Closed Form Pricing of European Options for a Family of Normal-Inverse Gaussian Processes

Иванов, Р. В.

doi:10.1080/15326349.2013.838509

Cited by 13 publications

(8 citation statements)

References 13 publications

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“…Combining together ( 16) and (17), one can obtain the result of Theorem 1 from Ivanov and Ano [20]. Now we will consider the case when the indicator stock S 1 t and the exchange rate S 3 t are strongly dependent but the underlying asset S 2 t is weakly dependent on them.…”

Section: Gamma Time Changementioning

confidence: 91%

“…In particular, it can be shown that this method cannot be applied to the pricing of digital options in the volatile variance-gamma model or in the normalinverse Gaussian one. The method of closed form solutions which had been introduced by Madan et al [33] was proceeded then in the papers by Ivanov and Ano [20], Ivanov [18] and Ivanov [19] for the variance-gamma distribution and by Ivanov [17] and Ivanov and Temnov [21] for the normal-inverse Gaussian one. This paper continues the elements of the research by Madan et al [33].…”

Section: Introductionmentioning

confidence: 99%

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Option pricing in time-changed Lévy models with compound Poisson jumps

Иванов¹,

Ano²

2018

Modern Stochastics: Theory and Applications

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The problem of European-style option pricing in time-changed Lévy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the time-changed Lévy models, the variance-gamma and the normal-inverse Gaussian models are discussed. Exact formulas are given for the price of digital asset-or-nothing call option on extra asset in foreign currency. The prices of simpler options can be derived as corollaries of our results and examples are presented. Various types of dependencies between stock prices are mentioned.

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Section: Gamma Time Changementioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Option pricing in time-changed Lévy models with compound Poisson jumps

Иванов¹,

Ano²

2018

Modern Stochastics: Theory and Applications

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“…The success of Fourier transform methods is strongly linked to the relative simplicity of the characteristic function of most exponential Lévy models, and has opened the way to a wide range of other transform based approaches: they include, among others, the COS method by Fang & Osterlee (2008), the Hilbert transform method (see notably a recent application to time-changed Lévy processes in Zeng and Kwok (2014)) or the local basis Frame PROJection (PROJ) method by Kirkby (2015). Efforts have also been made towards analytic evaluation or approximations: in Ivanov (2013), a closed-form formula (in terms of Appel functions) for the European call is derived in the particular case where the NIG distribution has a tail parameter of 1/2, and in Albrecher & Predota (2004) approximations and bounds are provided for Asian options.…”

Section: Introductionmentioning

confidence: 99%

Explicit option valuation in the exponential NIG model

Aguilar¹

2020

Preprint

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We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential Lévy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and take the form of simple and quickly convergent series, under some condition involving the log-forward moneyness and the maturity of instruments. Proofs are based on a factorized representation in the Mellin space for the price of an arbitrary path-independent payoff, and on tools from complex analysis. The validity of the results is assessed thanks to several comparisons with standard numerical methods (Fourier-related inversion, Monte-Carlo simulations) for realistic sets of parameters. Precise bounds for the convergence speed and the truncation error are also provided.

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“…For methods of the numerical calculation of the distributions of the extrema of time-changed Brownian motions, see the paper [7]. However, some explicit results on the NIG process are available: in optimal stopping, see the work [8], and in option pricing, see the paper [9].…”

Section: Introductionmentioning

confidence: 99%

On the exact distribution of the maximum of the exponential of the generalized normal-inverse Gaussian process with respect to a martingale measure

Иванов¹

2013

COSA

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In this paper we obtain explicit formulas for distributions of extrema of exponentials of time-changed Brownian motions with drift which generalize normal inverse Gaussian processes. The generalization is made by multiplying the normal inverse Gaussian process by a constant. The results are established with respect to the equivalent martingale measure. As examples of applications, problems of path-dependent option pricing are discussed.

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Closed Form Pricing of European Options for a Family of Normal-Inverse Gaussian Processes

Cited by 13 publications

References 13 publications

Option pricing in time-changed Lévy models with compound Poisson jumps

Option pricing in time-changed Lévy models with compound Poisson jumps

Explicit option valuation in the exponential NIG model

On the exact distribution of the maximum of the exponential of the generalized normal-inverse Gaussian process with respect to a martingale measure

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