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Valuation of inflation-linked annuities in a Lévy market. (English) Zbl 1229.91320

Summary: We study the problem of pricing an inflation adjusted annuity in a forward rates market with jumps. Since the market will be incomplete, we use the minimal \(f^q\)-martingale measure \(Q_q\) which we use for computing discounted expectations. We give explicit results for \(Q_q\) together with explicit results for the price of the annuity.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B30 Risk theory, insurance (MSC2010)
91G80 Financial applications of other theories
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References:

[1] R. Jarrow and Y. Yildirim, “Pricing treasury inflation protected securities and related derivatives using an HJM model,” Journal of Financial and Quantitative Analysis, vol. 38, no. 2, pp. 337-358, 2003.
[2] M. Jeanblanc, S. Klöppel, and Y. Miyahara, “Minimal fq-martingale measures of exponential Lévy processes,” The Annals of Applied Probability, vol. 17, no. 5-6, pp. 1615-1638, 2007. · Zbl 1140.60026
[3] M. Musiela and M. Rutkowski, Martingale Methods in Financial Modelling, Springer, 1998. · Zbl 0906.60001
[4] B. Øksendal and A. Sulem, Applied Stochastic Control of Jump Diffusions, Springer, 2nd edition, 2006.
[5] I. Fisher, The Theory of Interest, The Macmillan Company, 1930. · JFM 56.1108.04
[6] D. Applebaum, Lévy Processes and Stochastic Calculus, vol. 93, Cambridge University Press, Cambridge, UK, 2004. · Zbl 1073.60002
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