A note on stochastic polynomial chaos expansions for uncertain volatility and Asian option pricing

2021 ◽  
Vol 393 ◽  
pp. 125764
Author(s):  
Y.-T. Lin ◽  
Y.-T. Shih ◽  
C.-S. Chien ◽  
Q. Sheng
Keyword(s):  
Option Pricing ◽  
Polynomial Chaos ◽  
Asian Option ◽  
Uncertain Volatility ◽  
Polynomial Chaos Expansions

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

Modeling of Stochastic EMC Problems with Anisotropic Polynomial Chaos Expansions

2021 ◽  
Vol 10 (2) ◽  
pp. 70-79
Author(s):  
Theodoros Zygiridis ◽  
Georgios Kommatas ◽  
Aristeides Papadopoulos ◽  
Nikolaos Kantartzis
Keyword(s):  
Polynomial Chaos ◽  
Polynomial Chaos Expansions

scholarly journals mumpce_py: A Python Implementation of the Method of Uncertainty Minimization Using Polynomial Chaos Expansions

2017 ◽  
Vol 122 ◽  
Author(s):  
David A. Sheen
Keyword(s):  
Measurement Uncertainty ◽  
First Principles ◽  
Polynomial Chaos ◽  
Software Tool ◽  
Physical Models ◽  
Physical Parameters ◽  
Experimental Measurements ◽  
Uncertainty Minimization ◽  
Polynomial Chaos Expansions ◽  
Parameter Values

The Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) was developed as a software tool to constrain physical models against experimental measurements. These models contain parameters that cannot be easily determined from first principles and so must be measured, and some which cannot even be easily measured. In such cases, the models are validated and tuned against a set of global experiments which may depend on the underlying physical parameters in a complex way. The measurement uncertainty will affect the uncertainty in the parameter values.

scholarly journals The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 780-785 ◽  
Author(s):  
Sunday O. Edeki ◽  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Grace O. Akinlabi
Keyword(s):  
Analytical Solution ◽  
Option Pricing ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Asian Option ◽  
Pricing Model ◽  
Adomian Decomposition ◽  
Option Pricing Model ◽  
Option Model ◽  
High Level

Abstract The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

A Polynomial Chaos Method for Dispersive Electromagnetics

2015 ◽  
Vol 18 (5) ◽  
pp. 1234-1263 ◽  
Author(s):  
Nathan L. Gibson
Keyword(s):  
Polynomial Chaos ◽  
Fdtd Method ◽  
Debye Model ◽  
Dispersive Media ◽  
Dielectric Parameters ◽  
Polarization Model ◽  
Computational Framework ◽  
Spatial Dimensions ◽  
Yee Scheme ◽  
Polynomial Chaos Expansions

AbstractElectromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell's equations coupled to equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a novel computational framework for such problems involving Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Debye model and allow for easy simulation using the Finite Difference Time Domain (FDTD) method. Stability and dispersion analyzes are performed for the approach utilizing the second order Yee scheme in two spatial dimensions.

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