On the Minimal Entropy Martingale Measure and Multinomial Lattices with Cumulants

Ssebugenyi, Cyrus Seera; Mwaniki, Ivivi Joseph; Konlack, Virginie S.

doi:10.1080/1350486x.2012.714226

Cited by 6 publications

(4 citation statements)

References 16 publications

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“…• VG PIDE : We solve the VG PIDE following the method proposed by [9]. The Lévy measure is singular in the origin and this is a problem for the computation of the integral term in (24). Fixing a truncation parameter > 0, we approximate the infinite activity martingale jump component with sizes smaller than , with a Brownian motion with same variance.…”

Section: European Optionsmentioning

confidence: 99%

See 1 more Smart Citation

Multinomial method for option pricing under Variance Gamma

Cantarutti,

Guerra

2017

Preprint

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This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a continuous time process with the same first four cumulants, and then discretized in time and space. This approach is particularly convenient for pricing American and Bermudan options, which can be exercised before the expiration date. Numerical computations of European and American options are presented, and compared with results obtained with finite differences methods and with the Black-Scholes prices.

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Section: European Optionsmentioning

confidence: 99%

“…In [16] the authors consider a multinomial method for general exponential Lévy processes based on the moment matching condition. Other methods based on the moment matching condition are for instance [14], with applications to the Normal Inverse Gaussian process, and [24] with applications to the VG process.…”

Section: Introductionmentioning

confidence: 99%

Multinomial method for option pricing under Variance Gamma

Cantarutti,

Guerra

2017

Preprint

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“…The computation of MDMMs in discrete time models has been considered by several authors: Gzyl [17] and Ssebugenyi [31] considered the case of the MEMP, while Grandits [16] and Arai and Kawaguchi [2] considered p-optimal martingale measures. We begin by introducing some standard notations.…”

Section: Multiperiod Extensionmentioning

confidence: 99%

Convex Comparison of Minimal Divergence Martingale Measures in Discrete Time Models

Bellini

2012

SSRN Journal

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“…This measure is used by many authors for option pricing (see El Karoui and Rouge, 2000;Frittelli, 2000). The relation of the MEMM to market efficiency and maximisation of exponential utility makes the measure economically meaningful (see Ssebugenyi, 2011). As we have mentioned above, we use fuzzy set theory and fuzzy arithmetic (see Zadeh, 1965).…”

Section: Introductionmentioning

confidence: 99%

A fuzzy approach to option pricing in a Levy process setting

Nowak¹,

Romaniuk²

2013

International Journal of Applied Mathematics and Computer Science

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In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.

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On the Minimal Entropy Martingale Measure and Multinomial Lattices with Cumulants

Cited by 6 publications

References 16 publications

Multinomial method for option pricing under Variance Gamma

Multinomial method for option pricing under Variance Gamma

Convex Comparison of Minimal Divergence Martingale Measures in Discrete Time Models

A fuzzy approach to option pricing in a Levy process setting

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