risk-neutral pricing formula (5.2.30)

risk-neutral pricing formula (5.2.30)

Show that the risk-neutral pricing formula (5.2.30) may be rewritten as

Here Z(t) is the Radon-Nikodym derivative process (5.2.11) when the market price of risk process ⊝(t) is given by (5.2.21) and the conditional expectation on the right-hand side of (5.9.1) is taken under the actual probability measure ℙ, not the risk-neutral measure . In particular, if for some A ∈ ℱ(T) a derivative security pays off 𝕀A (i.e. , pays 1 if A occurs and 0 if A does not occur), then the value of this derivative security at time zero is 𝔼[D(T)Z(T)𝕀A] · The process D(t)Z(