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Submitted to the Journal of Computational Intelligence in Finance (8/4/99) FOLLOWING THE BAYES PATH TO OPTION PRICING
 

Summary: Submitted to the Journal of Computational Intelligence in Finance (8/4/99)
1
FOLLOWING THE BAYES PATH TO OPTION PRICING
MARCO AVELLANEDA, ANDREA CARELLI AND FABIO STELLA
Conventional modeling techniques for option pricing have systematic biases resulting from the assumption of
constant volatility (homoskedasticity) for the price of the underlying asset. Nevertheless, practitioners seldom
use stochastic volatility models since the latter require making unverifiable assumptions about the price process.
A different approach consists of ``letting the data speak for itself'', i.e. to make a few general assumptions about
the process to be modeled, and to exploit the information available from the prices of traded options. In this
paper we develop of a non-parametric model for specifying the volatility of the underlying asset based on
Feedforward Neural Networks and a Bayesian learning approach. We then develop of an option-pricing model
based on this volatility specification. Numerical experiments are presented for the case of the USD/DEM
options, accompanied by a graphical analysis of the resulting smiles.
1. INTRODUCTION
Options are some of the most important financial instruments traded in the markets today. The technical aspects of option-
pricing theory and practice have attracted the attention of mathematicians, statisticians, physicists and computer scientists.
According to Rubinstein [1985] and Eales et al. [1990], the celebrated Black & Scholes option-pricing formula has
systematic and persistent biases. These biases depend upon both the "time to maturity" and the "option moneyness ratio"
which is the relationship between the spot and the strike price. Among several plausible reasons accounting for these biases is
the one introduced in Hull and White [1987] where the conventional models bias is shown to be consistent with the theory of

  

Source: Avellaneda, Marco - Department of Mathematics, Courant Institute of Mathematical Sciences, New York University

 

Collections: Mathematics