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Optimal Bid-Ask Spread in Limit-Order Books under Regime Switching Framework

Author

Listed:
  • Farzad Alavi Fard

    (School of Economics, Finance and Marketing, RMIT University, 445 Swanson Street, Melbourne, VIC 3000, AUSTRALIA)

Abstract

This paper advocates a regime-switching model to capture the risk of structural changes in the economy, when determining the optimal bid-ask spread in limit order books. In our model, the market-maker faces an inventory risk due to the diffusive nature of the stocks¡¯ mid-price and a transactions risk due to a Poisson arrival of market ¡°buy¡± and ¡°sell¡± orders. We propose that the intensity of the orders depend on the state of the economy, and in the event of a structural change, market makers will face different intensity of order flows, reflecting the new market conditions. In our model, the dealer is a wealth maximizing agent who dynamically manages his portfolio. We employ Hamilton-Jacobi-Bellman equation for the dynamic programming problem, and we solve the problem numerically using the Galerkin method.

Suggested Citation

  • Farzad Alavi Fard, 2014. "Optimal Bid-Ask Spread in Limit-Order Books under Regime Switching Framework," Review of Economics & Finance, Better Advances Press, Canada, vol. 4, pages 33-48, November.
    • Handle: RePEc:bap:journl:140403
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    References listed on IDEAS

    as
    1. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    2. Ho, Thomas S Y & Macris, Richard G, 1984. "Dealer Bid-Ask Quotes and Transaction Prices: An Empirical Study of Some AMEX Options," Journal of Finance, American Finance Association, vol. 39(1), pages 23-45, March.
    3. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    4. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    5. Farzad Fard & Tak Siu, 2013. "Pricing and managing risks of European-style options in a Markovian regime-switching binomial model," Annals of Finance, Springer, vol. 9(3), pages 421-438, August.
    6. Naik, Vasanttilak, 1993. "Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-1984, December.
    7. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    8. Chen, Fei & Diebold, Francis X. & Schorfheide, Frank, 2013. "A Markov-switching multifractal inter-trade duration model, with application to US equities," Journal of Econometrics, Elsevier, vol. 177(2), pages 320-342.
    9. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    10. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    11. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    12. Harold Demsetz, 1968. "The Cost of Transacting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(1), pages 33-53.
    13. �lvaro Cartea & Sebastian Jaimungal, 2013. "Modelling Asset Prices for Algorithmic and High-Frequency Trading," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(6), pages 512-547, December.
    14. P. A. Forsyth & K. R. Vetzal & R. Zvan, 1999. "A finite element approach to the pricing of discrete lookbacks with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 87-106.
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    Cited by:

    1. Qing-Qing Yang & Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "On Optimal Pricing Model for Multiple Dealers in a Competitive Market," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 397-431, January.

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    More about this item

    Keywords

    Market micro-structure; Limit-order; Regime switching; HJB; Galerkin method;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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