Importance sampling for monte carlo simulation to evaluate collar options under stochastic volatility model

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dc.contributor.authorLi, Pengshi
dc.contributor.authorLi, Wei
dc.contributor.authorChen, Haidong
dc.date.accessioned2020-06-17T06:19:57Z
dc.date.available2020-06-17T06:19:57Z
dc.date.issued2020
dc.description.abstract-translatedThe collar option is one kind of exotic options which is useful when institutional investors wish to lock in the profit 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 finite difference method seems inefficient in the stochastic volatility scenario. For its easy and flexible 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 efficiency than the basic Monte Carlo simulation.en
dc.format12 s.cs
dc.format.mimetypeapplication/pdf
dc.identifier.citationE+M. Ekonomie a Management = Economics and Management. 2020, roč. 23, č. 2, s. 144-155.cs
dc.identifier.doihttps://doi.org/10.15240/tul/001/2020-2-010
dc.identifier.issn2336-5604 (Online)
dc.identifier.issn1212-3609 (Print)
dc.identifier.urihttp://hdl.handle.net/11025/36975
dc.language.isoenen
dc.publisherTechnická univerzita v Libercics
dc.rightsCC BY-NC 4.0cs
dc.rights.accessopenAccessen
dc.subjectvzorkování důležitostics
dc.subjectsimulace Monte Carlocs
dc.subjectlímec možnostics
dc.subjectstochastická volatilitacs
dc.subject.translatedimportance samplingen
dc.subject.translatedMonte Carlo simulationen
dc.subject.translatedcollar optionsen
dc.subject.translatedstochastic volatilityen
dc.titleImportance sampling for monte carlo simulation to evaluate collar options under stochastic volatility modelen
dc.typečlánekcs
dc.typearticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen

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