Monte Carlo Simulation for Trading Under a Lévy-Driven Mean-Reverting Framework

References

• Avellaneda, M., and J.-H. Lee. 2010. “Statistical Arbitrage in the US Equities Market.” Quantitative Finance 10 (7): 761–782. https://doi.org/10.1080/14697680903124632.
   Web of Science ®Google Scholar
• Avellaneda, M., and M. Lipkin. 2009. “A Dynamic Model for Hard-to-Borrow Stocks.” Risk 22 (6): 92–97.
   Google Scholar
• Barndorff-Nielsen, O. E., and N. Shephard. 2001. “Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (2): 167–241. https://doi.org/10.1111/1467-9868.00282.
   Web of Science ®Google Scholar
• Benth, F. E., and M. D. Schmeck. 2014. “Pricing Futures and Options in Electricity Markets.” In The Interrelationship Between Financial and Energy Markets, edited by S. Ramos and H. Veiga, 233–260. Berlin-Verlag: Springer.
   Google Scholar
• Bertoin, J. 1996. Lévy Processes. Cambridge: Cambridge University Press.
   Google Scholar
• Borovkov, K., and A. Novikov. 2008. “On Exit Times of Lévy-Driven Ornstein-Uhlenbeck Processes.” Statistics and Probability Letters 78 (12): 1517–1525. https://doi.org/10.1016/j.spl.2008.01.017.
   Web of Science ®Google Scholar
• Brennan, M. J., and E. S. Schwartz. 1990. “Arbitrage in Stock Index Futures.” Journal of Business 63 (1): S7–S31. https://doi.org/10.1086/jb.1990.63.issue-S1.
   Google Scholar
• Buchmann, B., K. W. Lu, and D. B. Madan. 2019. “Weak Subordination of Multivariate Lévy Processes and Variance Generalised Gamma Convolutions.” Bernoulli 25 (1): 742–770. https://doi.org/10.3150/17-BEJ1004.
   Web of Science ®Google Scholar
• Cariboni, J., and W. Schoutens. 2009. “Jumps in Intensity Models: Investigating the Performance of Ornstein-Uhlenbeck Processes in Credit Risk Modeling.” Metrika 69:73–198. https://doi.org/10.1007/s00184-008-0213-4.
   Web of Science ®Google Scholar
• Cont, R., and P. Tankov. 2004. Financial Modelling with Jump Processes. Boca Raton: Chapman & Hall/CRC.
   Google Scholar
• Cummins, M., G. Kiely, and B. Murphy. 2018. “Gas Storage Valuation Under Multifactor Lévy Processes.” Journal of Banking and Finance 95:167–184. https://doi.org/10.1016/j.jbankfin.2018.02.012.
   Web of Science ®Google Scholar
• Dai, M., Y. Zhong, and Y. K. Kwok. 2011. “Optimal Arbitrage Strategies on Stock Index Futures Under Position Limits.” Journal of Futures Markets 31 (4): 394–406. https://doi.org/10.1002/fut.v31.4.
   Web of Science ®Google Scholar
• Do, B., and R. Faff. 2012. “Are Pairs Trading Profits Robust to Trading Costs?” Journal of Financial Research 35 (2): 261–287. https://doi.org/10.1111/jfir.2012.35.issue-2.
   Google Scholar
• Elliott, R., Van Der Hoek J., and W. Malcolm. 2005. “Pairs Trading.” Quantitative Finance 5 (3): 271–276. https://doi.org/10.1080/14697680500149370.
   Web of Science ®Google Scholar
• Endres, S., and Stübinger J.. 2019. “Optimal Trading Strategies for Lévy-Driven Ornstein-Uhlenbeck Processes.” Applied Economics 51 (29): 3153–3169. https://doi.org/10.1080/00036846.2019.1566688.
   Web of Science ®Google Scholar
• Gardini, M., P. Sabino, and E. Sasso. 2022. “The Variance Gamma++ Process and Applications to Energy Markets.” Applied Stochastic Models in Business and Industry 38 (2): 391–418. https://doi.org/10.1002/asmb.v38.2.
   Web of Science ®Google Scholar
• Gatev, E., W. N. Goetzmann, and K. G. Rouwenhorst. 2006. “Pairs Trading: Performance of a Relative-Value Arbitrage Rule.” Review of Financial Studies 19 (3): 797–827. https://doi.org/10.1093/rfs/hhj020.
   Web of Science ®Google Scholar
• Glasserman, P. 2003. Monte Carlo Methods in Financial Engineering. New York: Springer.
   Google Scholar
• Huck, N., and K. Afawubo. 2015. “Pairs Trading and Selection Methods: Is Cointegration Superior?” Applied Economics 47 (6): 599–613. https://doi.org/10.1080/00036846.2014.975417.
   Web of Science ®Google Scholar
• Kanamura, T., S. Rachev, and F. Fabozzi. 2010. “A Profit Model for Spread Trading with an Application to Energy Futures.” The Journal of Trading 5 (1): 48–62. https://doi.org/10.3905/JOT.2010.5.1.048.
   Google Scholar
• Lee, K., T. Leung, and B. Ning. 2023. “A Diversification Framework for Multiple Pairs Trading Strategies.” Risks 11 (5). https://doi.org/10.3390/risks11050093.
   Web of Science ®Google Scholar
• Leung, T., and X. Li. 2015. “Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit.” International Journal of Theoretical and Applied Finance 18 (03): 1550020. https://doi.org/10.1142/S021902491550020X.
   Google Scholar
• Leung, T., and X. Li 2016. Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications. Modern Trends in Financial Engineering, World Scientific Publishing Company.
   Google Scholar
• Leung, T., and H. Nguyen. 2019. “Constructing Cointegrated Cryptocurrency Portfolios for Statistical Arbitrage.” Studies in Economics and Finance 36 (3): 581–599. https://doi.org/10.1108/SEF-08-2018-0264.
   Google Scholar
• Lipton, A., and López de Prado M.. 2020. “A Closed-Form Solution for Optimal Ornstein-Uhlenbeck Driven Trading Strategies.” International Journal of Theoretical and Applied Finance 23 (8): 2050056. https://doi.org/10.1142/S0219024920500569.
   Web of Science ®Google Scholar
• Lu, K. W. 2022. “Calibration for Multivariate Lévy-Driven Ornstein-Uhlenbeck Processes with Applications to Weak Subordination.” Statistical Inference for Stochastic Processes 25 (2): 365–396. https://doi.org/10.1007/s11203-021-09254-4.
   Google Scholar
• Madan, D. B., P. P. Carr, and E. C. Chang. 1998. “The Variance Gamma Process and Option Pricing.” European Finance Review 2 (1): 79–105. https://doi.org/10.1023/A:1009703431535.
   Google Scholar
• Madan, D. B., and E. Seneta. 1990. “The Variance Gamma (v.g.) Model for Share Market Returns.” The Journal of Business 63 (4): 511–524. https://doi.org/10.1086/jb.1990.63.issue-4.
   Web of Science ®Google Scholar
• Masuda, H. 2004. “On Multidimensional Ornstein-Uhlenbeck Processes Driven by a General Lévy Process.” Bernoulli 310 (1): 97–120.
   Google Scholar
• Michaelsen, M., and A. Szimayer. 2018. “Marginal Consistent Dependence Modeling Using Weak Subordination for Brownian Motions.” Quantitative Finance 18 (11): 1909–1925. https://doi.org/10.1080/14697688.2018.1439182.
   Web of Science ®Google Scholar
• Nelson, B. L. 1990. “Control Variate Remedies.” Operations Research 38 (6): 974–992. https://doi.org/10.1287/opre.38.6.974.
   Web of Science ®Google Scholar
• Qu, Y., A. Dassios, and H. Zhao. 2021. “Exact Simulation of Gamma-Driven Ornstein–Uhlenbeck Processes with Finite and Infinite Activity Jumps.” Journal of the Operational Research Society 72 (2): 471–484. https://doi.org/10.1080/01605682.2019.1657368.
   Web of Science ®Google Scholar
• Rencher, A. C., and G. B. Schaalje. 2008. Linear Models in Statistics. Hoboken: John Wiley & Sons, Inc.
   Google Scholar
• Sabino, P. 2020. “Exact Simulation of Variance Gamma-Related OU Processes: Application to the Pricing of Energy Derivatives.” Applied Mathematical Finance 27 (3): 207–227. https://doi.org/10.1080/1350486X.2020.1813040.
   Google Scholar
• Sato, K. 1999. Lévy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press.
   Google Scholar
• Sato, K., and M. Yamazato. 1983. “Stationary Processes of Ornstein-Uhlenbeck Type.” In Probability Theory and Mathematical Statistics, edited by K. Itô and J. V. Prohorov, 541–551. Berlin: Springer.
   Google Scholar
• Sato, K., and M. Yamazato. 1985. “Completely Operator-Selfdecomposable Distributions and Operator-Stable Distributions.” Nagoya Mathematical Journal 97:71–94. https://doi.org/10.1017/S0027763000021267.
   Web of Science ®Google Scholar
• Schoutens, W. 2003. Lévy Processes in Finance: Pricing Financial Derivatives. East Sussex: John Wiley & Sons Ltd.
   Google Scholar
• Valdivieso, L., W. Schoutens, and F. Tuerlinckx. 2009. “Maximum Likelihood Estimation in Processes of Ornstein-Uhlenbeck Type.” Statistical Inference for Stochastic Processes 12 (1): 1–19. https://doi.org/10.1007/s11203-008-9021-8.
   Google Scholar
• Wu, L., X. Zang, and H. Zhao. 2020. “Analytic Value Function for a Pairs Trading Strategy with a Lévy-Driven Ornstein-Uhlenbeck Process.” Quantitative Finance 20 (8): 285–1306. https://doi.org/10.1080/14697688.2020.1736613.
   Web of Science ®Google Scholar