Review of Derivatives Research

, Volume 12, Issue 1, pp 55–79 | Cite as

Option market making under inventory risk

Article

Abstract

We propose a mean-variance framework to analyze the optimal quoting policy of an option market maker. The market maker’s profits come from the bid-ask spreads received over the course of a trading day, while the risk comes from uncertainty in the value of his portfolio, or inventory. Within this framework, we study the impact of liquidity and market incompleteness on the optimal bid and ask prices of the option. First, we consider a market maker in a complete market, where continuous trading in a perfectly liquid underlying stock is allowed. In this setting, the market maker may remove all risk by Delta hedging, and the optimal quotes will depend on the option’s liquidity, but not on the inventory. Second, we model a market maker who may not trade continuously in the underlying stock, but rather sets bid and ask quotes in the option and this illiquid stock. We find that the optimal stock and option quotes depend on the relative liquidity of both instruments as well as on the net Delta of the inventory. Third, we consider an incomplete market with residual risks due to stochastic volatility and large overnight moves in the stock price. In this setting, the optimal quotes depend on the liquidity of the option and on the net Vega and Gamma of the inventory.

Keywords

Delta European options Gamma Inventory management Liquidity Market microstructure Vega 

JEL Classifications

G13 G11 C61 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Almgren R., Chriss N. (2001) Optimal execution of portfolio transactions. Journal of Risk 3: 5–39Google Scholar
  2. Boyle P., Emanuel D. (1980) Discretely adjusted option hedges. Journal of Financial Economics 8: 259–282CrossRefGoogle Scholar
  3. Cont R., da Fonseca J. (2002) Dynamics of implied volatility surfaces. Quantitative Finance 2: 45–60CrossRefGoogle Scholar
  4. Davis M.H.A., Panas V.G., Zariphopoulou T. (1993) European option pricing with transaction costs. SIAM Journal on Control and Optimization 31(2): 470–493CrossRefGoogle Scholar
  5. Engle, R., & Ferstenberg, R. (2006). Execution risk, Working paper.Google Scholar
  6. Garleanu, N., Pedersen, L. H., & Poteshman, A. M. (2006). Demand based option pricing, Working paper, Wharton School of Business.Google Scholar
  7. Hasbrouck J. (2007) Empirical market microstructure. Oxford University Press, New YorkGoogle Scholar
  8. Ho T.S.Y., Macris R.G. (1984) Dealer bid-ask quotes and transaction prices: An empirical study of some AMEX options. Journal of Finance 39(1): 23–45CrossRefGoogle Scholar
  9. Ho T.S.Y., Stoll H.R. (1981) Optimal dealer pricing under transactions and return uncertainty. Journal of Financial Economics 9: 47–73CrossRefGoogle Scholar
  10. Jameson M., Wilhelm W. (1992) Market making in the options markets and the costs of discrete hedge rebalancing. Journal of Finance 47: 765–779CrossRefGoogle Scholar
  11. Minina, V., & Vellekoop, M. (2008). A risk reserve model for hedging in incomplete markets rebalancing, Working paper.Google Scholar
  12. Schönbucher P.J. (1999) A market model for stochastic implied volatility. Philosophical Transactions: Mathematical, Physical and Engineering Sciences 357(1758): 2071–2092CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Cornell Financial Engineering ManhattanCornell UniversityNew YorkUSA
  2. 2.Graduate School of BusinessColumbia UniversityNew YorkUSA

Personalised recommendations