Valuation of correlation options under a stochastic interest rate model with regime switching

doi:10.1007/s11464-017-0608-5

Front. Math. China

2017, Vol. 12

Issue (5) : 1113-1130 https://doi.org/10.1007/s11464-017-0608-5

RESEARCH ARTICLE

Valuation of correlation options under a stochastic interest rate model with regime switching

Kun FAN, Rongming WANG(

)

School of Statistics, East China Normal University, Shanghai 200241, China

Download: PDF(757 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We consider the valuation of a correlation option, a two-factor analog of a European call option, under a Hull-White interest rate model with regime switching. More specifically, the model parameters are modulated by an observable, continuous-time, finite-state Markov chain. We obtain an integral pricing formula for the correlation option by adopting the techniques of measure changes and inverse Fourier transform. Numerical analysis, via the fast Fourier transform, is provided to illustrate the practical implementation of our model.

Keywords Correlation option stochastic interest rate regime-switching forward measure fast Fourier transform (FFT)

Corresponding Author(s): Rongming WANG

Issue Date: 30 September 2017

Cite this article:

Kun FAN,Rongming WANG. Valuation of correlation options under a stochastic interest rate model with regime switching[J]. Front. Math. China, 2017, 12(5): 1113-1130.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0608-5
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I5/1113

1	BakshiG, MadanD. Spanning and derivative-security valuation.J Financial Economics, 2000, 55: 205–238 https://doi.org/10.1016/S0304-405X(99)00050-1
2	CarrP, MadanD. Option valuation using the fast Fourier transform.J Comput Finance, 1999, 2: 61–73 https://doi.org/10.21314/JCF.1999.043
3	CoxJ, IngersollJ, RossS. A theory of the term structure of interest rates.Econometrica, 1985, 53: 385–407 https://doi.org/10.2307/1911242
4	DempsterM A H, HongS S G.Spread option valuation and the fast Fourier transform.In: Mathematical Finance-Bachelier Congress 2000. Berlin: Springer, 2002, 203–220 https://doi.org/10.1007/978-3-662-12429-1_10
5	ElliottR J, AggounL, MooreJ B. Hidden Markov Models: Estimation and Control.Berlin-Heidelberg-New York: Springer, 1994
6	ElliottR J, MamonR S. An interest rate model with a Markovian mean-reverting level.Quant Finance, 2002, 2(6): 454–458 https://doi.org/10.1080/14697688.2002.0000012
7	ElliottR J, SiuT K. On Markov-modulated exponential-affine bond price formulae.Appl Math Finance, 2009, 16(1): 1–15 https://doi.org/10.1080/13504860802015744
8	ElliottR J, SiuT K, BadescuA. Bond valuation under a discrete-time regime-switching term-structure model and its continuous-time extension.Managerial Finance, 2011, 37(11): 1025–1047 https://doi.org/10.1108/03074351111167929
9	ElliottR J, WilsonC A. The term structure of interest rates in a hidden Markov setting.In: Mamon R S, Elliott R J, eds. Hidden Markov Models in Finance. New York: Springer, 2007, 15–30 https://doi.org/10.1007/0-387-71163-5_2
10	FanK, ShenY, SiuT K, WangR. An FFT approach for option pricing under a regimeswitching stochastic interest rate model.Comm Statist Theory Methods, 2017, 46(11): 5292–5310 https://doi.org/10.1080/03610926.2015.1100740
11	HamiltonJ D. A new approach to the economic analysis of nonstationary time series and the business cycle.Econometrica, 1989, 57: 357–384 https://doi.org/10.2307/1912559
12	HullJ, WhiteA. Pricing interest-rate derivative securities.Rev Financial Studies, 1990, 3(4): 573–592 https://doi.org/10.1093/rfs/3.4.573
13	KwokY K, LeungK S, WongH Y. Efficient option pricing using the fast Fo urier transform.In: Duan J C, Härdle W K, Gentle J E, eds. Handbook of Computational Finance. Berlin: Springer-Verlag, 2012, 579–604 https://doi.org/10.1007/978-3-642-17254-0_21
14	LiuR H, ZhangQ, YinG. Option pricing in a regime-switching model using the fast Fourier transform.Int J Stoch Anal, 2006, Article ID: 18109 https://doi.org/10.1155/JAMSA/2006/18109
15	PalmowskiZ, RolskiT. A technique for exponential change of measure for Markov processes.Bernoulli, 2002, 8: 767–785
16	RolskiT, SchmidliH, SchmidliV, TeugelsJ L. Stochastic Processes for Insurance and Finance.New York: Wiley, 1999 https://doi.org/10.1002/9780470317044
17	ShenY, SiuT K. Pricing bond options under a Markovian regime-switching Hull-White model.Economic Modelling, 2013, 30: 933–940 https://doi.org/10.1016/j.econmod.2012.09.041
18	ShenY, SiuT K. Pricing variance swaps under a stochastic interest rate and volatility model with regime-switching.Oper Res Lett, 2013, 41: 180–187 https://doi.org/10.1016/j.orl.2012.12.008
19	SiuT K. Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic flows.Appl Math Comput, 2010, 216: 3184–3190 https://doi.org/10.1016/j.amc.2010.04.037
20	VasicekO. An equilibrium characterization of the term structure.J Financial Economics, 1977, 5: 177–188 https://doi.org/10.1016/0304-405X(77)90016-2
21	ZhangS, WangL. A fast Fourier transform technique for pricing European options with stochastic volaility and jump risk.Math Probl Eng, 2012, Article ID: 761637

[1]	Jie GUO, Guojing WANG. A reduced-form model with default intensities containing contagion and regime-switching Vasicek processes[J]. Front. Math. China, 2018, 13(3): 535-554.
[2]	Yinghui DONG, Kam Chuen YUEN, Guojing WANG. Valuation of CDS counterparty risk under a reduced-form model with regime-switching shot noise default intensities[J]. Front. Math. China, 2017, 12(5): 1085-1112.
[3]	Yinghui DONG, Guojing WANG. A contagion model with Markov regime-switching intensities[J]. Front Math Chin, 2014, 9(1): 45-62.

Viewed

Full text

Abstract

Cited

Shared

Discussed