Islamic Capital Markets: Theory and Practice

Chapter 6

Asset Pricing under Uncertainty

This chapter analyzes asset pricing under uncertainty. Asset pricing under certainty is fairly simple; the price of an asset is the present value of its certain future payoffs discounted by a risk-free return. However, with uncertainty, stocks’ and sukuks’ payoffs are uncertain; pricing of these assets is no longer as simple as under certainty. Moreover, with uncertainty, many assets that do not exist in a certainty environment appear; they are called derivatives and have also to be priced. Theories of asset pricing under uncertainty cover stocks, sukuks, and derivatives.

Uncertainty is described in terms of a statistical probability distribution with mean and standard deviation. Covariance plays a role in measuring risk among assets. It is used to determine the systemic risk of an asset in relation to market portfolio. Uncertainty is also described using two random processes that dominate debate in capital market efficiency theory; these are the random walk and the martingale processes.

Asset pricing theory under uncertainty relies on three equivalent approaches:

1. Arbitrage-free pricing

2. Risk-neutral pricing

3. Equilibrium consumption-based pricing

The theory of arbitrage-free pricing shows that each asset can be replicated by a hedging portfolio. Efficiency of capital markets requires that asset prices be free of arbitrage. The price of an asset is equal to that of its replicating portfolio to preclude arbitrage opportunities, defined ...