混合分数布朗运动下可分离交易可转债的定价

Pricing of warrant bonds under mixed fractional Brownian motion

可分离交易可转债的合理定价是其交易的前提。考虑到金融资产价格序列的长记忆性,因此,在假定股票支付连续红利且股票价格遵循几何混合分数布朗运动的条件下,提出可分离交易可转债定价模型。应用混合分数布朗运动的Ito式和无风险套利原理,建立混合分数布朗运动下可分离交易可转债定价模型,并利用Mellin变换求解定价模型。最后数值研究表明:1)混合分数布朗运动下可分离交易可转债的价值高于布朗运动、分数布朗运动这两种模型下定价结果。2)股票价格、股票价格序列的赫斯特指数、债券的剩余期限、执行价格、标的资产波动率都是可分离交易可转债定价时不可忽略的因素。

The reasonable pricing of warrant bonds is the premise of its transaction.Considering the long memory of financial asset price series,a pricing model of warrant bonds is proposed under the assumption that the stock pays continuous dividends and the stock price follows geometric mixed fractional Brownian motion.Based on the IToformula of mixed fractional Brownian motion and the principle of risk-free arbitrage,the pricing model of separable tradable convertible bonds under mixed fractional Brownian motion is established,and the pricing model is solved by Mellin transform.Finally,the numerical results show that:1)the value of separable tradable convertible bonds under mixed fractional Brownian motion is higher than that under Brownian motion and fractional Brownian motion.2)Stock price,Hurst index of stock price series,residual maturity of bond,strike price and underlying asset volatility are all factors that can not be ignored in the pricing of separable tradable convertible bonds.