Real World Pricing of Long Term Contracts
Quantitative Finance Research Centre Research Paper No. 262
32 Pages Posted: 9 Nov 2012
Date Written: November 1, 2009
Abstract
This paper proposes a paradigm shift in the valuation of long term contracts, away from classical no-arbitrage pricing towards pricing under the real world probability measure. In contrast to risk neutral pricing, which is a form of relative pricing, the long term average excess return of the equity market comes into play. Instead of the savings account, the numeraire portfolio is employed as the fundamental unit of value in the analysis. The numeraire portfolio is the strictly positive, tradable portfolio that when used as benchmark makes all bench marked non-negative portfolios supermartingales. Intuitively, bench marked portfolios are in the mean downward trending or trendless. The bench marked real world price of a bench marked contingent claim equals its real world conditional expectation. This yields the minimal possible price for its hedgable part and minimizes the variance for its hedge error. Classical actuarial and risk neutral pricing emerge as special cases of the proposed real world pricing. In long term liability and asset valuation, the proposed real world pricing can lead to significantly lower prices than suggested by classical approaches. The existence of an equivalent risk neutral probability measure is not required.
Keywords: long term contracts, real world pricing, actuarial pricing, risk neutral pricing, numeraire portfolio
JEL Classification: G13, G22
Suggested Citation: Suggested Citation