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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/27051
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| Title: | Why are Options Expensive? |
| Authors: | Subrahmanyam, Marti G
Franke, Günter
Stapleton, Richard C. |
| Issue Date: | Feb-1998 |
| Series/Report no.: | FIN-98-065 |
| 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. |
| URI: | http://hdl.handle.net/2451/27051 |
| Appears in Collections: | Finance Working Papers
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