免赔额保险公平定价的期权博弈分析

传统保险定价实质上是供给方定价,忽视了保险契约是保险人和投保人双方互动决策的结果.另一方面,保单具有或有权益的性质,这使得近年来金融定价方法得以引入到保险定价中,以反映风险和回报之间的长期均衡关系.借助期权博弈框架引入博弈论和期权定价理论,分析了免赔额保险的公平定价问题,给出了基本模型和扩展模型两种情形下博弈均衡结果,即保单的无套利价值,并发现在扩展模型情形下,投保人的最优投保策略和均衡保险合同均发生变化.     

随机利率下股价波动源模型的期权定价

假设风险利率是随机利率，我们在详细考虑基础变量——利率和股票价格行为特征的基础上，运用无套利原理推导出随机利率下股价波动源模型的期权定价方程。     

Currency options as theoretical and practical instrument in hedging the exchange risk in excess of loss reinsurance

The paper demonstrates that a ceding company can fully hedge itself against adverse movements of the exchange rate in the case of excess of loss foreign reinsurance by using the currency option markets.     

Simulation of coupon bond European and barrier options in quantum finance

Coupon bond European and barrier options are studied in the framework of quantum finance. The prices of European and barrier options are analyzed by generating sample values of the forward interest rates f(t,x) using a two-dimensional Gaussian quantum field A(t,x). The strong correlations of forward interest rates are described by the stiff propagator of the quantum field A(t,x). Using the Cholesky decomposition, A(t,x) is expressed in terms of white noise. The simulation results for European coupon bond and barrier options are compared with approximate formulas, which are obtained as power series in the volatility of the forward interest rates. The simulation shows that the simulated price deviates from the approximate value for large volatilities. The numerical algorithm is flexible and can be used for pricing any kind of option. It is shown that the three-factor HJM model can be derived from the quantum finance formulation.     

Optimal system of Lie group invariant solutions for the Asian option PDE

Asian options are useful financial products as they guard against large price manipulations near the termination date of the contract. In addition, they are often cheaper than their vanilla European counterparts. Previous analyses of the Asian option partial differential equation (PDE) have obtained analytical solutions for the fixed strike (arithmetically averaged) Asian option (and then only with certain assumptions on the boundary conditions). Using Lie symmetry analysis we obtain an optimal system of Lie point symmetries and demonstrate that many (usually ad hoc) reductions of the Asian option PDE are contained in this minimal set. We analyse each reduction member and the feasibility of its resulting invariant solution with the boundary conditions. We show that the numerical simulations on a reduced equation are more efficient than on the original specified problem. In addition, we have found new analytical solutions in terms of Fourier transforms for the floating strike Asian option as well as the fixed strike Asian option without the simplification of the domain. Copyright © 2011 John Wiley & Sons, Ltd.     

基于CEV过程带交易费的脆弱期权定价的数值算法

主要研究基于CEV过程且支付交易费的脆弱期权定价的数值计算问题.首先通过构造无风险投资组合,导出了基于CEV过程且支付交易费用的脆弱期权定价的偏微分方程模型;其次应用有限差分方法将定价模型离散化,并设计数值算法;最后以看跌期权为例进行数值试验,分析各定价参数对看跌期权价值的影响.     

Options on constant proportion portfolio insurance with guaranteed minimum equity exposure

In the present paper we study a new exotic option offering participation in a dynamic asset allocation strategy, which is an extension of the well‐known Constant Proportion Portfolio Insurance (CPPI) strategy. Our novel approach consists in assuming that the percentage of wealth invested in stocks cannot go under a fixed level, called guaranteed minimum equity exposure (GMEE). In particular, our proposal ensures to overcome the so‐called cash‐in risk, typically related to a standard CPPI technique, simultaneously guaranteeing the equity market participation. We look deeper into the valuation of call and put options linked to this new CPPI‐GMEE strategy. A particular attention is devoted to the analysis of key parameters' value as to gain a better understanding of the sensitivities of the option prices, when changing, for example, the embedded guarantee level. To show the effectiveness of our proposal we provide a detailed computational analysis within the Heston‐Vasicek framework, numerically comparing the evaluation of the price of European plain vanilla options when the underlying is either a purely risky asset, a standard CPPI portfolio and a CPPI with GMEE.     

基于CvaR的融入期权的投资组合模型

把期权作为一种投资对象融入到投资组合中,而不仅仅是作为风险对冲工具.用条件风险价值(CVaR)刻画组合风险,并求出最小化风险下的最优鲁棒投资组合策略.最后通过数值算例证明了模型的有效性,并得到融入期权后有效地提高了组合的收益,特别是当标的资产出现大的波动时,期权在组合中的表现更突出.     

需求依赖努力水平的农产品供应链期权契约优化

针对供应商和零售商组成的农产品供应链,研究市场需求受到努力水平影响的农产品供应链协调问题.由于双重边际效应,分散式供应链中的最优生产数量低于集中式供应链的情况,零售商努力水平也相对较低.引入期权契约时,在零售商主导期权契约的供应链中,研究得到零售商的最优初始订货量和最优期权价格,以及供应商的最优生产数量,实现供应链协调.数值分析证实了期权契约有助于提高零售商的努力水平以及整个供应链的利润.     

Esscher变换下扩展的欧式交换期权定价

文章研究Esscher变换下标的资产价格服从几何布朗运动的扩展的几种欧式交换期权(包括广义交换期权,复合交换期权,障碍交换期权,红绿灯期权)定价问题.首先,给出了带漂移布朗运动的反射原理和性质;其次,借助Gerber和Shiu (1994)给出了多维独立平稳增量过程和二维带漂移布朗运动的Esscher变换定义及其性质;最后,应用Esscher变换的相关理论给出了标的资产价格服从几何布朗运动的扩展的多种欧式交换期权定价公式.特别,本文所得到的期权定价公式与以往文献中给出的结果是一致的.