Stochastic Dominance and Option Pricing in Discrete and Continuous Time: An Alternative Paradigm

48 Pages Posted: 18 Mar 2006

See all articles by Ioan Mihai Oancea

Ioan Mihai Oancea

Concordia University, Quebec - John Molson School of Business

Stylianos Perrakis

Concordia University, Quebec - John Molson School of Business

Date Written: September 2007

Abstract

This paper examines option pricing in a universe in which it is assumed that markets are incomplete. It derives multiperiod discrete time option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution, discrete or continuous. It then considers the limit behavior of these bounds for special categories of such distributions as trading becomes progressively more dense, tending to continuous time. It is shown that these bounds nest as special cases most, if not all, existing arbitrage- and equilibrium-based option pricing models. Thus, when the underlying asset follows a generalized diffusion both bounds converge to a single value. For jump-diffusion processes, stochastic volatility models, and GARCH processes the bounds remain distinct and define several new option pricing results containing as special cases the arbitrage-based results.

Keywords: Option pricing, option bounds, incomplete markets, jump-diffusion processes, stochastic volatility, GARCH processes

Suggested Citation

Oancea, Ioan Mihai and Perrakis, Stylianos, Stochastic Dominance and Option Pricing in Discrete and Continuous Time: An Alternative Paradigm (September 2007). Available at SSRN: https://ssrn.com/abstract=891490 or http://dx.doi.org/10.2139/ssrn.891490

Ioan Mihai Oancea (Contact Author)

Concordia University, Quebec - John Molson School of Business ( email )

1455 de Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada
(514) 848-2424 (Phone)
(514) 848-4500 (Fax)

Stylianos Perrakis

Concordia University, Quebec - John Molson School of Business ( email )

1455 de Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada

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