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

Yıl 2022, Cilt: 11 Sayı: 4, 161 - 175, 31.12.2022

Bilgi Yılmaz A. Alper Hekımoglu

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• Akyapı, B. (2014). An Analysis of BIST30 index options market / [M.S. - Master of Science]. Middle East Technical University. http://etd.lib.metu.edu.tr/upload/12617381/index.pdf
• Alan, N. S., Karagozoglu, A. K., & Korkmaz, S. (2016). Growing pains: The evolution of new stock index futures in emerging markets. Research in International Business and Finance, 37, 1-16.
• Alp, Ö. S. (2016). The Performance of Skewness and Kurtosis Adjusted Option Pricing Model in Emerging Markets: A case of Turkish Derivatives Market. International Journal of Finance & Banking Studies, 5(3), 70-79.
• Barndorff-Nielsen, O. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 353(1674), 401-419.
• Barndorff‐Nielsen, O. E. (1997). Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of statistics, 24(1), 1-13.
• Barndorff-Nielsen, O. E. (1997). Processes of normal inverse Gaussian type. Finance and stochastics, 2(1), 41-68.
• Bastı, E., Kuzey, C., & Delen, D. (2015). Analyzing initial public offerings' short-term performance using decision trees and SVMs. Decision Support Systems, 73, 15-27.
• Behr, A., & Pötter, U. (2009). Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models. Annals of Finance, 5(1), 49-68.
• Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.
• Carr, P., Geman, H., Madan, D. B., & Yor, M. (2002). The fine structure of asset returns: An empirical investigation. The Journal of Business, 75(2), 305-332.
• Cont, R., & Da Fonseca, J. (2002). Dynamics of implied volatility surfaces. Quantitative finance, 2(1), 45.
• Coşkun, Y., Selcuk-Kestel, A. S., & Yilmaz, B. (2017). Diversification benefit and return performance of REITs using CAPM and Fama-French: Evidence from Turkey. Borsa Istanbul Review, 17(4), 199-215.
• Daal, E. A., & Madan, D. B. (2005). An empirical examination of the variance‐gamma model for foreign currency options. The Journal of Business, 78(6), 2121-2152.
• Demir, S., & Tutek, H. (2004). Pricing of options in emerging financial markets using martingale simulation: An example from Turkey. WIT Transactions on Modelling and Simulation, 38.
• Eberlein, E. (2001). Application of generalized hyperbolic Lévy motions to finance. In Lévy processes (pp. 319-336). Birkhäuser, Boston, MA.
• Eberlein, E. (2014). Fourier-based valuation methods in mathematical finance. In Quantitative energy finance (pp. 85-114). Springer, New York, NY.
• Eberlein, E., & Keller, U. (1995). Hyperbolic distributions in finance. Bernoulli, 281-299.
• Eriksson, A., Ghysels, E., & Wang, F. (2009). The normal inverse Gaussian distribution and the pricing of derivatives. The Journal of Derivatives, 16(3), 23-37.
• Ersoy, E., & Bayrakdaroğlu, A. (2013). The lead-lag relationship between ISE 30 index and the TURKDEX-ISE 30 index futures contracts. İstanbul Üniversitesi İşletme Fakültesi Dergisi, 42(1), 26-40.
• Geman, H., Madan, D. B., & Yor, M. (2001). Asset prices are Brownian motion: only in business time. In Quantitative Analysis In Financial Markets: Collected Papers of the New York University Mathematical Finance Seminar (Volume II) (pp. 103-146).
• Gokgoz, F., & Sezgin-Alp, O. (2014). Estimating the Turkish sectoral market returns via arbitrage pricing model under neural network approach. International Journal of Economics and Finance, 7(1), 154.
• Harrison, J. M., & Pliska, S. R. (1983). A stochastic calculus model of continuous trading: complete markets. Stochastic processes and their applications, 15(3), 313-316.
• Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The review of financial studies, 6(2), 327-343.
• Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. The journal of finance, 42(2), 281-300.
• Ivanov, R. V. (2013). Closed form pricing of European options for a family of normal-inverse Gaussian processes. Stochastic Models, 29(4), 435-450.
• Kayalidere, K., Araci, H., & Aktaş, H. (2012). Türev ve spot piyasalar arasındaki etkileşim: VOB üzerine bir inceleme. Muhasebe ve Finansman Dergisi, (56), 137-154.
• Konikov, M., & Madan, D. B. (2002). Option pricing using variance gamma Markov chains. Review of Derivatives Research, 5(1), 81-115.
• Leicht, J. J., & Rathgeber, A. W. (2014). Guaranteed stop orders as portfolio insurance–An analysis for the German stock market. Journal of Derivatives & Hedge Funds, 20(4), 257-278.
• Loregian, A., Mercuri, L., & Rroji, E. (2012). Approximation of the variance gamma model with a finite mixture of normals. Statistics & Probability Letters, 82(2), 217-224.
• Luciano, E., Marena, M., & Semeraro, P. (2016). Dependence calibration and portfolio fit with factor-based subordinators. Quantitative Finance, 16(7), 1037-1052.
• Luciano, E., & Schoutens, W. (2006). A multivariate jump-driven financial asset model. Quantitative finance, 6(5), 385-402.
• Luciano, E., & Semeraro, P. (2010). Multivariate Variance Gamma and Gaussian dependence: a study with copulas. In Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 193-203). Springer, Milano.
• Luciano, E., Marena, M., & Semeraro, P. (2013). Dependence calibration and portfolio fit with factor-based time changes. Carlo Alberto Notebooks, (307).
• Madan, D. B., & Seneta, E. (1987). Simulation of estimates using the empirical characteristic function. International Statistical Review/Revue Internationale de Statistique, 153-161.
• Madan, D. B., & Seneta, E. (1990). The variance gamma (VG) model for share market returns. Journal of business, 511-524.
• Madan, D. B., Carr, P. P., & Chang, E. C. (1998). The variance gamma process and option pricing. Review of Finance, 2(1), 79-105.
• Mandelbrot, B. (1963). New methods in statistical economics. Journal of political economy, 71(5), 421-440.
• Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of financial economics, 3(1-2), 125-144.
• Praetz, P. D. (1972). The distribution of share price changes. Journal of business, 49-55.
• Rathgeber, A. W., Stadler, J., & Stöckl, S. (2016). Modeling share returns-an empirical study on the Variance Gamma model. Journal of Economics and finance, 40(4), 653-682.
• Semeraro, P. (2008). A multivariate variance gamma model for financial applications. International journal of theoretical and applied finance, 11(01), 1-18.
• Stein, E. M., & Stein, J. C. (1991). Stock price distributions with stochastic volatility: an analytic approach. The review of financial studies, 4(4), 727-752.
• Tankov, P. (2003). Financial modelling with jump processes. Chapman and Hall/CRC.
• Tokat, H. A. (2009). Re-examination of volatility dynamics in Istanbul Stock Exchange. Investment management and financial innovations, (6, Iss. 1 (contin.)), 192-198.
• Viens, F. G., Mariani, M. C., & Florescu, I. (2011). Handbook of modeling high-frequency data in finance (Vol. 4). John Wiley & Sons.
• Zwillinger, D., & Jeffrey, A. (Eds.). (2007). Table of integrals, series, and products. Elsevier