Marti G Subrahmanyam, Günter Franke, Richard C Stapleton
ABSTRACT
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.
Subrahmanyam: (212) 998-0348 msubrahma@stern.nyu.edu
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