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Volume 56, Issue 7 -8

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Model Dependency of the Digital Option Replication ? Replication under an Incomplete Model (in English)

Tichý, Tomáš

Year: 2006   Volume: 56   Issue: 7 -8   Pages: 361-379

Abstract: The paper focuses on the replication of digital options under an incomplete model. Digital options are regularly applied in the hedging and static decomposition of many path-dependent options. The author examines the performance of static and dynamic replication. He considers the case of a market agent for whom the right model of the underlying asset-price evolution is not available. The observed price dynamic is supposed to follow four distinct models: (i) the Black and Scholes model, (ii) the Black and Scholes model with stochastic volatility driven by Hull and White model, (iii) the variance gamma model, defined as time changed Brownian motion, and (iv) the variance gamma model set in a stochastic environment modelled as the rate of time change via a Cox-Ingersoll-Ross model. Both static and dynamic replication methods are applied and examined within each of these settings. The author verifies the independence of the static replication on underlying processes.

JEL classification: G13, G20, D52, C1

Keywords: digital options; dynamic and static replication; internal time; Lévy models; replication error; stochastic environment; stochastic volatility; variance gamma process

RePEc: http://ideas.repec.org/a/fau/fauart/v56y2006i7-8p361-379.html

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