Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지
DOI QR코드

DOI QR Code

Stock Returns and Market Making with Inventory

  • Park, Seyoung (Department of Industrial and Management Eng., POSTECH) ;
  • Jang, Bong-Gyu (Department of Industrial and Management Eng., POSTECH)
  • Received : 2012.04.23
  • Accepted : 2012.06.11
  • Published : 2012.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

We study optimal trading strategy of a market maker with stock inventory. Following Avellaneda and Stoikov (2008), we assume the stock price follows a normal distribution. However, we take a constant expected rate of the stock return and assume that the stock volatility is an inverse function of the stock price level. We show that the optimal bid-ask spread of the market maker is wider for a higher expected rate of stock returns.

Keywords

References

  1. Avellaneda, M. and S. Stoikov, "High-Frequency Trading in a Limit Order Book," Quantitative Finance 8 3 (2008), 217-224. https://doi.org/10.1080/14697680701381228
  2. Biais, B., C. Bisière, and C. Spatt, "Imperfect Competition in Financial Markets: An Empirical Study of Island and Nasdaq," Management Science 56, 12 (2010), 2237-2250. https://doi.org/10.1287/mnsc.1100.1243
  3. Chen, H. and J. Ritter, "The Seven Percent Solution," Journal of Finance 55, 3 (2000), 1105-1131. https://doi.org/10.1111/0022-1082.00242
  4. Christie, W. and P. Schultz, "Why do Nasdaq Market Makers Avoid Odd-Eighth Quotes?," Journal of Finance 49, 5 (1994), 1813-1840. https://doi.org/10.1111/j.1540-6261.1994.tb04782.x
  5. Copeland, T. E. and D. Galai, "Information Effects and the Bid-Ask Spread," Journal of Finance 38, 5 (1983), 1457-1469. https://doi.org/10.1111/j.1540-6261.1983.tb03834.x
  6. Glosten, L. R. and P. R. Milgrom, "Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders," Journal of Financial Economics 14, 1 (1985), 71-100. https://doi.org/10.1016/0304-405X(85)90044-3
  7. Ho, T. and H. R. Stoll, "Optimal Dealer Pricing under Transactions and Return Uncertainty," Journal of Financial Economics 9, 1 (1981), 47-73. https://doi.org/10.1016/0304-405X(81)90020-9
  8. Kyle, A., "Continuous Auctions and Insider Trading," Econometrica 53, 6 (1985), 1315-1335. https://doi.org/10.2307/1913210
  9. Lyons, R. K., "Test of Microstructural Hypotheses in the Foreign Exchange Market," Journal of Financial Economics 39, 2/3 (1995), 321-351. https://doi.org/10.1016/0304-405X(95)00832-Y
  10. O'Hara, M., "Market Microstructure Theory," Bl-ackwell: Cambridge, 1997.
  11. Stoll, H. R., "Market Microstructure," Handbook of the Economics of Finance (edited by Constantinides, G. M.), North Holland: Amsterdam, 2003.