Paper Info
Title
Option pricing impact of alternative continuous-time dynamics for discretely-observed stock prices
Abstract
.   In the present paper we construct stock-price processes with the same marginal lognormal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes differ from Black and Scholes', in that option prices can assume any value in-between the no-arbitrage lower and upper bounds. We also explain that this is due to the particular way one models the stock-price process in between the grid time instants that are relevant for trading. The findings of the paper are inspired by a theoretical result, linking density-evolution of diffusion processes to exponential families. Such result is briefly reviewed in an appendix.
Year
DOI
Venue
2000
10.1007/s007800050009
Finance and Stochastics
Keywords
Field
DocType
black and scholes model,discrete time versus continuous time,option pricing,discrete -volatility,stock-price dynamics,discrete time,exponential family,geometric brownian motion,diffusion process
Economics,Mathematical economics,Financial economics,Valuation of options,Transition density,Log-normal distribution,Grid,Geometric Brownian motion
Journal
Volume
Issue
Citations 
4
2
1
PageRank 
References 
Authors
0.35
2
2
Name
Order
Citations
PageRank
Damiano Brigo1178.42
Fabio Mercurio2113.77