By Ser-Huang Poon
This ebook covers the pricing of resources, derivatives, and bonds in a discrete time, whole markets framework. It is based seriously at the lifestyles, in a whole industry, of a pricing kernel. it really is essentially aimed toward complex Masters and PhD scholars in finance. issues lined contain CAPM, non-marketable historical past dangers, ecu sort contingent claims as in Black-Scholes and in situations the place hazard impartial valuation dating doesn't exist, multi-period asset pricing below rational expectancies, ahead and futures contracts on resources and derivatives, and bond pricing lower than stochastic rates of interest. all of the 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
If the representative investor has exponential utility, the market price of risk, E[φ′(xm)], is non-stochastic. We will use this property in Chapter 5, when deriving a tractable multi-period asset pricing model. The above property of exponential utility is closely related to the fact that for this function In general, for any utility function, the ratio a(w) = −u″(w)/u′(w) is known as the coefﬁcient of absolute risk aversion. The degree of risk aversion is measured by a(w). In the case of exponential utility, a(w)= α, a constant.
9) does not include the pricing kernel parameter β or the mean of the asset μx. This is an example of what Heston (1993) calls a missing parameters valuation relationship. One parameter of the PDF of the underlying asset (μx) and one parameter of the pricing kernel OPTION PRICING IN A SINGLE-PERIOD MODEL 47 (β) are missing from the valuation formula. In this case the option can be valued without the knowledge of these two parameters. However, in this case, the relationship between the forward price of the claim and the forward price of the underlying asset is also a RNVR.
So the exponential utility investor will not react to background risk by becoming more risk averse to marketable risks. Risk Aversion, Background Risk, and the Pricing Kernel 29 Note that the power function (CRRA) is a special case where A = 0. 15 Also, the exponential utility function is a special case where γ → −∞. The relative risk aversion of the utility function is directly affected by the constant A. If A < 0 the utility function exhibits declining relative risk aversion. To see this, differentiate the marginal utility function and obtain The relative risk aversion is hence which declines in w when A < 0.
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