Options with Standard Options

In this article, we first establish a theorem that represents the price of an Asian option in terms of standard European options with a shorter term and different strikes. Then using Gauss–Hermite numerical integration, we discretize our theorem so as to use Monte Carlo simulation to examine the error of the static hedging under the Black–Scholes model and the Merton jump-diffusion model. For ease of comparison, we also provide the error of the dynamic hedging. The numerical results show that the static hedging strategy performs better than the dynamic one under both models.     

Local Linear Estimation of Second-order Jump-diffusion Model

In this article, we propose the local linear estimators of the drift coefficient and diffusion coefficient in the second-order jump-diffusion model. We also show the consistency and asymptotic normality of these estimators under mild conditions.     

Optimal investment and life insurance strategies in a mixed jump-diffusion framework

Abstract

This article investigates an optimal investment and life insurance strategies in a mixed jump-diffusion framework. The individual life insurance policyholder who has CRRA preferences. The market consists of riskless asset, a zero-coupon bond, a stock and life insurance. The instantaneous interest rate is modeled as the O-U model, while a zero-coupon bond with credit risk follows a BSDE and a risky asset be driven by MJD-fBm model. The problem is solved by the mixed jump diffusion fractional HJB SDE which satisfied the admissible strategy, then the closed form solution and optimal strategies are derived and the simulation of the various parameters are also given.     

Moment-Implied Densities: Properties and Applications

Suppose one uses a parametric density function based on the first four (conditional) moments to model risk. There are quite a few densities to choose from and depending on which is selected, one implicitly assumes very different tail behavior and very different feasible skewness/kurtosis combinations. Surprisingly, there is no systematic analysis of the tradeoff one faces. It is the purpose of the article to address this. We focus on the tail behavior and the range of skewness and kurtosis as these are key for common applications such as risk management.     

Exchange option pricing in jump-diffusion models based on esscher transform

In the real world, we introduce a dynamic model about the risky asset which is governed by Brownian motion, stationary compound Poisson process and its compensation process. By choosing Esscher transform parameters, we obtain a risk-neural measure Q under which the discounted value of the risky underlying asset is a martingale. Then, we give the pricing formulas of Exchange option by change of numeraire. At last, we analyze the option pricing formula and provide numerical illustrations by introducing BBY stock and SBUX stock.     

一类高新技术企业专利权价值的实物期权评估方法——基于跳扩散过程和随机波动率的美式期权的建模与模拟

由于经典的Black-Scholes期权定价模型的假设忽略了突发事件对资产价格的影响和"波动率微笑"对期权价值的影响而与实际情形往往存在偏差,因此学者们对Black-Scholes模型的改进则主要分别集中在带跳扩散过程的期权定价模型与具随机波动率的期权定价模型等两个方面,然而却少见将这两种模型结合起来的研究。本文首先在带跳扩散过程的期权定价模型与具随机波动率的期权定价模型的研究工作的基础上,建立了一种同时带跳扩散过程和具随机波动率的美式期权定价模型,并通过伊藤引理推导出了资产价格、随机波动率和期权满足的偏微分方程;然后,利用特征函数法和傅里叶变换导出了资产价格的随机分布,进而通过马尔科夫链方法给出了基于跳扩散过程和随机波动率的美式期权的数值解;最后,运用已建立的带跳扩散过程和随机波动率的美式期权定价模型对高新技术企业项目投资的专利权价值进行实物期权定价评估的案例研究,并对跳扩散强度参数和随机波动率参数进行敏感性分析,研究结果表明:将项目收益跳扩散过程和市场环境随机波动率加入到专利权实物期权定价模型中,可以有效避免专利权的期权价值被高估。     

Bayesian Inference for the Jump-Diffusion Model with M Jumps

In this article, we propose a new class of models—jump-diffusion models with M jumps (JD(M)J). These structures generalize the discretized arithmetic Brownian motion (for logarithmic rates of return) and the Bernoulli jump-diffusion model. The aim of this article is to present Bayesian tools for estimation and comparison of JD(M)J models. Presented methodology is illustrated with two empirical studies, employing both simulated and real-world data (the S&P100 Index).