Abstract
In the presence of transaction costs, a risk-return trade-off exists between the quality and the cost of a replicating strategy. In that context, I show how to expand the set of all possible time-based strategies through the introduction of a multi-scale class of strategies, which consist in rebalancing different fractions of an option portfolio at different time frequencies. The method, based on time-scale diversification, is to dynamic replication what investment in diversified portfoliosis to static portfolio selection: in a dynamic context, one may enjoy the benefits of diversification by using different time scales in trading the same asset.
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References
Bensaid, B., J. P. Lesne, H. Pages, and J. Scheinkman. (1992). “Derivative Asset Pricing with Transaction Costs,” Mathematical Finance 2, 63–86.
Black, F., and M. S. Scholes. (1973). “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81, 637–654.
Boyle, P. P., and T. Vorst. (1992). “Option Replication in Discrete Time with Transaction Costs,” The Journal of Finance 47, 271–293.
Constantinides, G. M. (1993). “Option Pricing Bonds with Transaction Costs,” working paper, University of Chicago.
Constantinides, G. M., and T. Zariphopoulou. (1993). “Bounds on Prices of Contingent Claims in an Intertemporal Economy with Proportional Transaction Costs,” working paper, University of Chicago.
Cootner, P. (1964). The Random Character of Stock Market Prices. Cambridge: MIT Press.
Davis, M. H. A., and J. M. C. Clark. (1994). “A Note on Super Replicating Strategies,” Phil. Trans. Roy. Soc. London Ser., A347, 485–494.
Davis, M. H. A., V. G. Panas, and T. Zariphopoulou. (1993). “European Option Pricing with Transaction Costs,” SIAM J. Control Optim. 31, 470–493.
Dixit, A. (1991). “A Simplified Treatment of Some Results Concerning Regulated Brownian Motion,” Journal of Economic Dynamics and Control 15, 657–674.
Edirisinghe, C., V. Naik, and R. Uppal. (1993). “Optimal Replication of Options with Transaction Costs and Trading Restrictions,” Journal of Financial and Quantitative Analysis 28, 117–138.
El Bied, S., L. Martellini, and P. Priaulet. (2000). “Optimal asset management in the presence of transaction costs,” working paper, University of Southern California.
El Karoui, N., and H. Geman. (1994). “A Probabilistic Approach to the Valuation of General Floating-Rate Notes with an Application to Interest Rate Swaps,” Advances in Futures and Options Research, 7, 47–64.
Fama, E. F. (1965). “The Behavior of Stock Market Prices,” Journal of Business 38.
Grannan, E. R., and G. H. Swindle. (1996). “Minimizing Transaction Costs of Option Hedging Strategies,” Mathematical Finance 6, 341–364.
Henrotte, P. (1993). “Transaction Costs and Duplication Strategies,” working paper, Stanford University and Groupe HEC.
Hodges, S. D., and A. Neuberger. (1989). “Optimal Replication of Contingent Claims under Transaction Costs,” Review of Futures Market 8, 222–239.
Hoggard, T., A. E. Whalley, and P. Wilmott. (1994). “Hedging Option Portfolios in the Presence of Transaction Costs,” Adv. Futures Opt. Res. 7, 21.
Jegadeesh, N. (1990). “Evidence of Predictable Behavior of Security Return,” The Journal of Finance 45, 881–898.
Jouini, E. and H. Kallal. (1995). “Martingales and Arbitrage in Securities Markets with Transaction Costs,” The Journal of Economic Theory 6, 178–197.
Lacoste, V. (1996). “Wiener Chaos: A New Approach to Option Hedging,” Mathematical Finance 6, 197–213.
Lehmann, B. (1990). “Fads, Martingales and Market Efficiency,” Quarterly Journal of Economics 105, 1–28.
Leland, H. E. (1985). “Option Pricing and Replication with Transaction Costs,” The Journal of Finance 40, 1283–1301.
Magill, M. J. P., and G. M. Constantinides. (1976). “Portfolio Selection with Transaction Costs,” Journal of Economic Theory 13, 245–63.
Markowitz, H. (1952). “Portfolio Selection,” The Journal of Finance 77–91.
Martellini, L., and P. Priaulet. (2000a). “Optimal Dynamic Hedging in the Presence of Transaction Costs: An Empirical Investigation,” working paper, University of Southern California.
Martellini, L., and P. Priaulet. (2000b). “Fixed-Income Securities: Dynamic Methods for Pricing and Hedging Interest Rate Risk,” Frontiers in Finance. John Wiley.
Merton, R. C. (1990). Continuous-Time Finance. Oxford: Basil Blackwell.
Naik, V. (1995). “Finite State Securities Markets Models and Arbitrage.” In Handbooks in Operation Research and Management Science Vol. 9 Finance, R. Jarrow et al. Editions, Amsterdam: North Holland.
Ortu, F. (2000). “Arbitrage, Linear Programming and Martingales in Securities Markets with Bid-Ask Spreads,” Decisions in Economics and Finance, forthcoming.
Roll, R. (1984). “A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market,” The Journal of Finance 39, 115–134.
Soner, H. M., S. Shreve and J. Cvitanic. (1995). “There is No Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs,” Annals of Applied Probability 5 (2), 327–355.
Toft, K. (1996). “On the Mean-Variance Trade-Off in Option Replication with Transaction Costs,” Journal of Financial and Quantitative Analysis 31, 233–263.
Whalley, A E., and P. Wilmott. (1993). “A Hedging Strategy and Option Valuation Model with Transaction Costs,” OCIAM working paper, Mathematical Institute, Oxford.
Whalley, A. E., and P. Wilmott. (1997). “An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs,” Mathematical Finance Vol. 7, No. 3, 307–324.
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Martellini, L. Efficient Option Replication in the Presence of Transactions Costs. Review of Derivatives Research 4, 107–131 (2000). https://doi.org/10.1023/A:1009632624999
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DOI: https://doi.org/10.1023/A:1009632624999