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

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Author Info
Damiano Brigo () (Product and Business Development Group, Banca IMI, San Paolo-IMI Group, Corso Matteotti 6, 20121 Milano, Italy Manuscript)
Fabio Mercurio () (Product and Business Development Group, Banca IMI, San Paolo-IMI Group, Corso Matteotti 6, 20121 Milano, Italy Manuscript)

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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.

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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 4 (2000)
Issue (Month): 2 ()
Pages: 147-159
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Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:147-159

Note: received: March 1998; final version received: March 1999
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Related research
Keywords: Stock-price dynamics; Black and Scholes model; option pricing; discrete;

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Luciano Campi, 2004. "Arbitrage and completeness in financial markets with given N-dimensional distributions," Decisions in Economics and Finance, Springer, vol. 27(1), pages 57-80, 08. [Downloadable!] (restricted)
  2. Damiano Brigo & Fabio Mercurio, 2008. "Discrete Time vs Continuous Time Stock-price Dynamics and implications for Option Pricing," Quantitative Finance Papers 0812.4010, arXiv.org. [Downloadable!]
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