扩散市场模型中带交易费和红利的欧式未定权益的保值与定价

Hedging and Pricing of European Contingent Claims under Transaction Costs and Dividend Payments in Diffusion Markets

期权的定价是衍生证券交易的核心问题.本文基于数理金融学的一般框架,对金融市场中常见的带交易费和红利的欧式期权的保值和定价问题进行研究.通过构造辅助鞅的方法,定义了扩散市场模型中的可行和可取策略,讨论了市场的套利问题,从买方和卖方的角度推导了欧式未定权益的价格表达式,给出了扩散市场模型中辅助鞅存在的一个充分条件.

Option pricing is one of key issues in financial derivatives trading market. On the basis of the mathematical finance theory, the hedging and pricing method of European option with transaction costs and dividend payments was studied. By constructing auxiliary martingales, the feasible strategy and the admissible strategy in diffusion markets were defined, and the arbitrage problem was discussed. Both put and call prices of European contingent claims were derived. In the end, a sufficient condition for the existence of auxiliary martingales in diffusion markets was analyzed and presented.