Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T06:34:41.705Z Has data issue: false hasContentIssue false
  • English
  • Français

FINITE MATURITY AMERICAN-STYLE STOCK LOANS WITH REGIME-SWITCHING VOLATILITY

Part of: Mathematical finance

Published online by Cambridge University Press:  19 August 2021

XIAOPING LU Open the ORCID record for XIAOPING LU [Opens in a new window]  and
ENDAH R. M. PUTRI Open the ORCID record for ENDAH R. M. PUTRI [Opens in a new window]
XIAOPING LU*
Affiliation:
School of Mathematics and Applied Statistics, University of WollongongNSW2522, Australia
ENDAH R. M. PUTRI
Affiliation:
Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia; e-mail: [email protected]
*
e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study finite maturity American-style stock loans under a two-state regime-switching economy. We present a thorough semi-analytic discussion of the optimal redeeming prices, the values and the fair service fees of the stock loans, under the assumption that the volatility of the underlying is in a state of uncertainty. Numerical experiments are carried out to show the effects of the volatility regimes and other loan parameters.

Keywords

stock loansregime-switchingPDE approachsemi-analytic methodvolatility

MSC classification

Primary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 2 , April 2021 , pp. 163 - 177
Check for updates
Copyright
© Australian Mathematical Society 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boyle, P. and Draviam, T., “Pricing exotic options under regime-switching”, Insurance Math. Econom. 40 (2007) 267–282; doi:10.1016/j.insmatheco.2006.05.001.CrossRefGoogle Scholar
Buffington, J. and Elliot, R. J., “American options with regime-switching”, Int. J. Theor. Appl. Finance 5 (2002) 497–514; doi:10.1142/S0219024902001523.CrossRefGoogle Scholar
Buffington, J. and Elliott, R. J., “Regime-switching and European options”, in: Stochastic theory and control, Volume 280 of Lect. Notes Control Inform. Sci. (ed. Pasik-Duncan, B.), (Springer-Verlag, Berlin, Heidelberg, 2002) 73–82; doi:10.1007/3-540-48022-6_5.Google Scholar
Dai, M. and Xu, Z. Q., “Optimal redeeming strategy of stock loans with finite maturity”, Math. Finance 21 (2010) 775–793; doi:10.1111/j.1467-9965.2010.00449.x.Google Scholar
Guo, X. and Zhang, Q., “Closed-form solutions for perpetual American put options with regime-switching”, SIAM J. Appl. Math. 64 (2004) 2034–2049; https://www.jstor.org/stable/4096108.Google Scholar
Holmes, A. D., Yang, H., and Zhang, S., “A front-fixing finite element method for the valuation of American options with regime-switching”, Int. J. Comput. Math. 89 (2012) 1094–1111; doi:10.1080/00207160.2012.663911.CrossRefGoogle Scholar
Huang, Y., Forsyth, P. A. and Labahn, G., “Methods for pricing American options under regime-switching”, SIAM J. Sci. Comput. 33 (2011) 2144–2168; doi:10.1137/110820920.CrossRefGoogle Scholar
Itô, K., “Stochastic integral”, Proc. Imp. Acad. 20 (1944) 519–524; doi:10.3792/pia/1195572786.Google Scholar
Khaliq, A. Q. M. and Liu, R., “New numerical scheme for pricing American options with regime-switching”, Int. J. Theor. Appl. Finance 12 (2009) 319–340; doi:10.1142/S0219024909005245.CrossRefGoogle Scholar
Liang, Z., Nie, Y. and Zhao, L., “Valuation of infinite maturity stock loans with geometric Lévy model in a risk-neutral framework” (2012) https://www.semanticscholar.org/paper/VALUATION-OF-INFINITE-MATURITY-STOCK-LOANS-WITH-IN-Liang-Nie/7cd27b51fc509822ec02e130bc93fc7cd86f8396.Google Scholar
Liu, R. H., Zhang, Q. and Yin, G., “Option pricing in a regime-switching model using the fast Fourier transform”, J. Appl. Math. Stoch. Anal. 2006 (2006) 018109; doi:10.1155/JAMSA/2006/18109.CrossRefGoogle Scholar
Lu, X. and Putri, E. R. M., “Semi-analytic valuation of finite maturity stock loans”, Commun. Nonlinear Sci. Numer. Simul. 27 (2015) 206–215; doi:10.1016/j.cnsns.2015.03.007.CrossRefGoogle Scholar
Lu, X. and Putri, E. R. M., “Finite maturity margin call stock loans”, Oper. Res. Lett. 44 (2016) 12–18; doi:10.1016/j.orl.2015.10.007.CrossRefGoogle Scholar
Lu, X. and Putri, E. R. M., “A semi-analytic valuation of American options under a two-state regime-switching economy”, Phys. A Stat. Mech. Appl. 538 (2020) 12–18; doi:10.1016/j.physa.2019.122968.CrossRefGoogle Scholar
Mamon, R. S. and Rodrigo, M. R., “Explicit solutions to European options in a regime-switching economy”, Oper. Res. Lett. 33 (2005) 581–586; doi:10.1016/j.orl.2004.12.003.CrossRefGoogle Scholar
Naik, V., “Option valuation and hedging strategies with jumps in the volatility of asset returns”, J. Finance 48 (1993) 1969–1984; doi:10.1111/j.1540-6261.1993.tb05137.x.CrossRefGoogle Scholar
Prager, D. and Zhang, Q., “Stock loan valuation under a regime-switching model with mean-reverting and finite maturity”, J. Syst. Sci. Complex. 3 (2010) 572–583; doi:10.1007/s11424-010-0146-7.CrossRefGoogle Scholar
Stehfest, H., “Algorithm 368: numerical inversion of Laplace transforms [D5]”, Commun. ACM 13 (1970) 47–49; doi:10.1145/361953.361969.CrossRefGoogle Scholar
Wilmott, P., Howison, S. and Dewynne, J., The mathematics of financial derivatives: a student introduction, 1st edn (Cambridge University Press, Cambridge, 1995); doi:10.1017/CBO9780511812545.CrossRefGoogle Scholar
Wong, T. W. and Wong, H. Y., “Stochastic volatility asymptotics of stock loans: valuation and optimal stopping”, J. Math. Anal. Appl. 394 (2012) 337–346; doi:10.1016/j.jmaa.2012.04.067.CrossRefGoogle Scholar
Wong, T. W. and Wong, H. Y., “Valuation of stock loans using exponential phase-type Levy models”, Appl. Math. Comput. 222 (2013) 275–289; doi:10.1016/j.amc.2013.07.049.Google Scholar
Xia, J. and Zhou, X. Y., “Stock loans”, Math. Fin. 17 (2007) 307–317; doi:10.1111/j.1467-9965.2006.00305.x.CrossRefGoogle Scholar
Yang, H., “A numerical analysis of American options with regime-switching”, J. Sci. Comput. 44 (2010) 69–91; doi:10.1007/s10915-010-9365-2.CrossRefGoogle Scholar
Yao, D., Zhang, Q. and Zhou, X. Y., “A regime-switching model for European options”, in: Stochastic processes, optimization, and control theory: applications in financial engineering, queueing networks, and manufacturing systems, Volume 94 of Int. Ser. Oper. Res. Manag. Sci. (eds Yan, H., Yin, G. and Zhang, Q.), (Springer, Boston, MA, 2006) 281–300; doi:10.1007/0-387-33815-2_14.CrossRefGoogle Scholar
Yi, F., “American put option with regime-switching volatility (finite time horizon) variational inequality approach”, Math. Methods Appl. Sci. 31 (2008) 1461–1477; doi:10.1002/mma.984.CrossRefGoogle Scholar
Yuen, F. L. and Yang, H., “Option pricing with regime-switching by trinomial tree method”, J. Comput. Appl. Math. 233 (2010) 1821–1833; doi:10.1016/j.cam.2009.09.019.CrossRefGoogle Scholar
Zhang, Q. and Zhou, X. Y., “Valuation of stock loans with regime-switching”, SIAM J. Control Optim. 3 (2009) 1229–1250; doi:10.1137/070708998.CrossRefGoogle Scholar
Zhu, S-P., Badran, A. J., and Lu, X., “A new exact solution for pricing European options in a two state regime-switching economy”, Comput. Math. Appl. 64 (2012) 2744–2755; doi:10.1016/j.camwa.2012.08.005.CrossRefGoogle Scholar