PRICING EQUITY-LINKED FOREIGN EXCHANGE OPTION UNDER A REGIME-SWITCHING MULTI-SCALE JUMP-DIFFUSION MODEL

TitlePRICING EQUITY-LINKED FOREIGN EXCHANGE OPTION UNDER A REGIME-SWITCHING MULTI-SCALE JUMP-DIFFUSION MODEL
Publication TypeJournal Article
Year of Publication2018
AuthorsHAN MIAO, SONG XUEFENG, WANG WEI, NIU HUAWEI
JournalDynamic Systems and Applications
Volume27
Issue3
Start Page475
Pagination20
Date Published2018
ISSN1056-2176
AMS Subject Classification65C30, 91B24, 91B70
Abstract

This paper studies the valuation of equity-linked foreign exchange call option under a regime-switching multi-scale jump diffusion model. The foreign equity price is driven by a regime-switching multi-scale jump-diffusion process and the foreign exchange rate is assumed to follow a regime-switching mean-reversion multiscale jump-diffusion process. In addition, the correlations of the two processes are not only manifested in the diffusion parts but also in the jump components. The measure change and Fourier transform technique are adopted to calculate the price of equitylinked foreign exchange call option. Numerical examples and comparative analysis are also provided by fast Fourier transform algorithm to illustrate our results.

PDFhttps://acadsol.eu/dsa/articles/27/3/3.pdf
DOI10.12732/dsa.v27i3.3
Refereed DesignationRefereed
Full Text

REFERENCES
[1] A.R. Dravid, M. Richardson, T. Sun, Pricing foreign index contingent claims: an
application to Nikkei index warrants, J. Derivatives, 1(1) (1993), 33-51.
[2] K.B. Toft, E.S. Reiner, Currency-translated foreign equity options: the American
case, Adv. in Futures and options Res., 9 (1997), 233-264.
[3] Y.K. Kwok, H.Y. Wong, Currency-translated foreign equity options with path
dependent features and their multi-asset extensions, Int. J. Theor. Appl. Finance,
3(2) (2000), 257-278.
[4] S.C. Huang, M.W. Hung, Pricing foreign equity options under L´evy processes.
J. Future Markets, 25(10) (2005), 917-944.
[5] W.D. Xu, C.F. Wu, H.Y. Li, Foreign equity option pricing under stochastic
volatility model with double jumps, Econ. Model., 28 (2011a), 1857-1863.
[6] W.D. Xu, C.F. Wu, H.Y. Li, Accounting for the impact of higher order moments
in foreign equity option pricing model, Econ. Model., 28 (2011b), 1726-1729.
[7] J.D. Hamilton, A new approach to the economic analysis of nonstationary time
series and the business cycle, Econometrica, 57 (1989), 357-384.
[8] R.J. Elliott, L. Aggoun, J.B. Moore, Hidden Markov Models: estimation and
Control, Berlin Heidelberg New York: Springer (1994).
[9] J.Buffington, R.J. Elliott, Regime switching and European options, In: Stoch.
Theor. Control, Springer Berlin Heidelberg, (2002), 73-82.
[10] R.J. Elliott, L. Chan, T.K. Siu, Option pricing and Esscher transform under
regime switching, Ann. Finance, 1(4) (2005), 423-432.
[11] T.K. Siu, H.L. Yang, J.W. Lau, Pricing currency options under two-factor Markovmodulated
stochastic volatility models, Insur. Math. Econ., 43(3) (2008), 295- 302.
[12] Y. Shen, T.K. Siu, Pricing bond options under a Markovian regime-switching
Hull-White model, Econ. Model., 30 (2013), 933-940.
[13] W. Wang, Option Pricing under regime switching models, PhD thesis, East China
Normal University, (2010).
[14] M. Fr¨ommel, R. MacDonald, L. Menkhoff, Markov switching regimes in a monetary
exchange rate model, Econ. Model., 22(3) (2005), 485-502.
[15] K. Fan, Y. Shen, T.K. Siu, R. Wang, Pricing foreign equity options with regimeswitching,
Econ. Model., 37 (2014), 296-305.
[16] M.S. Martin, A two-asset jump diffusion model with correlation, MSC thesis,
University of Oxford, (2007).
[17] L.H. Tian, G.Y. Wang, X.C. Wang, Y.J. Wang, Pricing Vulnerable Options
with Correlated Credit Risk Under Jump-Diffusion Processes, J. Future Markets,
34(10) (2014), 957-979.
[18] H.W. Niu, D.C. Wang, Pricing vulnerable options with correlated jump-diffusion
processes depending on various states of the economy, Quant. Financ., 16 (2016), 1129-1145.
[19] P. Carr, D.B. Madan, Option valuation using the fast Fourier transform, J.
Comput. Financ, 2 (1999), 61-73.
[20] H.Y. Wong, J. Zhao, Currency option pricing: mean reversion and multi-scale
stochastic volatility, J. Future Markets, 30(10) (2010), 938-956.
[21] M.A.H. Dempster, S.S.G. Hong, Spread option valuation and the fast Fourier
transform, In: Mathematical Finance-Bachelier Congress 2000, Springer Berlin,
Heidelberg, (2002), 203-220.
JUMP-DIFFUSION MODEL 493
[22] Y.K. Kwok, K.S. Leung, H.Y. Wong, Efficient options pricing using the fast
Fourier transform, In: Handbook of Computational Finance, Springer, Berlin,
Heidelberg, (2012), 579-604.