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In order to define a RNM, must we have defined a model for the asset price?

+1 vote
asked Jun 10 in BUS 4028F - Financial Economics by anonymous

In order to define a risk neutral measure must we have defined a model for the asset price? Like in the interest rate and credit risk section, there is reference to the RNM but the RNM is the measure under which the discounted asset is a martingale. So without the asset and/or without a specific model for the asset, can we still have a RNM?

1 Answer

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answered Jun 12 by ABackwell (560 points)
Best answer

Yes, one must specify the model/dynamics for the underlying/risky asset before one identifies/constructs/specifies the risk-neutral measure. You need to begin with the risky asset's process/dynamics, and then i) discount (e.g. with Ito's lemma) and ii) change measure (with Girsanov's theorem), and ensure that the resulting process is a martingale under the new measure (e.g., the dynamics have no drift), so that the definition of the risk-neutral measure will be satisfied.