论文标题
重新审视的Black-Scholes-Merton选项定价：我们是否发现了致命缺陷？
Black-Scholes-Merton Option Pricing Revisited: Did we Find a Fatal Flaw?
论文作者
论文摘要
Black and Scholes（1973）的选项定价公式取决于连续的自我融资条件，这是Merton（1971）连续预算方程的特殊情况。据信，自给自足的条件将投资组合重新平衡的经济概念形式化而没有流入或外部资金流出，但从未在连续的时间内正式得出。此外，甚至更有问题，我们在默顿（Merton）（1971）的模型中发现了一个时机错误，并表明他的自我融资状况在离散和连续时间都被弄清楚了。我们的结果使对文献的开创性贡献无效，包括Merton（1971），Black and Scholes的期权定价公式（1973），Harrison和Pliska的连续交易模型以及Cox，Ross和Rubinstein（1979）的二项式期权定价模型。我们还表明，Black and Scholes（1973）及其公式的替代推导暗中假设了复制结果。
The option pricing formula of Black and Scholes (1973) hinges on the continuous-time self-financing condition, which is a special case of the continuous-time budget equation of Merton (1971). The self-financing condition is believed to formalize the economic concept of portfolio rebalancing without inflows or outflows of external funds, but was never formally derived in continuous time. Moreover, and even more problematically, we discover a timing mistake in the model of Merton (1971) and show that his self-financing condition is misspecified both in discrete and continuous time. Our results invalidate seminal contributions to the literature, including the budget equation of Merton (1971), the option pricing formula of Black and Scholes (1973), the continuous trading model of Harrison and Pliska (1981), and the binomial option pricing model of Cox, Ross and Rubinstein (1979). We also show that Black and Scholes (1973) and alternative derivations of their formula implicitly assumed the replication result.
