Stochastic dominance bounds on derivatives prices in a multiperiod economy with proportional transaction costs. (English) Zbl 1131.91332

Summary: By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option. A tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put. These results jointly impose tight upper and lower bounds on the implied volatility.


91B28 Finance etc. (MSC2000)
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[1] Avellaneda, M.; Paras, A., Optimal hedging portfolios for derivative securities in the presence of large transaction costs., Applied mathematical finance, 1, 165-194, (1994)
[2] Bensaid, B.; Lesne, J-P.; Pagés, H.; Scheinkman, J., Derivative asset pricing with transaction costs, Mathematical finance, 2, 63-86, (1992) · Zbl 0900.90100
[3] Black, F.; Scholes, M.S., The pricing of options and corporate liabilities, Journal of political economy, 81, 637-654, (1973) · Zbl 1092.91524
[4] Boyle, P.P.; Vorst, T., Option replication in discrete time with transaction costs, Journal of finance, 47, 271-293, (1992)
[5] Brennan, M.J.; Schwartz, E.S., Alternative investment strategies for the issuers of equity linked life insurance policies with an asset value guarantee, Journal of business, 52, 63-93, (1979)
[6] Constantinides, G.M., Multiperiod consumption and investment behavior with convex transactions costs, Management science, 25, 1127-1137, (1979) · Zbl 0466.90005
[7] Constantinides, G.M.; Zariphopoulou, T., Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences, Finance and stochastics, 3, 345-369, (1999) · Zbl 0935.91014
[8] Constantinides, G.M.; Zariphopoulou, T., Bounds on derivative prices in an intertemporal setting with proportional transaction costs and multiple securities, Mathematical finance, 11, 331-346, (2001) · Zbl 0980.91019
[9] Davis, M.H.A., Clark, J.M.C., 1993. Analysis of financial models including transaction costs. Royal Society Discussion Meeting in Mathematical Models in Finance, November 10-11, London.
[10] Davis, M.H.A.; Panas, V.G.; Zariphopoulou, T., European option pricing with transaction costs, SIAM journal of control and optimization, 31, 470-493, (1993) · Zbl 0779.90011
[11] Edirisinghe, C.; Naik, V.; Uppal, R., Optimal replication of options with transactions costs and trading restrictions, Journal of financial and quantitative analysis, 28, 117-138, (1993)
[12] Figlewski, S., Options arbitrage in imperfect markets, Journal of finance, 44, 1289-1311, (1989)
[13] Grannan, E.R.; Swindle, G.H., Minimizing transaction costs of option hedging strategies, Mathematical finance, 6, 341-364, (1996) · Zbl 0915.90019
[14] Hodges, S.D.; Neuberger, A., Optimal replication of contingent claims under transaction costs, Review of futures markets, 8, 222-239, (1989)
[15] Hoggard, T., Whalley, A. E., Wilmott, P., 1993. Hedging option portfolios in the presence of transaction costs. In: Chance, D.M., Trippi, R.R. (Eds.), Advances in Futures and Options Research, vol. 7. JAI Press, Greenwich.
[16] Leland, H.E., Option pricing and replication with transactions costs, Journal of finance, 40, 1283-1301, (1985)
[17] Levy, H., Upper and lower bounds of put and call option value: stochastic dominance approach, Journal of finance, 40, 1197-1217, (1985)
[18] Merton, R. C., 1990. Continuous-Time Finance. Basil Blackwell, Oxford. · Zbl 1019.91502
[19] Perrakis, S., Option bounds in discrete time: extensions and the pricing of the American put, Journal of business, 59, 119-141, (1986)
[20] Perrakis, S., Preference-free option prices when the stock return can go up, go down, or stay the same, Advances in futures and options research, 3, 209-235, (1988)
[21] Perrakis, S.; Lefoll, J., Derivative asset pricing with transaction costs: an extension, Computational economics, 10, 359-376, (1997) · Zbl 0893.90044
[22] Perrakis, S.; Ryan, P.J., Option pricing bounds in discrete time, Journal of finance, 39, 519-525, (1984)
[23] Ritchken, P.H., On option pricing bounds, Journal of finance, 40, 1219-1233, (1985)
[24] Ritchken, P.H.; Kuo, S., Option bounds with finite revision opportunities, Journal of finance, 43, 301-308, (1988)
[25] Soner, H.M.; Shreve, S.E.; Cvitanic, J., There is no nontrivial hedging portfolio for option pricing with transaction costs, The annals of applied probability, 5, 327-355, (1995) · Zbl 0837.90012
[26] Toft, K.B., On the Mean-variance tradeoff in option replication with transaction costs, Journal of financial and quantitative analysis, 31, 233-263, (1996)
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