Asset Pricing in Discrete Time: A Complete Markets Approach by Ser-Huang Poon
By Ser-Huang Poon
This e-book covers the pricing of resources, derivatives, and bonds in a discrete time, whole markets framework. It is based seriously at the life, in a whole industry, of a pricing kernel. it truly is essentially geared toward complicated Masters and PhD scholars in finance. subject matters lined comprise CAPM, non-marketable history dangers, ecu sort contingent claims as in Black-Scholes and in instances the place chance impartial valuation dating doesn't exist, multi-period asset pricing below rational expectancies, ahead and futures contracts on resources and derivatives, and bond pricing below stochastic rates of interest. the entire proofs, together with a discrete time evidence of the Libor industry version, are proven explicitly.
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Extra resources for Asset Pricing in Discrete Time: A Complete Markets Approach (Oxford Finance Series)
A log utility investor is one who is myopic. 15 In the case of the logarithmic utility function, we have: Since r(w) is a constant, log utility is an example of the class of Constant Relative Risk Averse utility functions. a(w) is positive but a′(w) = −1/w2 < 0, which means that the investor is decreasing absolute risk averse. A log utility investor is one who is myopic. 30 Risk Aversion, Background Risk, and the Pricing Kernel which is greater than 1 when A < 0, conﬁrming that the elasticity of the pricing kernel declines when A < 0.
Non-dividend paying assets: In this case, spot-forward parity for the underling asset means that the spot price of the asset is where Bt,t+T = e−rT and where r is the continuously compounded interest rate and T is in years. 14) annualised volatility of the asset by 2. Assets paying a non-stochastic dividend: Assume that the underlying asset is a stock or bond, paying a known dividend Dt+T at time t + T. In this case, spot-forward parity implies since the forward contract does not receive the dividend.
We show there that θ(xm) > 0 when a background risk exists. Also, except in the case of exponential utility, θ′(xm) < 0. The non-negativity of θ(xm) reﬂects the fact that the risk premium is also non-negative. Intuitively, θ′(xm)< 0 follows from the fact that 34 Risk Aversion, Background Risk, and the Pricing Kernel a given background risk has less effect at high income level than at low income level. Similarly, we would expect rich individuals to have a smaller precautionary premium than poor individuals.