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Mental Accounting: A Closed-Form Alternative to the Black Scholes Model

Siddiqi, Hammad (2013): Mental Accounting: A Closed-Form Alternative to the Black Scholes Model.

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Abstract

Experimental evidence and opinions of market professionals suggest that people rely on mental accounting while valuing a call option. I show that mental accounting generates a closed-form alternative to the Black Scholes formula that does not require a complete market. The new formula is arbitrage free. The new formula differs from the Black Scholes formula only due to the appearance of a parameter in the formula that captures the risk premium on the underlying. The new formula, called the analogy option pricing formula, provides a new explanation for the implied volatility skew puzzle. I also show that the key aspects of the analogy formula are consistent with empirical evidence.

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