Variance Gamma Model in Hedging Vanilla and Exotic Options

Bartłomiej Bollin and Robert Ślepaczuk
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Bartłomiej Bollin: Quantitative Finance Research Group; Faculty of Economic Sciences, University of Warsaw

No 2020-31, Working Papers from Faculty of Economic Sciences, University of Warsaw

Abstract: The aim of this research is to explore the performance of different option pricing models in hedging the exotic options using the FX data. We analyze the narrow class of Lévy processes - the Variance Gamma process in hedging vanilla, Asian and lookback options. We pose a question of whether or not using additional level of complexity, by introducing more sophisticated models, improves the effectiveness of hedging options, assuming that hedging errors are measured as the differences between portfolio values according to the model and not real market data (which we don’t have). We compare this model with its special case and the Black-Scholes model. We use the data for EURUSD currency pair assuming that option prices change according to the model (as we don’t observe them directly). We use Monte Carlo methods in fitting the model’s parameters. Our results are not in line with the previous literature as there are no signs of the Variance Gamma process being better than the Black-Scholes and it seems that all three models perform equally well.

Keywords: Monte Carlo; option pricing; Variance Gamma; BSM model; Lévy processes; FX market; hedging; Asian and lookback options (search for similar items in EconPapers)
JEL-codes: C02 C14 C15 C22 C4 C45 C53 C58 C63 G12 G13 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2020
New Economics Papers: this item is included in nep-fmk, nep-ore, nep-rmg and nep-sea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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