An Option Pricing Model with Memory
Pricing of Securities
2020-11-17 v1
Abstract
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential equation. A model with full memory is obtained via approximation through a stock price model in which the continuous path dependence does not go up to the present: there is a memory gap. A strong solution is obtained by closing the gap. Fair option prices are obtained through an equivalent (local) martingale measure via Girsanov's Theorem and therefore are given in terms of a conditional expectation. The models maintain the completeness of the market and have no arbitrage opportunities.
Keywords
Cite
@article{arxiv.1709.00468,
title = {An Option Pricing Model with Memory},
author = {Flavia Sancier and Salah Mohammed},
journal= {arXiv preprint arXiv:1709.00468},
year = {2020}
}