Accession Number : AD1015370

Title :   Option Pricing with a Levy-Type Stochastic Dynamic Model for Stock Price Process Under Semi-Markovian Structural Perturbations

Descriptive Note : Journal Article

Corporate Author : University of South Florida Tampa United States

Personal Author(s) : Assonken,Patrick ; Ladde,G S

Full Text :

Report Date : 30 Nov 2015

Pagination or Media Count : 75

Abstract : In this work, we consider a stock price process subjected to idiosyncratic Levy jumps andglobal structural changes attributed to interventions due to a semi-Markov process. Thesemi-Markov process decomposes both the time and state domains of the price processinto sub-intervals and price state sub-domains respectively, where a LevyIto processoperates. The Levy jumps decompose the space domain of the currently operating Levyprocess. We derive an infinitesimal generator for a stock price process and a closed formexpression for the conditional characteristic function of a log price. The former resultis used to derive a PIDE satisfied by option prices, while the latter could be used toretrieve risk neutral densities via Fourier transform and price European vanilla options.In the sequel, we derive the characteristic function of the residence time of a semi-Markovprocess. Incompleteness of the market is exhibited through a general change of measure.For pricing purpose, the minimum entropy martingale measure is defined as an Esschertransform.

Descriptors :   markov processes , calibration , costs , finance , stochastic processes , perturbations

Subject Categories : Statistics and Probability
      Economics and Cost Analysis

Distribution Statement : APPROVED FOR PUBLIC RELEASE