Option Pricing with Discrete Rebalancing

Jean-Luc Prigent, Olivier Renault and Olivier Scaillet
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Olivier Renault: Financial Markets Group, London School of Economics

FAME Research Paper Series from International Center for Financial Asset Management and Engineering

Abstract: We consider option pricing when dynamic portfolios are discretely rebalanced. The portfolio adjustments only occur after ¯xed relative changes in the stock price. The stock price follows a marked point process and the market is incomplete. We first characterisethe equivalent martingale measures. An explicit pricing formula based on the minimal martingale measure is then provided together with the hedging strategy underlying port-folio adjustments. Two examples illustrate our pricing framework : a jump process driven by a latent geometric Brownian motion and a marked Poisson process. We establish the convergence to the Black-Scholes model when the triggering price increment shrinks to zero. For the empirical application we use IBM, France Telecom and CAC 40 intraday transaction data, and compare option prices given by the marked Poisson model, the Black-Scholes model and observed option prices.

Keywords: weak convergence; incomplete market; option pricing; minimal martin-gale measure; discrete rebalancing; marked point process (search for similar items in EconPapers)
JEL-codes: D52 G13 (search for similar items in EconPapers)
Date: 2002-07
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Related works:
Journal Article: Option pricing with discrete rebalancing (2004)
Working Paper: Option pricing with discrete rebalancing (2004)
Working Paper: Option Pricing with Discrete Rebalancing (1999)
Working Paper: Option Pricing with Discrete Rebalancing (1999)
Working Paper: Option pricing with discrete rebalancing (1999)
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