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23 pages, 867 KB

Open AccessArticle

Bachelier’s Market Model for ESG Asset Pricing

by Svetlozar Rachev, Nancy Asare Nyarko, Blessing Omotade and Peter Yegon

J. Risk Financial Manag. 2024, 17(12), 553; https://doi.org/10.3390/jrfm17120553 - 10 Dec 2024

Cited by 2 | Viewed by 2362

Environmental, Social, and Governance (ESG) finance is a cornerstone of modern finance and investment, as it changes the classical return-risk view of investment by incorporating an additional dimension to investment performance: the ESG score of the investment. We define the ESG price process [...] Read more.

(This article belongs to the Section Economics and Finance)

39 pages, 1044 KB

Open AccessEditor’s ChoiceArticle

Option Pricing under a Generalized Black–Scholes Model with Stochastic Interest Rates, Stochastic Strings, and Lévy Jumps

by Alberto Bueno-Guerrero and Steven P. Clark

Mathematics 2024, 12(1), 82; https://doi.org/10.3390/math12010082 - 26 Dec 2023

Viewed by 5449

Abstract

We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes. Full article

(This article belongs to the Special Issue Financial Mathematics and Applications)

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13 pages, 710 KB

Open AccessArticle

Derivation of the Fractional Fokker–Planck Equation for Stable Lévy with Financial Applications

by Reem Abdullah Aljethi and Adem Kılıçman

Mathematics 2023, 11(5), 1102; https://doi.org/10.3390/math11051102 - 22 Feb 2023

Cited by 2 | Viewed by 2787

Abstract

This paper aims to propose a generalized fractional Fokker–Planck equation based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion. Due to the Lévy process, this fractional equation can provide a better description of heavy tails and skewness. The analytical solution is chosen to solve the fractional equation and is expressed using the H-function to demonstrate the indicator entropy production rate. We model market data using a stable distribution to demonstrate the relationships between the tails and the new fractional Fokker–Planck model, as well as develop an R code that can be used to draw figures from real data. Full article

(This article belongs to the Special Issue Advanced Research in Mathematical Economics and Financial Modelling)

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21 pages, 364 KB

Open AccessFeature PaperArticle

A Measure-on-Graph-Valued Diffusion: A Particle System with Collisions and Its Applications

by Shuhei Mano

Mathematics 2022, 10(21), 4081; https://doi.org/10.3390/math10214081 - 2 Nov 2022

Cited by 1 | Viewed by 2227

Abstract

A diffusion-taking value in probability-measures on a graph with vertex set V,

\sum_{i \in V} x_{i} δ_{i}

is studied. The masses on each vertex satisfy the stochastic differential equation of the form [...] Read more.

A diffusion-taking value in probability-measures on a graph with vertex set V,

\sum_{i \in V} x_{i} δ_{i}

is studied. The masses on each vertex satisfy the stochastic differential equation of the form

d x_{i} = \sum_{j \in N (i)} \sqrt{x_{i} x_{j}} d B_{i j}

on the simplex, where

{B_{i j}}

are independent standard Brownian motions with skew symmetry, and

N (i)

is the neighbour of the vertex i. A dual Markov chain on integer partitions to the Markov semigroup associated with the diffusion is used to show that the support of an extremal stationary state of the adjoint semigroup is an independent set of the graph. We also investigate the diffusion with a linear drift, which gives a killing of the dual Markov chain on a finite integer lattice. The Markov chain is used to study the unique stationary state of the diffusion, which generalizes the Dirichlet distribution. Two applications of the diffusions are discussed: analysis of an algorithm to find an independent set of a graph, and a Bayesian graph selection based on computation of probability of a sample by using coupling from the past. Full article

(This article belongs to the Special Issue Random Combinatorial Structures)

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