The Evaluation of Discrete Barrier Options in a Path Integral Framework

ANALYTICAL PATH-INTEGRAL PRICING OF DETERMINISTIC MOVING-BARRIER OPTIONS UNDER NON-GAUSSIAN DISTRIBUTIONS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024920500053 ◽

2020 ◽

Vol 23 (01) ◽

pp. 2050005

Author(s):

ANDRÉ CATALÃO ◽

ROGÉRIO ROSENFELD

Keyword(s):

Path Integral ◽

First Passage Time ◽

Passage Time ◽

Barrier Options ◽

Barrier Option ◽

Entropy Model ◽

Gaussian Distributions ◽

Pricing Options ◽

Barrier Option Pricing ◽

Non Gaussian

In this work, we present an analytical model, based on the path-integral formalism of statistical mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possibly non-Gaussian distributions of the underlying object. We adapt to our problem a model originally proposed by De Simone et al. (2011) to describe the formation of galaxies in the universe, which uses cumulant expansions in terms of the Gaussian distribution, and we generalize it to take into account drift and cumulants of orders higher than three. From the probability density function, we obtain an analytical pricing model, not only for vanilla options (thus removing the need of volatility smile inherent to the Black & Scholes (1973) model), but also for fixed or deterministically moving barrier options. Market prices of vanilla options are used to calibrate the model, and barrier option pricing arising from the model is compared to the price resulted from the relative entropy model.

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Hydrogen adsorption on graphite and in carbon slit pores from path integral simulations

Molecular Physics ◽

10.1080/002689798167223 ◽

1998 ◽

Vol 95 (2) ◽

pp. 299-309 ◽

Cited By ~ 5

Author(s):

QINYU WANG J. KARL JOHNSON

Keyword(s):

Path Integral ◽

Hydrogen Adsorption ◽

Slit Pores ◽

Carbon Slit Pores

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Path integral analysis of paraxial radiowave propagation over a cliff edge

IEE Proceedings H Microwaves Antennas and Propagation ◽

10.1049/ip-h-2.1992.0014 ◽

1992 ◽

Vol 139 (1) ◽

pp. 84 ◽

Cited By ~ 1

Author(s):

D.E. Eliades

Keyword(s):

Path Integral ◽

Radiowave Propagation ◽

Integral Analysis

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Vapour Pressure Isotope Eﬀect on Evaporation from Pure Organic Phases - a PIMD Approach

10.26434/chemrxiv.12003186.v1 ◽

2020 ◽

Author(s):

Luis Vasquez ◽

Agnieszka Dybala-Defratyka

Keyword(s):

Path Integral ◽

Vapour Pressure ◽

Density Functional ◽

Isotope Effects ◽

Tight Binding ◽

Decomposition Analysis ◽

Energy Decomposition Analysis ◽

Special Importance ◽

Non Covalent Interactions ◽

Covalent Interactions

Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods. In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations. Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.

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