摘要
主流期权定价理论总是对标的资产价格过程的分布给出严格假设,而没有考虑Knight不确定性。本文放松标的资产价格过程的严格假设,在仅知到期日标的资产价格的一阶矩和二阶矩的条件下对期权进行定价。由于信息不充分及分布不确定,无法得到精确的期权价格,因此本文推导出在有限信息条件下期权价格的上下界的显性表达式,并对此上下界和Black-Scholes价格进行对比分析。在使用香港恒生指数权证数据进行的实证中发现,市场价格确实介于上下界之间,上下界区间随年化波动率及剩余存续期的减小而缩小。此外,与Black-Scholes价格进行对比后发现,上下界加权价格能对市场价格做出更为稳健的预测。
Mainstream option pricing theories were always based on the strict assumptions about underlying asset price process,which did not take Knightian uncertainty into consideration.In this article,those strict assumptions are relaxed and options are priced with only first and second order moment information.Due to insufficient information and the uncertainty of underlying price distribution,the option price can not be priced accurately.Explicit Functions of upper and lower bounds for option prices under Knightian uncertainty are derived. The arbitrage-free property of the bounds is testified.A comparative analysis between bounds and Black-Scholes price is made afterwards.In the empirical research of Hong Kong＇s Hang Seng Index warrants,we have found that the market prices indeed lie within the bounds.When volatility and remaining duration is small,upper and lower bounds interval is quite narrow.In addition,compared with the Black-Scholes model,the weighted price can make a more accurate estimation of market price.
出处
《系统工程》
CSSCI
CSCD
北大核心
2010年第10期1-7,共7页
Systems Engineering
基金
国家自然科学基金资助项目(70671005)
