Liu Xiao, Zhou Rongxi, Xiong Yahui, Yang Yuexiang
School of Banking and Finance, University of International Business and Economics, Beijing 100029, China.
School of Management, China University of Mining and Technology (Beijing), Beijing 100083, China.
Entropy (Basel). 2019 Aug 13;21(8):788. doi: 10.3390/e21080788.
This paper develops the interval maximum entropy model for the interval European option valuation by estimating an underlying asset distribution. The refined solution for the model is obtained by the Lagrange multiplier. The particle swarm optimization algorithm is applied to calculate the density function of the underlying asset, which can be utilized to price the Shanghai Stock Exchange (SSE) 50 Exchange Trades Funds (ETF) option of China and the Boeing stock option of the United States. Results show that maximum entropy distribution provides precise estimations for the underlying asset of interval number situations. In this way, we can get the distribution of the underlying assets and apply it to the interval European option pricing in the financial market.
本文通过估计标的资产分布，建立了区间最大熵模型用于区间欧式期权估值。利用拉格朗日乘数法得到了该模型的精确解。应用粒子群优化算法计算标的资产的密度函数，该函数可用于对中国上海证券交易所50交易型开放式指数基金（ETF）期权和美国波音股票期权进行定价。结果表明，最大熵分布为区间数情形下的标的资产提供了精确估计。通过这种方式，我们可以得到标的资产的分布，并将其应用于金融市场的区间欧式期权定价。
