ABSTRACT
In this work we show how to use efficient online trading algorithms to price the current value of financial instruments, such as an option. We derive both upper and lower bounds for pricing an option, using online trading algorithms.Our bounds depend on very minimal assumptions and are mainly derived assuming that there are no arbitrage opportunities.
- Peter Auer, Nicolò Cesa-Bianchi, Yoav Freund, and Robert E. Schapire. The nonstochastic multiarmed bandit problem. SIAM J. on Computing, 32(1), 2002. A preliminary version appeared in FOCS 1995 as "Gambling in a rigged casino: The adversarial multi-armed bandit problem". Google ScholarDigital Library
- Antonio E. Bernardo and Olivier Ledoit. Gain, loss and asset pricing. Journal of Political Economy, 108(1):144--172, 2000.Google ScholarCross Ref
- Fisher Black and Myron Scholes. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637--654, 1973.Google ScholarCross Ref
- Blum and Kalai. Universal portfolios with and without transaction costs. In COLT: Proceedings of the Workshop on Computational Learning Theory, Morgan Kaufmann Publishers, 1997. Google ScholarDigital Library
- Nicolò Cesa-Bianchi, Yoav Freund, David P. Helmbold, David Haussler, Robert E. Schapire, and Manfred K. Warmuth. How to use expert advice. Journal of the Association for Computing Machinery, 44(3), 1997. A preliminary version appeared in STOC 1993. Google ScholarDigital Library
- Nicolò Cesa-Bianchi, Yishay Mansour, and Gilles Stoltz. Improved second-order bounds for prediction with expert advice. to appear in COLT, 2005. Google ScholarDigital Library
- A. Chou, J. Cooperstock, R. El-Yaniv, M. Klugerman, and T. Leighton. The statistical adversary allows optimal money-making trading strategies. In Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 467--476, 1995. Google ScholarDigital Library
- John H. Cochrane and Jesus Saa-Requejo. Beyond arbitrage: Good-deal asset price bounds in incomplete markets. Journal of Political Economy, 108(1):79--119, 2000.Google ScholarCross Ref
- T. Cover. Universal portfolios. Mathematical Finance, 1(1):1--29, 1991.Google ScholarCross Ref
- T. Cover and E. Ordentlich. Universal portfolios with side information. IEEE Transactions on Information Theory, 42(2):348--368, 1996. Google ScholarDigital Library
- T. Cover and E. Ordentlich. The cost of achieving the best portfolio in hindsight. Mathematics of Operations Research, 23(4):960--982, 1998. Google ScholarDigital Library
- Darrell Duffie. Dynamic Asset Pricing Theory. Princeton University Press, 2001.Google Scholar
- R. El-Yaniv, A. Fiat, R.M. Karp, and G. Turpin. Optimal search and one-way trading online algorithms. Algorithmica, 30(1):101--139, 2001.Google ScholarCross Ref
- Ran El-Yaniv, Amos Fiat, Richard M. Karp, and G. Turpin. Competitive analysis of financial games. In IEEE Symposium on Foundations of Computer Science, pages 327--333, 1992.Google ScholarDigital Library
- Bjorn Eraker. Do stock prices and volatility jump? reconciling evidence from spot and option prices. Journal of Finance, 59:1367--1403, 2004.Google ScholarCross Ref
- Bjorn Eraker, Michael Johannes, and Nicholas G. Polson. The impact of jumps in returns and volatility. Journal of Finance, 53:1269--1300, 2003.Google ScholarCross Ref
- D. Foster and R. Vohra. Regret in the on-line decision problem. Games and Economic Behavior, 21:40--55, 1997.Google ScholarCross Ref
- D. Foster and R. Vohra. Asymptotic calibration. Biometrika, 85:379--390, 1998.Google ScholarCross Ref
- Yoav Freund and Robert E. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. In Euro-COLT, pages 23--37. Springer-Verlag, 1995. Google ScholarDigital Library
- S. Hart and A. Mas-Colell. A simple adaptive procedure leading to correlated equilibrium. Econometrica, 68:1127--1150, 2000.Google ScholarCross Ref
- David P. Helmbold, Robert E. Schapire, Yoram Singer, and Manfred K. Warmuth. On-line portfolio selection using multiplicative updates. In International Conference on Machine Learning, pages 243--251, 1996.Google Scholar
- Sham Kakade, Michael Kearns, Yishay Mansour, and Luis Ortiz. Competitive algorithms for vwap and limit order trading. In In the Proceedings of the ACM Electronic Commerce Conference, 2004. Google ScholarDigital Library
- Sham M. Kakade and Michael Kearns. Trading in markovian price models. Unpublished manuscript, 2005.Google Scholar
- Adam Kalai and Santosh Vempala. Efficient algorithms for universal portfolios. In IEEE Symposium on Foundations of Computer Science, pages 486--491, 2000. Google ScholarDigital Library
- E. Lehrer. A wide range no-regret theorem. Games and Economic Behavior, 42:101--115, 2003.Google ScholarCross Ref
- Nick Littlestone and Manfred K. Warmuth. The weighted majority algorithm. Information and Computation, 108:212--261, 1994. Google ScholarDigital Library
- Robert C. Merton. Theory of rational option pricing. Bell Journal of Economics and Management Science, 4(1):141--183, 2004.Google ScholarCross Ref
- Per Aslak Mykland. Conservative delta hedging. The Annals of Applied Probability, 10(2):664--683, 2000.Google ScholarCross Ref
- Jun Pan. The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics, 63:3--50, 2002.Google ScholarCross Ref
- P. Raghavan. A statistical adversary for online algorithms. DIMACS Series, 7:79--83, 1992.Google ScholarCross Ref
- Steven E. Shreve, N. El Karoui, and M. Jeanblanc-Picque. Robustness of the black and scholes formula. Mathematical Finance, 8:93--126, 1998.Google ScholarCross Ref
- Yoram Singer. Switching portfolios. pages 488--495.Google Scholar
- V. Vovk and C. Watkins. Universal portfolio selection. In COLT: Proceedings of the Workshop on Computational Learning Theory, Morgan Kaufmann Publishers, 1998. Google ScholarDigital Library
Index Terms
- Online trading algorithms and robust option pricing
Recommendations
Option Pricing with Stochastic Volatility: Information-Time vs. Calendar-Time
Empirical evidence has shown that subordinated processes represent well the price changes of stocks and futures. Using either transaction counts or trading volume as a proxy for information arrival, it supports the contention that volatility is ...
Approximate option pricing
FOCS '96: Proceedings of the 37th Annual Symposium on Foundations of Computer ScienceAs increasingly large volumes of sophisticated options are traded in world financial markets, determining a "fair" price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, ...
Asset Pricing in a Monetary Economy with Heterogeneous Beliefs
In this paper, we shed new light on the role of monetary policy in asset pricing by examining the case in which investors have heterogeneous expectations about future monetary policy. This case is realistic because central banks are typically less than ...
Comments