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Optimal Dynamic Basis Trading

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  • Bahman Angoshtari
  • Tim Leung

Abstract

We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization problem under hyperbolic absolute risk aversion (HARA) risk preferences. By analyzing the associated Hamilton-Jacobi-Bellman equation, we derive the exact conditions under which the equation admits a solution and solve the utility maximization explicitly. A series of numerical examples are provided to illustrate the optimal strategies and examine the effects of model parameters.

Suggested Citation

  • Bahman Angoshtari & Tim Leung, 2018. "Optimal Dynamic Basis Trading," Papers 1809.05961, arXiv.org, revised May 2019.
    • Handle: RePEc:arx:papers:1809.05961
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    References listed on IDEAS

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    1. Tourin, Agnès & Yan, Raphael, 2013. "Dynamic pairs trading using the stochastic control approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1972-1981.
    2. Min Dai & Yifei Zhong & Yue Kuen Kwok, 2011. "Optimal arbitrage strategies on stock index futures under position limits," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(4), pages 394-406, April.
    3. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    4. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," IJFS, MDPI, vol. 6(3), pages 1-23, August.
    5. Álvaro Cartea & Sebastian Jaimungal, 2016. "Algorithmic Trading Of Co-Integrated Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-18, September.
    6. Chan, Kalok, 1992. "A Further Analysis of the Lead-Lag Relationship between the Cash Market and Stock Index Futures Market," The Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 123-152.
    7. Sangmin Lee & Andrew Papanicolaou, 2016. "Pairs Trading Of Two Assets With Uncertainty In Co-Integration'S Level Of Mean Reversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-36, December.
    8. Stoll, Hans R. & Whaley, Robert E., 1990. "The Dynamics of Stock Index and Stock Index Futures Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 441-468, December.
    9. Ralf Korn & Holger Kraft, 2004. "On The Stability Of Continuous‐Time Portfolio Problems With Stochastic Opportunity Set," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 403-414, July.
    10. Philip Garcia & Scott H. Irwin & Aaron Smith, 2015. "Futures Market Failure?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 97(1), pages 40-64.
    11. Jun Liu, 2004. "Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," The Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 611-641.
    12. Álvaro Cartea & Sebastian Jaimungal & Damir Kinzebulatov, 2016. "Algorithmic Trading With Learning," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-30, June.
    13. David M. Modest & Mahadevan Sundaresan, 1983. "The relationship between spot and futures prices in stock index futures markets: Some preliminary evidence," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 3(1), pages 15-41, March.
    14. Chiu, Mei Choi & Wong, Hoi Ying, 2011. "Mean-variance portfolio selection of cointegrated assets," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1369-1385, August.
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    17. Scott H. Irwin & Philip Garcia & Darrel L. Good & Eugene L. Kunda, 2011. "Spreads and Non-Convergence in Chicago Board of Trade Corn, Soybean, and Wheat Futures: Are Index Funds to Blame?," Applied Economic Perspectives and Policy, Agricultural and Applied Economics Association, vol. 33(1), pages 116-142.
    18. Alvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2018. "Trading Cointegrated Assets with Price Impact," Papers 1807.01428, arXiv.org.
    19. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2017. "Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    20. Tim Leung & Xin Li, 2016. "Optimal Mean Reversion Trading:Mathematical Analysis and Practical Applications," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9839, August.
    21. Tim Leung & Raphael Yan, 2019. "A stochastic control approach to managed futures portfolios," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-22, March.
    22. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    23. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    24. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages 7-31, January.
    25. Kawaller, Ira G & Koch, Paul D & Koch, Timothy W, 1987. "The Temporal Price Relationship between S&P 500 Futures and the S and P 500 Index," Journal of Finance, American Finance Association, vol. 42(5), pages 1309-1329, December.
    26. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
    27. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 32(3), pages 278-297, August.
    28. Dorje C. Brody & Lane P. Hughston & Andrea Macrina, 2008. "Information-Based Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 107-142.
    29. Adjemian, Michael K. & Garcia, Philip & Irwin, Scott & Smith, Aaron, 2013. "Non-Convergence in Domestic Commodity Futures Markets: Causes, Consequences, and Remedies," Economic Information Bulletin 155381, United States Department of Agriculture, Economic Research Service.
    30. Jun Liu & Allan Timmermann, 2013. "Optimal Convergence Trade Strategies," The Review of Financial Studies, Society for Financial Studies, vol. 26(4), pages 1048-1086.
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    Cited by:

    1. Xiaodong Chen & Tim Leung & Yang Zhou, 2022. "Constrained dynamic futures portfolios with stochastic basis," Annals of Finance, Springer, vol. 18(1), pages 1-33, March.
    2. Tim Leung & Raphael Yan, 2019. "A stochastic control approach to managed futures portfolios," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-22, March.
    3. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Jul 2024.
    4. Tim Leung & Yang Zhou, 2019. "Optimal dynamic futures portfolio in a regime-switching market framework," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-27, December.
    5. Bahman Angoshtari & Tim Leung, 2020. "Optimal trading of a basket of futures contracts," Annals of Finance, Springer, vol. 16(2), pages 253-280, June.
    6. Jun Deng & Huifeng Pan & Shuyu Zhang & Bin Zou, 2021. "Optimal Bitcoin trading with inverse futures," Annals of Operations Research, Springer, vol. 304(1), pages 139-163, September.

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    More about this item

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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