2.3 Equilibrium expected return on any contingent claim


2.3 Equilibrium expected return on any contingent claim

Considering optimal physical investment a *, and substituting the equilibrium interest rate (2.8) into (2.7e) we get the equilibrium expected return on any contingent claim:

Now, applying Ito's lemma to F ( W, Y, t ), and making use of (2.5) and (2.2):

with:

Now comparing the volatility components of (2.10) and (2.3) we have:

Substitution into (2.9) gives:

which by (2.8) becomes:

So the equilibrium expected return on any contingent claim may be written as the risk-free return rF , plus a linear combination of the first derivatives of the contingent claim price with respect to wealth W , and the state variables Y . The coefficients of these derivatives are independent of the contractual specification for that claim; hence they are the same for all contingent claims. CIR [ 17 ] explain that these coefficients may be interpreted as factor risk premia [4] .

[4] Specifically from (2.11), the risk premium for the i th state variable Y i is




Interest Rate Modelling
Interest Rate Modelling (Finance and Capital Markets Series)
ISBN: 1403934703
EAN: 2147483647
Year: 2004
Pages: 132

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