Dynamic option pricing with endogenous stochastic arbitrage
Contreras
M
author
Montalva
R
author
Pellicer
R
author
Villena
M
author
2010
English
Only few efforts have been made in order to relax one of the key assumptions of the Black-Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called "arbitrage bubble", based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B-S model to that new trajectory even when the arbitrage already started. (C) 2010 Elsevier B.V. All rights reserved.
Black-Scholes model
Arbitrage
Option pricing
WOS:000280118100023
exported from refbase (show.php?record=91), last updated on Thu, 12 Aug 2010 22:47:29 -0400
text
files/91_Contreras_etal2010.pdf
10.1016/j.physa.2010.04.019
Contreras_etal2010
Physica A-Statistical Mechanics And Its Applications
Physica A
2010
Elsevier Science Bv
continuing
periodical
academic journal
389
17
3552
3564
0378-4371