光滑树图期权定价模型的叉熵分析法

The Smooth Tree Option Pricing Model Based on the Minimum Cross Entropy

为了克服CRR模型收敛的波动性,以及强调历史信息的预测作用的情况,提出了一个新奇的光滑收敛的树图模型.新模型基于历史信息,运用最小叉熵原理来推导树图的关键参数p,u,d,然后使用倒推法推断期权的价格.显然,新模型所得的期权的价格隐含着历史信息.由于最小叉熵原理是一个凸规划问题,能求得唯一的最优解,所以,新模型也适用于不完全金融市场期权定价.最后,数值算例表明,相比于CRR模型,新模型收敛光滑平稳且有更高的计算精度;对上涨(下跌)的二元期权、欧式期权,新模型都能光滑收敛于B-S公式.

To overcome the volatility of the binomial tree option price model＇s con- vergence, and to strengthen the predictive effect of the historical data information, we propose a novel tree model that is smooth and convergent. Based on the historical data information, the new model applies the minimum cross entropy formalism to derive the crucial parameters p, u and d of the binomial tree option price model, and the backward induction is used to compute the option price. Obviously, option price computed by the new model implies the historical data information. Because the minimum cross entropy formalism is a convex optimization problem, it has the unique optimal solution. Further- more, the new model is also suitable for pricing the option in the incomplete market. Finally, compared with the CRR model, the new one can smoothly converge and have more accurate results in numerical examples. Moreover, the new model can converge to the B-S formula for the call （put） European option （binary option）.