skip to main content

SciTech ConnectSciTech Connect

Title: Financial derivative pricing under probability operator via Esscher transfomation

The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing{sup 9} where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula using the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φ{sub x}(u) of X{sub t} we recuperate the Black-Scholes formula for financial derivative prices.
Authors:
 [1]
  1. Department of Mathematics, Abia State Polytechnic Aba, P.M.B. 7166, Aba, Abia State (Nigeria)
Publication Date:
OSTI Identifier:
22308884
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1621; Journal Issue: 1; Conference: ICSAS 2014: 3. international conference on fundamental and applied sciences: Innovative research in applied sciences for a sustainable future, Kuala Lumpur (Malaysia), 3-5 Jun 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BROWNIAN MOVEMENT; COMPARATIVE EVALUATIONS; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; PROBABILITY; STOCHASTIC PROCESSES; TRANSFORMATIONS