Utility Indifference Pricing of Interest-Rate Guarantees

International Journal of Theoretical and Applied Finance, Vol. 12, No. 1, pp. 63-82, 2009

Posted: 2 Dec 2009

See all articles by Fred Espen Benth

Fred Espen Benth

University of Oslo

Frank Proske

University of Oslo - Department of Mathematics

Abstract

We consider the problem of utility indifference pricing of a put option written on a non-tradeable asset, where we can hedge in a correlated asset. The dynamics are assumed to be a two-dimensional geometric Brownian motion, and we suppose that the issuer of the option have exponential risk preferences. We prove that the indifference price dynamics is a martingale with respect to an equivalent martingale measure (EMM) Q after discounting, implying that it is arbitrage-free. Moreover, we provide a representation of the residual risk remaining after using the optimal utility-based trading strategy as the hedge.

Our motivation for this study comes from pricing interest-rate guarantees, which are products usually offered by companies managing pension funds. In certain market situations the life company cannot hedge perfectly the guarantee, and needs to resort to sub-optimal replication strategies. We argue that utility indifference pricing is a suitable method for analysing such cases.

We provide some numerical examples giving insight into how the prices depend on the correlation between the tradeable and non-tradeable asset, and we demonstrate that negative correlation is advantageous, in the sense that the hedging costs become less than with positive correlation, and that the residual risk has lower volatility. Thus, if the insurance company can hedge in assets negatively correlated with the pension fund, they may offer cheaper prices with lower Value-at-Risk measures on the residual risk.

Keywords: interest-rate guarantees, utility indifference pricing, hedging, arbitrage-free pricing, correlation, risk

Suggested Citation

Benth, Fred Espen and Proske, Frank, Utility Indifference Pricing of Interest-Rate Guarantees. International Journal of Theoretical and Applied Finance, Vol. 12, No. 1, pp. 63-82, 2009, Available at SSRN: https://ssrn.com/abstract=1515433

Fred Espen Benth (Contact Author)

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Frank Proske

University of Oslo - Department of Mathematics

Blindern, N-0162, Os
Norway

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