Importance Sampling for Monte Carlo Simulation to Evaluate Collar Options under Stochastic Volatility Model

Simple item page
dc.contributor.authorLi, Pengshi
dc.contributor.authorLi, Wei
dc.contributor.authorChen, Haidong
dc.contributor.otherEkonomická fakultacs
dc.date.accessioned2020-06-04T08:31:47Z
dc.date.available2020-06-04T08:31:47Z
dc.description.abstractThe collar option is one kind of exotic options which is useful when institutional investors wish to lock in the profi t they already have on the underlying asset. Under the constant volatility assumption, the pricing problem of collar options can be solved in the classical Black Scholes framework. However the smile-shaped pattern of the Black Scholes implied volatilities which extracted from options has provided evidence against the constant volatility assumption, so stochastic volatility model is introduced. Because of the complexity of the stochastic volatility model, a closed-form expression for the price of collar options may not be available. In such case, a suitable numerical method is needed for option pricing under stochastic volatility. Since the dimensions of state variable are usually more than two after the introduction of another volatility diffusion process, the classical fi nite difference method seems ineffi cient in the stochastic volatility scenario. For its easy and fl exible computation, Monte Carlo method is suitable for evaluating option under stochastic volatility. This paper presents a variance reduction method for Monte Carlo computation to estimate collar option under stochastic volatility model. The approximated price of the collar option under fast mean reverting stochastic volatility model is derived from the partial differential equation by singular perturbation technique. The importance sampling method based on the approximation price is used to reduce the variance of the Monte Carlo simulation. Numerical experiments are carried out under the context of different mean reverting rate. Numerical experiment results demonstrate that the importance sampling Monte Carlo simulation achieves better variance reduction effi ciency than the basic Monte Carlo simulation.en
dc.formattext
dc.identifier.doi10.15240/tul/001/2020-2-010
dc.identifier.eissn2336-5604
dc.identifier.issn1212-3609
dc.identifier.urihttps://dspace.tul.cz/handle/15240/154924
dc.language.isoen
dc.publisherTechnická Univerzita v Libercics
dc.publisherTechnical university of Liberec, Czech Republicen
dc.publisher.abbreviationTUL
dc.relation.isbasedonAgarwal, A., Juneja, S., & Sircar, R. (2016). American options under stochastic volatility. Quantitative Finance, 16(1), 17–30. https://doi. org/10.1080/14697688.2015.1068443
dc.relation.isbasedonBates, D. (1991). The Crash of 87: Was it expected? The evidence from option markets. The Journal of Finance, 46(3), 1009–1044. https://doi.org/10.1111/j.1540-6261.1991. tb03775.x
dc.relation.isbasedonBoyle, P. (1977). Option: A Monte Carlo approach. Journal of Financial Economics, 4(3), 323–338. https://doi.org/10.1016/0304- 405X(77)90005-8
dc.relation.isbasedonBroadie, M., & Glasserman, P. (1996). Estimating Security Price Derivatives Using Simulation. Management Science, 42(2), 269–285. http://dx.doi.org/10.1287/mnsc.42.2.269
dc.relation.isbasedonDu, K., Liu, G., & Gu, G. (2013). A class of control variates for pricing Asian options under stochastic volatility models. IAENG International Journal of Applied Mathematics, 42(2), 45–53.
dc.relation.isbasedonFouque, J. P., & Han, C. H. (2004). Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models. Quantitative Finance, 4(5), 597–606. http://dx.doi. org/10.1080/14697680400000041
dc.relation.isbasedonFouque, J. P., & Han, C. H. (2007). A martingale control variate method for option pricing with stochastic volatility. ESAIM: Probability and Statistics, 11, 40–54. http://dx.doi.org/10.1051/ps:2007005
dc.relation.isbasedonFouque, J. P., & Han, C. H. (2007). A martingale control variate method for option pricing with stochastic volatility. ESAIM: Probability and Statistics, 11, 40–54. http://dx.doi.org/10.1051/ps:2007005
dc.relation.isbasedonFouque, J. P., Papanicolaou, G., & Sircar, R. (2000). Mean-reverting stochastic volatility. International Journal of Theoretical and Applied Finance, 3(1), 101–142. http://dx.doi. org/10.1142/S0219024900000061
dc.relation.isbasedonFouque, J. P., Papanicolaou, G., Sircar, R., & Solna, K. (2003). Singular perturbations in option pricing. SIAM Journal on Applied Mathematics, 63(5), 1648–1665. http://dx.doi. org/10.1137/S0036139902401550
dc.relation.isbasedonFu, M. C., Laprise, S. B., Madan, D. B., Su. Y., & Wu, R. W. (2001). Pricing American options: a comparison of Monte Carlo simulation approaches. The Journal of Computational Finance, 4(3), 39–88. http://dx.doi.org/10.21314/JCF.2001.066
dc.relation.isbasedonGiles, M. (2008). Multilevel Monte Carlo path simulation. Operations Research, 56(3), 607– 617. http://dx.doi.org/10.1287/opre.1070.0496
dc.relation.isbasedonGlasserman, P., Heidelberger, P., & Shahabuddin, P. (1999). Asymptotically optimal importance sampling and Stratifi cation for Pricing Path-Dependent Options. Mathematical Finance, 9(2), 117–152. http://dx.doi. org/10.1111/1467-9965.00065
dc.relation.isbasedonHeston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6(2), 327–343. http://dx.doi.org/10.1093/rfs/6.2.327
dc.relation.isbasedonHull, J. C., & White, A. (1987). The pricing of options on assets with stochastic volatilities. The Journal of Finance, 42(2), 281–300. https://doi.org/10.1111/j.1540-6261.1987.tb02568.x
dc.relation.isbasedonKassim, K. B., Lelong, J., & Loumrhari, I. (2015). Importance Sampling for Jump Processes and Applications to Finance. The Journal of Computational Finance, 19(2), 109–139. http://dx.doi.org/10.21314/JCF.2015.292
dc.relation.isbasedonLai, Y. Z., Li, Z. F., & Zeng, Y. (2015). Control variate methods and applications to Asian and Basket options under jump-diffusion models. IMA Journal of Management Mathematics, 26(1), 11–37. http://dx.doi.org/10.1093/imaman/dpt016
dc.relation.isbasedonLiang, S., Garvin, M. J., & Kumar, R. (2010). Collar options to manage revenue risks in real toll public-private partnership transportation projects. Construction Management and Economics, 28(10), 1057–1069. https://doi.org /10.1080/01446193.2010.506645
dc.relation.isbasedonLiu, Q. (2010). Pricing American options by canonical least-square Monte Carlo. Journal of Futures Markets, 30(2), 175–187. http://dx.doi. org/10.1002/fut.20409
dc.relation.isbasedonLongstaff, F., & Schwartz, E. (2001). Valuing American Options by Simulation: A Simple Least-Squares Approach. Review of Financial Studies, 14(1), 113–147. http://dx.doi. org/10.1093/rfs/14.1.113
dc.relation.isbasedonMa, J. M., & Xu, C. L. (2010). An effi cient control variate method for pricing variance derivatives. Journal of Computational and Applied Mathematics, 235(1), 108–119. http://dx.doi.org/10.1016/j.cam.2010.05.017
dc.relation.isbasedonRogers, L. C. G. (2002). Monte Carlo valuation of American options. Mathematical Finance, 12(3), 271–286. http://doi. org/10.1111/1467-9965.02010
dc.relation.isbasedonScott, L. O. (1987). Option pricing when the variance changes randomly: theory, estimation and an application. Journal of Financial and Quantitative Analysis, 22, 419–438. http://dx.doi.org/10.2307/2330793
dc.relation.isbasedonStein, E. M., & Stein, J. C. (1991). Stock price distribution with stochastic volatility: an analytic approach. Review of Financial Studies, 4(4), 727–752. https://doi.org/10.1093/ rfs/4.4.727
dc.relation.isbasedonSu, Y., & Fu, M. C. (2000). Importance sampling in derivative securities pricing. 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165). http://dx.doi. org/10.1109/WSC.2000.899767
dc.relation.ispartofEkonomie a Managementcs
dc.relation.ispartofEconomics and Managementen
dc.relation.isrefereedtrue
dc.rightsCC BY-NC
dc.subjectimportance samplingen
dc.subjectMonte Carlo simulationen
dc.subjectcollar optionsen
dc.subjectstochastic volatilityen
dc.subject.classificationC40
dc.titleImportance Sampling for Monte Carlo Simulation to Evaluate Collar Options under Stochastic Volatility Modelen
dc.typeArticleen
local.accessopen
local.citation.epage155
local.citation.spage144
local.facultyFaculty of Economics
local.filenameEM_2_2020_10
local.fulltextyes
local.relation.abbreviationE+Mcs
local.relation.abbreviationE&Men
local.relation.issue2
local.relation.volume23
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
EM_2_2020_10.pdf
Size:
1011.57 KB
Format:
Adobe Portable Document Format
Description:
článek
Download
Collections
Číslo 2