有交易费和随机分红时的欧式期权定价

European option pricing with transaction costs and stochastic dividends

在股票价格服从对数正态分布,波动率为常数的假设下,考虑了有与股票价格成比例的交易费和股票的离散随机分红时的期权定价问题.运用无套利定价理论,构造分红远期合约和标准远期合约,给出了显示的期权定价公式,它是标的资产为远期的期权定价公式的推广(当股票的交易费和分红均为零时,它简化为标的资产为远期的期权定价公式).结果表明期权价格随股票交易费用的增加而增加,随股票分红的增加而减少,这对现实中金融市场期权定价具有一定的理论意义和实际应用价值.

Based on the assumption that prices of stocks follow log-normal distribution, and their volatility is constant, considering pricing European option problems with transaction costs are proportional to stocks′ value and discrete stochastic dividends of stocks. An arbitrage-free pricing theory was used and a dividend forward contract and a standard forward contract was constructed, an explicit expression of option pricing was given, which extends option pricing formula underlying assets being forward contracts (when both transaction costs and dividends become zero, it reduces to the option pricing formula where underlying assets are forward contracts). The result indicates that option price increases as transaction costs of stocks increases and decreases as dividends of stocks increase. This conclusion has important theoretical and practical significance to option pricing in the real financial market.