ABSTRACT
“The essential feature of modern option pricing theory is the derivation of the risk neutral valuation relationships (RNVRs) for contingent claims” (Brennan 1979: 53). An RNVR is a formula relating the value of the contingent claim to the value of the underlying assets and other directly or indirectly observable exogenous variables. With risk neutrality, the value of the contingent claim does not involve any parameters of investor’s risk aversion, as if the investors were risk neutral. In the continuous trading option pricing models in the spirt of Black and Scholes (1973) and Merton (1973), the risk-neutral formula is derived mainly from the self-financing riskless hedge. Cox and Ross (1976) argues that whenever a portfolio can be constructed which includes the contingent claim and the underlying asset in such proportions that the instantaneous return on the portfolio is nonstochastic, the resulting valuation relationship is risk neutral. The investors’ preferences are arbitrary in these continuous models. However, in the majority of the literature, investors are most often assumed to be risk averse. In the counterpart of the continuous models, the discrete models in the spirit of Rubinstein (1976), the same RNVR is obtained by restricting the preferences of the representative investor. As shown by Brennan (1979) and Stapleton and Subrahmanyam (1984), that the representative investor exhibits constant proportional (absolute) risk aversion for arbitrary bivariate log-normal (normal) distributions of the price of the underlying asset and aggregate wealth is necessary and sufficient for the RNVRs to exist. Thus the representative investor is actually risk averse in the discrete models though the resulting valuation relationship is risk neutral.
