Posted: 12 Nov 2010
Date Written: December 2010
The fact that properly normalized asset prices are martingales is the basis of modern asset pricing. One normalizes asset prices to adjust for risk and time preferences. Both adjustments can be made simultaneously via a stochastic discount factor, or one can adjust for risk by changing probabilities and adjust for time using the return on an asset, for example, the risk-free return. This paper reviews this methodology and the circumstances in which it is feasible. Three examples are given to illustrate the delicate link in continuous-time models between the absence of arbitrage opportunities and the feasibility of martingale pricing.
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