Why are Options Expensive?
38 Pages Posted: 11 Nov 2008
Date Written: February 1998
Many valuation models in financial economics are developed using the pricing kernel approach to adjust for risk through the equivalent martingale representation. Often it is assumed, explicitly or implicitly, that the pricing kernel exhibits constant elasticity with respect to the price of the market portfolio. In a representative agent economy this would be close to assuming that the representative agent has constant proportional risk aversion. The elasticity of the pricing kernel has also implications for the pricing of options. This paper shows, first, that given the forward price of the market portfolio, all European options would have higher prices if the elasticity of the pricing kernel was declining instead of constant. Moreover, a volatility smile-effect is generated. Second, the paper shows that the standard geometric Brownian motion underlying the Black/Scholes model requires constant elasticity of the pricing kernel . Third, if the price of the market portfolio at the expiration date of an option is lognormally distributed, then declining elasticity of the pricing kernel implies a stochastic process which is characterized by higher volatility and negative autocorrelation. Thus, declining elasticity of the pricing kernel can explain several empirical findings.
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