Option Pricing with Discrete Rebalancing

Jean-Luc Prigent, O. Renault and Olivier Scaillet
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O. Renault: UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES)

No 1999029, LIDAM Discussion Papers IRES from Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES)

Abstract: We consider option pricing when dynamic portfolios are discretely rebalanced. The portfolio adjustments only occur after fixed relative variation of the stock price. The stock price follows a marked point process and the market is incomplete. We first characterize the equivalent martingale measures. An explicit formula based on the minimal martingale measure is then provided together with the hedging strategy underlying portfolio adjustments. Under adequate conditions on the stock price dynamics, the minimal pricing formula converges to the Black-Scholes formula when the triggering price increment shrinks to zero. This is shown theoretically and numerically on two examples : a marked Poisson process and a jump process driven by a latent geometric Brownian motion. For the empirical application we use IBM intraday transaction data and compare option prices given by the marked Poisson model and the Black-Scholes model.

Keywords: Weak convergence; incomplete markets; option pricing; minimal martingale measure; discrete rebalancing; marked point process (search for similar items in EconPapers)
JEL-codes: D52 G13 (search for similar items in EconPapers)
Pages: 18
Date: 1999-02-01, Revised 1999-10
New Economics Papers: this item is included in nep-fmk
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Citations: View citations in EconPapers (1)

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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 (2002)
Working Paper: Option Pricing with Discrete Rebalancing (1999)
Working Paper: Option pricing with discrete rebalancing (1999)
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