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This paper aims to construct and compare various total‐return world stock indices based on daily data.

Because of diversification, these indices are noticeably similar. A diversification theorem identifies any diversified portfolio as a proxy for the growth optimal portfolio.

The paper constructs a diversified world stock index that outperforms a number of other indices and argues that it is a good proxy for the growth optimal portfolio.

The diversified world stock index has applications to derivative pricing and investment management.

The purpose of this paper is to provide a framework of replication pricing of derivatives and identify funding valuation adjustment (FVA) and credit valuation adjustments (CVA) as price components.

The authors propose the notion of bilateral replication pricing. In the absence of funding cost, it reduces to unilateral replication pricing. The absence of funding costs, it introduces bid–ask spreads.

The valuation of CVA can be separated from that of FVA, so-called split up. There may be interdependence between FVA and the derivatives value, which then requires a recursive procedure for their numerical solution.

The authors have assume deterministic interest rates, constant CDS rates and loss rates for the CDS. The authors have also not dealt with re-hypothecation risks.

The results of this paper allow user to identify CVA and FVA, and mark to market their derivatives trades according to the recent market standards.

For the first time, a line between the risk-neutral pricing measure and the funding risk premiums is drawn. Also, the notion of bilateral replication pricing extends the unilateral replication pricing.