Reduction of the Mean Hedging Transaction Costs

Miklavž Mastinšek

Miklavž Mastinšek

Ključne besede: finančni derivati, transakcijski stroški, delta hedging tehnika

Povzetek

Na finančnih trgih se pri uporabi hedging tehnike pojavijo transakcijski stroški. V tem članku se obravnava problem uporabe delta hedging tehnike ter redukcije proporcionalnih transakcijskih stroškov. V literaturi navedene metode običajno temeljijo le na uporabi tako imenovanega faktorja gama, ki ponavadi predstavlja največji člen v aproksimacijski vrsti. Toda pri opcijah s kratkim časom dospetja, mesec ali nekaj tednov, lahko drugi členi vrste postanejo celo večji. Tedaj so potrebne natančnejše aproksimacije. V tem članku so analizirane aproksimacije višjega reda in njihova uporaba pri zmanjšanju povprečnih proporcionalnih transakcijskih stroškov. Na podlagi analize je podan ustrezno prilagojen faktor delta, s katerim se povprečni aproksimativni proporcionalni transakcijski stroški lahko zmanjšajo. Pripadajoča napaka hedging tehnike se pri tem ne poveča. Za ilustracijo metode je dodanih nekaj primerov.

Prenosi

Biografija avtorja

Miklavž Mastinšek

University of Maribor, Faculty of Economics and Business, Slovenija
E-pošta: miklavz.mastinsek@um.si

Dr. Miklavž Mastinšek is a professor of mathematics at the Department of Quantitative Economic Analysis at the Faculty of Economics and Business, University of Maribor. He teaches mathematics and financial engineering at the Faculty of Economics and Business and the Faculty of Natural Sciences and Mathematics in Maribor. His current fields of research cover stability methods of dynamical systems, functional analysis, financial derivatives analysis, and delta-gamma hedging techniques. Scientific results of his research have been published in internationally renowned scientific and professional journals of mathematics, finance, and operations research.

Literatura

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659. http://dx.doi.org/10.1086/260062

Boyle, P., & Emanuel, D. (1980). Discretely adjusted option hedges. Journal of Financial Economics, 8, 259–282. http://dx.doi.org/10.1016/0304-405X(80)90003-3

Hull, J. C. (2006). Option, futures & other derivatives. Pearson Prentice-Hall.

Leland, H. E. (1985). Option pricing and replication with transaction costs. Journal of Finance, 40, 1283–1301. http://dx.doi.org/10.1111/j.1540-6261.1985.tb02383.x

Mastinsek, M. (2006). Discrete-time delta hedging and the Black-Scholes model with transaction costs. Mathematical Methods of Operations Research, 64, 227–236. http://dx.doi.org/10.1007/s00186-006-0086-0

Mastinsek, M. (2012). Charm-adjusted delta and delta gamma hedging. Journal of Derivatives, 19(3), 69–76. http://dx.doi.org/10.3905/jod.2012.19.3.069

Merton, R. C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141–183. http://dx.doi.org/10.2307/3003143

Toft, K. B. (1996). On the mean-variance tradeoff in option replication with transactions costs. The Journal of Financial and Quantitative Analysis, 31(2), 233–263. http://dx.doi.org/10.2307/2331181