Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)
This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries and a quadratic diffusion coefficient. The paper shows in particular how to interpret the option price formula in terms of exercise probabilities which are calculated under the martingale measures associated with two specific numeraire portfolios. An application to the pricing of bond options and certain interest rate derivatives illustrates the main results.
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Volume (Year): 1 (1997)
Issue (Month): 4 ()
|Note:||received: January 1996; final version received: December 1996|
|Contact details of provider:|| Web page: http://www.springer.com|
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References listed on IDEAS
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- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997.
" Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Journal of Finance,
American Finance Association, vol. 52(1), pages 409-30, March.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
- Rady, Sven, 1994. "The Direct Approach to Debt Option Pricing," Munich Reprints in Economics 3404, University of Munich, Department of Economics.
- Rubinstein, Mark, 1983. " Displaced Diffusion Option Pricing," Journal of Finance, American Finance Association, vol. 38(1), pages 213-17, March.
- Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March.
- Sondermann, Dieter, 1987. "Currency options: Hedging and social value," European Economic Review, Elsevier, vol. 31(1-2), pages 246-256.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- S. D. Jacka, 1992. "A Martingale Representation Result and an Application to Incomplete Financial Markets," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 239-250.
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