混合高斯模型下带红利的永久美式期权定价

Perpetual American Pricing Option in the Mixed Gaussian Model with Dividend

本文建立混合高斯模型下支付连续红利的永久美式期权定价模型.利用自融资策略和分数伊藤公式,得到永久美式期权价值所满足的偏微分方程.其次,由永久美式期权的实施条件与看涨-看跌期权的对称关系,获得看涨与看跌期权的定价公式与最佳实施边界.最后,利用平安银行的日收盘价对标的资产进行实证分析,结果表明:用混合高斯模型模拟出的股票价格与真实股票价格比较接近,能够反映股票的整体走势.

In this paper, the pricing model for American option of stock paying continuous dividend is constructed under mixed Gaussian model environment. The partial differential equation is obtained for the value of perpetual American option by self-financing strategy and fractional It？o formula. Secondly,the pricing formula and optional exercise boundary of call and put are obtained by the option application condition and symmetric relation of call and put option. Finally, taking the Ping An bank stock closing price as an example, the result shows that using the mixed Gaussian model for simulating stock price is close to the real stock price, which can reflect the overall trend of the stock.