Handbook of Quantitative Finance and Risk Management

pp 605-616

The Valuation of Uncertain Income Streams and the Pricing of Options

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A simple formula is developed for the valuation of uncertain income streams consistent with rational investor behavior and equilibrium in financial markets. Applying this formula to the pricing of an option as a function of its associated stock, the Black–Scholes formula is derived even though investors can trade only at discrete points in time.


CRRA intertemporal CAPM Pricing uncertain income streams Single-price law of markets Arbitrage State-prices Consumption-based CAPM Local expectations hypothesis Unbiased term structure Random walk Option pricing Time-additive utility Logarithmic utility Black– Scholes formula Equity risk premium puzzle Joint normality covariance theorem