Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime
Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime
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DOI：
10.1016/j.physa.2011.09.008
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发表时间：
2012-02
影响因子：
3.3
通讯作者：
Jun Wang;Jin-Rong Liang;Longjin Lv;Wei-Yuan Qiu;F. Ren
中科院分区：
文献类型：
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作者：
Jun Wang;Jin-Rong Liang;Longjin Lv;Wei-Yuan Qiu;F. Ren
本文利用齐次次扩散分数布朗运动（HFBM） Z(t)=X(Sα(t)), 0<α<1，用dX(τ)=μX(τ)(dτ)2H+σX(τ)dBH（τ）作为资产价格模型，研究了具有交易费用的连续时间期权定价问题，该模型捕捉了金融市场的次扩散特征。针对欧式期权的公平价格、复制策略的周转率和交易成本，建立了相应的次扩散Black-Scholes方程和Black-Scholes公式。我们也给出了总交易成本。
In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)2H+σX(τ)dBH(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black–Scholes equation and the Black–Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.