Growth optimal portfolios and real world pricing

[摘要] In the Benchmark Approach to Finance, it has been shown that by taking theGrowth Optimal Portfolio as numéraire, a candidate for a pricing derivativesformula under the real world probability can be given. This result allowsus to price in an incomplete financial market model. The result comes fromtwo different approaches. In the first approach we use the supermartingaleproperty of portfolios in units of the benchmark portfolio which leads to thefact that an equivalent measure is not needed. In the second approach thenuméraire property of the Growth Optimal Portfolio is used. The numéraireportfolio defines an equivalent martingale measure and by change of measureusing the Radon-Nikodým derivative, a real world pricing formula is derivedwhich is the same as the one given by the first approach stated above.

[发布机构] Stellenbosch University