离散时间下有交易成本的期权定价模型及在金融产品创新中的运用

The Option Pricing Model under Discrete Time and Transaction Cost and Its Application to Financial Product Innovation

经典的BSM模型计算得到的期权价格因模型自身的缺陷常常背离市场价格,特别是模型中关于交易成本或税收为零的假设更与实际情况不符,使连续实时的调整策略失效。分析了离散时间下带有交易成本的期权定价模型,通过修正BSM模型中的波动率与套头比来确定与实际情况更相吻合的期权价格和避险策略,计算了影响修正波动率的各项因素以及与BSM模型波动率相一致的头寸调整时间间隔。作为对修正模型的进一步拓展,简要分析了金融中介在参与市场分工中所具有的比较优势,即连续持有大量和分散的标的资产,组合管理这些头寸可以进一步减少交易成本和风险,使金融中介能够专门从事衍生产品的创造,并以递减的成本、规模经济的方式大量生产衍生产品,创新性金融产品由此而出现。

Although the classic B-S-M Model has succeeded in the academic and practical fields, the option prices provided by it often deviate from the market prices seriously because of its＇ own defective. Especially, the hypothesis of the absence of transaction cost or zero tax is out of accordance with the real world environment. Thus, the hedging strategy with real time will break up. This paper analyzes the option pricing model with transaction cost under discrete time and gets the hedging strategy and option prices by the adjustment of volatility and hedging ratio, calculating the adjusting time interval according with B-S-M Model as well as the variable factors in the adjusting volatility. Finally, this paper analyzes the comparative predominance of the financial intermediations in the process of taking part in the division of labour, which makes them become main body of financial product innovation.