次分数布朗运动下可分离交易可转债的定价及其风险参数

Pricing and Risk Parameters of Warrant Bonds in the Sub-fractional Brownian Motion

科学合理的定价是可分离交易可转债交易的基础.考虑到金融资产价格序列的长记忆性,应用次分数布朗运动的Ito公式和无风险套利原理,建立标的资产支付连续红利且资产价格遵循几何次分数布朗运动的可分离交易可转债定价模型.并利用Mellin变换求解得到定价模型的解析解.最后,分析几个风险参数对可分离交易可转债价值的影响,并通过数值模拟直观地呈现了可分离交易可转债价值随着相关参数变化的趋势.结果表明:股票价格、执行价格、债券的剩余期限、无风险利率、股票价格的波动率及股票价格的赫斯特指数都是可分离交易可转债定价时不可忽略的因素.

considering the long memory of financial asset price series,the pricing model of warrant bonds is constructed by using formula of the sub-fractional brownian motion and the principle of risk-free arbitrage in which the underlying asset price with dividends follows geometric sub-fractional brownian motion.then we obtain the pricing formula of warrant bonds by applying mellin transform.finally,we analyze some risk parameters of the warrant bonds,and further the influences of different parameters on value of the warrant bonds are presented by numerical simulations.the results show that stock price,strike price,remaining maturity of bonds,risk-free interest rate,volatility of stock price and long memory of stock price are all factors that cant be ignored in pricing warrant bonds.