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Real World Pricing for Forward Contracts

M’hamed Eddahbi, Yassine El Qalli


This paper derives a term structure for forward prices under the benchmark approach. This approach uses the growth optimal portfolio (GOP) as a benchmark or numeraire. We employ the fair pricing methodology to derive a relationship between the zero-coupon bond price and the forward price. The resulting forward prices are not in general real world martingales. This real world martingale property can only be captured for contingent claims
that are independent of the GOP value at the settlement date. To overcome this problem, we introduce the benchmarked forward measure to retrieve the martingale property. We establish then an actuarial pricing formula for any contingent claim and we derive a real world term structure for the forward price.


Term structure, Benchmark approach, GOP, Forward contract.

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