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Valuation and hedging of contingent claims in the HJM model with deterministic volatilities

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  • M. Rutkowski

Abstract

The aim of the present paper is mostly expository, namely, we intend to provide a concise presentation of arbitrage pricing and hedging of European contingent claims within the Heath, Jarrow and Morton frame-work introduced in Heath et al. (1992) under deterministic volatilities. Such a special case of the HJM model, frequently referred to as the Gaussian HJM model, was studied among others in Amin and Jarrow (1992), Jamshidian (1993), Brace and Musiela (1994a, 1994b). Here, we focus mainly on the partial differential equations approach to the valuation and hedging of derivative securities in the HJM framework. For the sake of completeness, the risk neutral methodology (more specifically, the forward measure technique) is also exposed.

Suggested Citation

  • M. Rutkowski, 1996. "Valuation and hedging of contingent claims in the HJM model with deterministic volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 237-267.
    • Handle: RePEc:taf:apmtfi:v:3:y:1996:i:3:p:237-267
    DOI: 10.1080/13504869600000012
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    Cited by:

    1. Carl Chiarella & Oh-Kang Kwon, 1999. "Classes of Interest Rate Models Under the HJM Framework," Research Paper Series 13, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.
    3. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.

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