J. Phys. IV France 08 (1998) Pr6-3-Pr6-12
Risk-return arguments applied to options with trading costsE. Aurell1, 2 and K. Zyczkowski3
1 Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
2 PDC/KTH, 100 44 Stockholm, Sweden
3 Department of Physics, Jagiellonian University, 30 057 Krakow, Poland
We study the problem of option pricing and hedging strategies within the frame-work of risk-return arguments. An economic agent is described by a utility function that depends on profit (an expected value) and risk (a variance). In the ideal case without transaction costs the optimal strategy for any given agent is found as the explicit solution of a constrained optimization problem. Transaction costs are taken into account on a perturbative way. A rational option price, in a world with only these agents, is then determined by considering the points of view of the buyer and the writer of the option. Price and strategy are determined to first order in the transaction costs.
© EDP Sciences 1998