# On the Pricing and Hedging of Long Dated Zero Coupon Bonds

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## Abstract

The pricing and hedging of long dated derivative contracts is a challenging area of research. As a result of utility indifference pricing for general payoffs the growth optimal portfolio turns out to be the appropriate numeraire or benchmark with the real world probability measure as corresponding pricing measure. This concept of real world pricing can be applied for valuing long dated derivatives. An equivalent risk neutral probability measure does not need to exist under this benchmark approach. This paper develops a parsimonious model for a stock index dynamics, which is based on a time transformed squared Bessel process. It uses a diversified world stock index as proxy for the growth optimal portfolio. Surprisingly low prices result for long dated zero coupon bonds that can be replicated using historical data. Such prices and hedges are difficult to explain under the prevailing risk neutral approach.

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