(Stellenbosch : Stellenbosch University, 2008-12) Ramarimbahoaka, Dimbinirina; Kopp, Ekkehard; Capinski, Maciej; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
In the Benchmark Approach to Finance, it has been shown that by taking the
Growth Optimal Portfolio as numéraire, a candidate for a pricing derivatives
formula under the real world probability can be given. This result allows
us to price in an incomplete financial market model. The result comes from
two different approaches. In the first approach we use the supermartingale
property of portfolios in units of the benchmark portfolio which leads to the
fact that an equivalent measure is not needed. In the second approach the
numéraire property of the Growth Optimal Portfolio is used. The numéraire
portfolio defines an equivalent martingale measure and by change of measure
using the Radon-Nikodým derivative, a real world pricing formula is derived
which is the same as the one given by the first approach stated above.