Summary
A partial Laplace transform is used to study the valuation of American call options with constant dividend yield, and to derive an integral equation for the location of the optimal exercise boundary, which is the main result of this paper.
The integral equation differs depending on whether the dividend yield is less than or exceeds the risk-free rate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
. Alobaidi G, Mallier R (2006) The American straddle close to expiry. Boundary Value Problems 2006 article ID 32835.
Black F, Scholes M (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81:637–659.
Brekke KA, Oksendal B (1991) The high contact principle as a sufficiency condition for optimal stopping. In: Lund D, Oksendal B (eds) Stochastic Models and Option Values: Applications to Resources, Environment and Investment Problems. North-Holland, Amsterdam.
Carr P, Jarrow R, Myneni R (1992) Alternative characterizations of the American put. Mathematical Finance 2:87–106. Laplace Transforms and the American Call Option 27.
Chesney M, Gibson R (1993) State space symmetry and two-factor option pricing models. Advances in Futures and Options Research 8:85–112.
Crank J (1984) Free and moving boundary problems. Clarendon, Oxford.
Evans GW, Isaacson E, MacDonald JKL (1950) Stefan-like problems. Quarterly of Applied Mathematics 8:312–319.
Evans JD, Kuske RE, Keller JB (2002) American options with dividends near expiry. Mathematical Finance 12:219–237.
Geske R (1979) A note on an analytical valuation formula for unprotected American call options on stocks with known dividends. Journal of Financial Economics 7:375–380.
Geske R (1981) Comments on Whaley’s note. Journal of Financial Economics 9:213–215.
Jacka SD (1991) Optimal stopping and the American put. Mathematical Finance 1:1–14.
Karatzas I (1988) On the pricing of American options. Applied Mathematics and Optimization 17:37–60.
Kim IJ (1990) The analytic valuation of American options. Review of Financial Studies 3:547–572.
Knessl C (2001) A note on a moving boundary problem arising in the American put option. Studies in Applied Mathematics 107:157–183.
Kolodner II (1956) Free Boundary Problem for the Heat Equation with Applications to Problems of Change of Phase. I. General Method of Solution. Communications in Pure and Applied Mathematics 9:1–31.
Kuske RE, Keller JB (1998) Optimal exercise boundary for an American put option. Applied Mathematical Finance 5:107–116.
McDonald R, Scroder M (1998) A parity result for American options. Journal of Computational Finance 1:5–13.
McKean HP Jr. (1965) Appendix A: A free boundary problem for the heat equation arising from a problem in mathematical economics. Industrial Management Review 6:32–39.
Merton RC (1973) The theory of rational option pricing. Bell Journal of Economics and Management Science 4:141–183.
Myneni R (1992) The Pricing of the American Option. Annals of Applied Probability 2:1–23.
Peskir G (2005) On the American option problem. Mathematical Finance 15:169–181.
Polyanin AD, Manzhirov V (1998) Handbook of integral equations. CRC Press, New York.
Roll R (1977) An analytical formula for unprotected American call options on stocks with known dividends. Journal of Financial Economics 5:251–258.
Samuelson PA (1965) Rational theory of warrant pricing. Industrial Management Review 6:13–31.
Stamicar R, Sevcovic D, Chadam J (1999) The early exercise boundary for the American put near expiry: numerical approximation. Canadian Applied Mathematics Quarterly 7:427–444.
Van Moerbeke J (1976) On optimal stopping and free boundary problems. Archive for Rational Mechanics Analysis 60:101–148.
Whaley RE (1981) On the valuation of American call options on stocks with known dividends. Journal of Financial Economics 9:207–211.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Alobaidi, G., Mallier, R. (2008). Laplace Transforms and the American Call Option. In: Sarychev, A., Shiryaev, A., Guerra, M., Grossinho, M.d.R. (eds) Mathematical Control Theory and Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69532-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-69532-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69531-8
Online ISBN: 978-3-540-69532-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)