OPTION PRICING IN EMERGING MARKETS USING PURE JUMP PROCESSES: EXPLICIT CALIBRATION OF BIST30 EUROPEAN OPTION

Year 2022, Volume: 11 Issue: 4, 161 - 175, 31.12.2022

Bilgi Yılmaz A. Alper Hekımoglu

Abstract

Purpose- This study aims to illustrate the efficiency of pure jump processes, more specifically Variance Gamma (VG) and Normal Inverse Gaussian models (NIG), in option pricing by comparing with the Black Scholes (BS) option pricing model for emerging markets.
Methodology- This study presents an alternative derivation of option pricing formulas for VG and NIG models. Then, it investigates the VG and NIG models' option pricing performance with the help of new derivation by comparing them with the BS option pricing model for emerging markets for an emerging country, Turkey. The data consists of the BIST30 index daily price and European options written on this index extend from 05 May 2018 to 05 May 2020 for given exercise prices with a maturity of 90 days. In this period, the European call options' strike prices range from 1200 to 1650, and the European put options' strike prices range from 1000 to 1400. To compare the models' efficiency, first, we calibrate the models by minimizing the sum of squared deviations between the observed and theoretical option prices. Second, we compute the option prices and compare the results with the observed option prices.
Findings- The significant contribution to the literature is the calibration of the pure jump processes (VG and NIG processes) using the characteristic functions, the continuous BS prices for an emerging market, and the computation of European options prices in BIST. We find that while the NIG process performs better than VG and BS models, the BS model is the worst in option pricing.
Conclusion- The pure jump processes (VG and NIG processes) can be calibrated using the characteristic functions, and option price estimations with them are better than the continuous BS prices for an emerging market. Thus, the pure jump processes are more efficient in market modeling than the BS model.

Keywords

Variance Gamma Process, Normal Inverse Gaussian Process, Black-Scholes Model, Options Pricing, Calibration

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