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Investigating Levy's model in financial series prediction(case of vanilla option) | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 4، شماره 2، اسفند 2024، صفحه 65-82 اصل مقاله (609.92 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2024.81540.1144 | ||
| نویسنده | ||
| Seyed Jalal Tabatabaei* | ||
| Department of Management, Payamenoor University, Tehran, Iran | ||
| چکیده | ||
| In recent years, there has been growing interest in the application of stochastic processes to model financial markets, particularly in the pricing and prediction of derivative instruments such as options. One of the more advanced models that has emerged for capturing the dynamics of financial time series is the Lévy process, which generalizes the traditional Brownian motion by incorporating jumps and heavy tails, features often observed in real financial data. This paper investigates the applicability of Lévy processes in predicting the evolution of financial series, with a specific focus on vanilla option pricing. In our methodology,By reviewing the theoretical underpinnings of Lévy processes, highlighting key aspects such as the characteristic function and the variance-gamma process, we calibrate a Lévy-based model to 77 mid-prices of a set of European call options on the S&P 500 Index at the close of the market on 11 April 2022. We employ maximum likelihood estimation (MLE) and the expectation-maximization (EM) algorithm to fit the parameters of the Lévy process. Our results indicate that the Lévy process model provides a significantly better fit to market data than the Black-Scholes model, particularly in capturing the heavy tails and jump behavior observed in option price movements. Additionally, the Lévy model demonstrates superior predictive performance in out-of-sample testing, improving the accuracy of option pricing and hedging strategies. These findings suggest that Lévy processes hold substantial promise for enhancing financial series prediction and derivative pricing in markets characterized by volatility clustering and sudden jumps. | ||
| کلیدواژهها | ||
| Stochastic Processes؛ Brownian Motion؛ Poisson Process؛ Fourier Transform؛ Lè vy-Khinchtine Formula | ||
| مراجع | ||
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[1] Peter Carr, H´elyette Geman, Dilip B Madan, and Marc Yor, Stochastic volatility for l´evy processes, Mathematical finance 13 (2003), no. 3, 345–382. [2] Peter Carr and Liuren Wu, The finite moment log stable process and option pricing, The journal of finance 58 (2003), no. 2, 753–777. [3] Rama Cont, Empirical properties of asset returns: stylized facts and statistical issues, Quantitative finance 1 (2001), no. 2, 223. [4] Nathalie Eisenbaum, Andreas Kyprianou, Ana-Maria Matache, and Goran Peskir, Local time-space calculus with applications, SIAM Journal of Control and Optimization (2003), 1343. [5] Fang Fang and Cornelis W Oosterlee, A novel pricing method for european options based on fourier-cosine series expansions, SIAM Journal on Scientific Computing 31 (2009), no. 2, 826–848. [6] John C Hull and Sankarshan Basu, Options, futures, and other derivatives, Pearson Education India, 2016. [7] Zuzana Jankov´a, Drawbacks and limitations of black-scholes model for options pricing, Journal of Financial Studies and Research 2018 (2018), 1–7. [8] Jorge A Le´on, Josep L Sol´e, Frederic Utzet, and Josep Vives, On l´evy processes, malliavin calculus and market models with jumps, Finance and Stochastics 6 (2002), 197–225. [9] Dilip B Madan and Marc Yor, Representing the cgmy and meixner l´evy processes as time changed brownian motions, Journal of Computational Finance 12 (2008), no. 1, 27. [10] Alejandro Morales-Hern´andez, Inneke Van Nieuwenhuyse, and Sebastian Rojas Gonzalez, A survey on multi-objective hyperparameter optimization algorithms for machine learning, Artificial Intelligence Review 56 (2023), no. 8, 8043–8093. [11] Ernesto Mordecki, Optimal stopping and perpetual options for l´evy processes, Finance and Stochastics 6 (2002), 473–493. [12] David Nualart and Wim Schoutens, Chaotic and predictable representations for l´evy processes, Stochastic processes and their applications 90 (2000), no. 1, 109–122. [13] Bernt Øksendal and Frank Proske, White noise of poisson random measures, Potential Analysis 21 (2004), 375–403. [14] Jan Rosi´nski, Series representations of l´evy processes from the perspective of point processes, L´evy processes: theory and applications, Springer, 2001, pp. 401–415. [15] Boris Salazar, Mandelbrot, fama and the emergence of econophysics, Cuadernos de Econom´ıa 35 (2016), no. 69, 637–662. [16] Ren´e L Schilling, An introduction to l´evy and feller processes, L´evy-type processes to parabolic SPDEs. Birkh¨auser, Cham (2016), 1–30. [17] F Shokrollahi, D Ahmadian, and LV Ballestra, Pricing asian options under the mixed fractional brownian motion with jumps, Mathematics and Computers in Simulation 226 (2024), 172–183. [18] W Shoutens, L´evy processes in finance, 2003. [19] Ritik Soni and Ashok Kumar Pathak, Generalized iterated poisson process and applications, Journal of Theoretical Probability (2024), 1–30. [20] Seyed Jalal Tabatabaei and Alireza Pakgohar, Time series modeling of extreme losses values based on a spectral analysis approach, Financial Research Journal 22 (2021), no. 4, 594–611. [21] Peter Tankov, Financial modelling with jump processes, Chapman and Hall/CRC, 2003. | ||
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