guarantees using longdated derivatives. This paper extends the benchmark approach to price and hedge long-dated equity index …

specifying the short rate and the discounted stock index under the benchmark approach. Comparison with empirical evidence …

over long time periods. The method is widely applicable and is demonstrated here in the general setting of the benchmark … approach, where spatial boundary limiting conditions for the PDE need to be appropriately chosen and approximated. The PDE …

be valued and hedged. This benchmark approach values both assets and liabilities consistently under the real world … probability measure using the best performing portfolio, the growth optimal portfolio, as benchmark and numeraire. The benchmark … approach identifies the investment strategy which is replicating a given claim at minimal cost. Should the liability under …

In this paper, we discuss how to model credit risk under the benchmark approach. Firstly we introduce an affine credit …