Faculty of Actuarial Science & Insurance Seminar with Jennifer Alonso-Garcia - University of Groningen

Title: Utility indifference pricing of a coupon-yielding bond

Abstract:
When valuing claims on assets or indices which are not fully hedgeable, well-known option pricing expressions are no longer valid (see e.g. \cite{amin,black}) and incomplete market techniques need to be used. We use the theory of utility indifference pricing to derive a general framework to price claims on securities which are not traded \cite{musiela,young}. The utility indifferent price is the one that makes the issuer indifferent between issuing the claim, which involves receiving a premium and paying cash-flows throughout the duration of the contract and at maturity, and not issuing the claim. The strength of this technique is that it can incorporate the risk appetite of the issuer in the price and that it provides closed-form solutions when individuals have exponential preferences. We calculate the price for a security which is partially correlated with the financial markets and which makes regular coupon payments throughout the duration of the contract. Contrary to most frameworks found in the literature, we generalize the two-step pricing procedure and incorporate intermediate payments. The framework can be applied to the valuation of over-the-counter securities. In the specific insurance context, it can be used to price catastrophic-linked bonds or longevity bonds.

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