二元数字期权定价与copula的关系

首先简要介绍了 copula的一些基本概念和性质 ,然后探讨了一种多元未定权益——二元数字期权的价格与 copula的关系 .结论表明 ,一个二元数字期权的价格恰好是一个 copula函数 ,由此结论进而给出了根据实际数据获得二元数字期权价格的基本思路和步骤 .     

跳-扩散模型下的再装期权定价

本文建立股票价格的跳过程为Poisson过程,跳跃高度服从对数正态分布时股票价格过程的随机微分方程,在风险中性的假设下找到等价鞅测度,利用鞅方法,用较简单的数学推导得到了股票价格服从跳-扩散过程的欧式再装期权定价公式.     

连续支付红利及有交易成本的领子期权定价模型

在无风险利率r(t)和波动率σ(t)均为时间t的函数及市场无套利假设下,分别考虑了连续红利率q(t)和有交易成本情况下的领子期权定价,通过建立相应定价模型,得到了领子期权不同的定价公式.     

延迟期权与风险投资决策研究

本在传统投资方法基础上，通过引入延迟期权定价理论，建立风险投资项目时机选择模型，增加了风险投资项目决策的科学性。     

A Discrete-Time American Put Option Model with Fuzziness of Stock Prices

To solve a mathematical model for American put option with uncertainty, we utilize two essentials, i.e., a λ-weighting function and a mean value of fuzzy random variables simultaneously. Estimation of randomness and fuzziness as uncertainty should be important when we deal with a reasonable and natural model extended from the original optimization/decision making. Three kinds of mean values by fuzzy measures, which are based on Possibility, Necessity and Credibility, are demonstrated particularly. We consider the optimal expected price of the American put option by dynamic programming under a reasonable assumption. A numerical example is given to illustrate our idea.     

Estimation and empirical evaluation of the time-dependent Extended-CIR term structure model

Email: ym{at}onetel.net.uk Empirical study of 25 years US Treasury bills data shows thateven when the spot interest rate remains fixed, its volatilityvaries significantly over time. Constant-coefficient modelscannot capture these changes as they give rise to time-homogeneousdistributions. Maximum likelihood fitting of a one-factor time-dependentExtended-CIR model of the term structure, whose closed-formsolution was previously obtained by the author, shows that itcan capture these changes, as well as achieve significantlyhigher likelihood value. It is shown that exploitation of theclosed-form solutions substantially improves the accuracy andefficiency of Monte Carlo simulations over high-order discretizationalgorithms. It is also shown that the feasibility of exact one-to-onecalibration of the model to any continuous yield curve allowsvaluation of bond options significantly more accurately andefficiently.     

Martingales and stochastic integrals in the theory of continuous trading

This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain class, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we discuss the modern theory of contingent claim valuation, including the celebrated option pricing formula of Black and Scholes. It is shown that the security market is complete if and only if its vector price process has a certain martingale representation property. A multidimensional generalization of the Black-Scholes model is examined in some detail, and some other examples are discussed briefly.     

A stochastic calculus model of continuous trading: Complete markets

A paper by the same authors in the 1981 volume of Stochastic Processes and Their Applications presented a general model, based on martingales and stochastic integrals, for the economic problem of investing in a portfolio of securities. In particular, and using the terminology developed therein, that paper stated that every integrable contingent claim is attainable (i.e., the model is complete) if and only if every martingale can be represented as a stochastic integral with respect to the discounted price process. This paper provides a detailed proof of that result as well as the following: The model is complete if and only if there exists a unique martingale measure.     

指数屏障期权定价模型

本文在股票价格服从几何布朗运动的假设下,采用一种简化的方法,推导了指数屏障期权定价公式。该方法具有一般性,能用来解决其它该类型的屏障期权的定价问题。     

含有衍生证券的投资组合问题初探

针对投票投资所面临的风险,本文在一定的市场假设下,采用V aR风险度量方法,运用衍生证券“套期保值”的特性,通过股票与其期权的组合,使投资者最大限度地降低投资风险,获得最大收益,最后用实例进行分析.