How do investors' expectations drive asset prices?

To derive the elasticity of the pricing kernel we compare this to

hΦ₀,_t  =  -φ₀,'■, о ≤ t ≤ τ,

Φ₀,0 = 1∙

Equation (8) shows that in the economy under consideration the ratio of the
instantaneous volatility of the Girsanov-process, i.e. the market price of risk,
and the instantaneous volatility of the asset are equal to the elasticity of the
pricing kernel. In T the following relation holds

∂ ,       ₄             ∂²     , ₄

7E^h (T,F_τ)           '' (Ft)

^κt    _dx 'x _  ∂x²       Z7

F                    F

^_t ,,_τ h ^{τ F}) ^T      θ_χu (f_t)

thus the realtive risk aversion of the representative agent equals the elasticity
of the pricing kernel.⁷

In the remainder of this paper we will not rely on the existence of an
equilibrium. Instead we will only make the assumption that no arbitrage
possibilities exist and thus that the transformation of measure is given by
an appropriate Girsanov-functional. In this more general case, the pricing
kernel is not necessarily a deterministic function of the asset price.⁸

5 Derivation of Asset Price Processes

In this section we derive the forward price process of the asset in the market
defined in section 3. The point of start is

F — E^p (Φ_t,_τF_τ ∣σ {I_uI 0 ≤ и ≤ t}) , 0 ≤ t ≤ T,

⁷For a more detailed derivation and discussion see for example Decamps, Lazrak [6]
and Franke, Stapleton, Subralimanyam [12]. For a derivation and discussion of the pricing
kernel in an equilibrium model not relying on the representative agent assumption see for
example Franke, Stapleton, Subrahmanyam [11].

⁸See for example Decamps, Lazrak [6].

12

<<   10   11   12   13   14   15   16   >>

More intriguing information