Option pricing impact of alternative continuous-time dynamics for discretely-observed stock prices

Damiano Brigo and Fabio Mercurio ()

Finance and Stochastics, 2000, vol. 4, issue 2, 147-159

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.

Keywords: Stock-price dynamics; Black and Scholes model; option pricing; discrete (search for similar items in EconPapers)
JEL-codes: G12 (search for similar items in EconPapers)
Date: 2000-02-10
Note: received: March 1998; final version received: March 1999
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Citations: View citations in EconPapers (7)

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