Asset Pricing in Discrete Time: A Complete Markets Approach (Oxford Finance Series)

This book covers the pricing of assets, derivatives, and bonds in a discrete time, complete markets framework. It relies heavily on the existence, in a complete market, of a pricing kernel. It is primarily aimed at advanced Masters and PhD students in finance. Topics covered include CAPM, non-marketable background risks, European style contingent claims as in Black-Scholes and in cases where risk neutral valuation relationship does not exist, multi-period asset pricing under rational expectations, forward and futures contracts on assets and derivatives, and bond pricing under stochastic interest rates. All the proofs, including a discrete time proof of the Libor market model, are shown explicitly. Relying on the existence, in a complete market, of a pricing kernel, this book covers the pricing of assets, derivatives, and bonds in a discrete time, complete markets framework. It is primarily aimed at advanced Masters and PhD students in finance. -- Covers asset pricing in a single period model, deriving a simple complete market pricing model and using Stein's lemma to derive a version of the Capital Asset Pricing Model. -- Looks more deeply into some of the utility determinants of the pricing kernel, investigating in particular the effect of non-marketable background risks on the shape of the pricing kernel. -- Derives the prices of European-style contingent claims, in particular call options, in a one-period model; derives the Black-Scholes model assuming a lognormal distribution for the asset and a pricing kernel with constant elasticity, and emphasizes the idea of a risk-neutral valuation relationship between the price of a contingent claim on an asset and the underlying asset price. -- Extends the analysis to contingent claims on assets with non-lognormal distributions and considers the pricing of claims when risk-neutral valuation relationships do not exist. -- Expands the treatment of asset pricing to a multi-period economy, deriving prices in a rational expectations equilibrium. -- Uses the rational expectations framework to analyse the pricing of forward and futures contracts on assets and derivatives. -- Analyses the pricing of bonds given stochastic interest rates, and then uses this methodology to model the drift of forward rates, and as a special case the drift of the forward London Interbank Offer Rate in the LIBOR Market Model. A graduate text focusing on pricing methods for financial assets, this book provides an excellent link between the key concepts of asset pricing and derivative pricing, using some simple economic and statistical concepts