Pricing rule based on non-arbitrage arguments for random volatility and volatility smile
Probability
2008-12-02 v1 Optimization and Control
Pricing of Securities
Abstract
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that gives Black-Scholes price for at-money options and such that the market is arbitrage free for any number of tradable options, even if there are two Brownian motions only: one drives the stock price, the other drives the volatility process. This problem is reduced to solving a parabolic equation.
Keywords
Cite
@article{arxiv.math/0205120,
title = {Pricing rule based on non-arbitrage arguments for random volatility and volatility smile},
author = {Nikolai Dokuchaev},
journal= {arXiv preprint arXiv:math/0205120},
year = {2008}
}
Comments
18 pages