西安交大特聘教授、北京大学、日本筑波大学 (Tsukuba University)、美国Rutgers, The State University of New Jersey客座教授
Abstract: This paper has used the Arbitrage Theorem (Gordan Theorem) to clarify some misconceptions in the literature of derivative pricing. First, unlike the claim of the irrelevancy of the underlying asset‘s (stock’s) expected return, it is found that the value of an option depends on the probability of the underlying asset (stock) rising or falling. Using the relationship between the relative price ratio between the two states:π/(1-π) and the probability of the up move, the paper also derives discrete-time versions of the Greeks. Second, since with no arbitrage, μ is a function of rf and σ, the Black-Scholes option pricing formula contains the underlying asset’s expected rate of return μ. Third, with a two-step contract, it has been shown that within a company, there is no first claim or seniority between bond and stock, but there is first claim among fixed-income assets (e.g., labor and bond), and labor is senior to bond.
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