基于粒子群优化算法的期权波动率估计

Estimation of option’s volatility based on particle swarm optimization algorithm

摘要:

首先介绍了Black-Scholes期权定价公式，并分析了波动率对期权定价的重要性。波动率是Black-Scholes公式里的一个相当重要参数，期权价格对它的变动非常敏感。然后，在计算粒子位置和速度时，根据全局最优位置的历史数据以及变异操作，提出了一种基于全局最优位置修正的粒子群优化算法。最后，在数值实验中运用修正的粒子群优化算法获得了基于期货合约的欧式看涨期权公式中波动率的估计值，并通过实验结果比较，展现了该算法具有更好的收敛性。

Abstract:

Firstly, Black-Scholes option pricing formula is introduced, and the importance of volatility in option pricing is analyzed. Volatility is a critical parameter for option pricing, and option prices are very sensitive to volatility's fluctuation. Then when computing particle's position and velocity, the particle swarm optimization algorithm with the adjustment of global best position is proposed according to these history data of global best positions and mutation operation. Finally, the adjusted particle swarm optimization algorithm is used to look for the approximate value of volatility in European call option on a futures contract in numerical experiments. And compared with related experiment results, the modified algorithm displays better in convergence.