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A combinatorial model of option portfolio

Vol. 9, Iss. 25, JULY 2016

PDF  Article PDF Version

Received: 20 April 2016

Received in revised form: 7 June 2016

Accepted: 14 June 2016

Available online: 18 July 2016

Subject Heading: FINANCIAL INSTRUMENTS

JEL Classification: C58, C61, G11, G17, G24

Pages: 2-13

Mitsel' A.А. Tomsk State University of Control Systems and Radio Electronics, Tomsk, Russian Federation
maa@asu.tusur.ru

Semenov M.E. National Research Tomsk Polytechnic University, Tomsk, Russian Federation
sme@tpu.ru

Fat'yanova M.E. National Research Tomsk Polytechnic University, Tomsk, Russian Federation
mef1@tpu.ru

Subject The study addresses an approach to building complex portfolios of stock options.
Objectives The aim is to design complex portfolios, namely, bull and bear market collars based on equity options. The objectives are to study the basic procedure for building complex portfolios of equity options; to implement the proposed approach using the MATLAB software.
Methods The optimum plan for call and put options is prepared under the Simplex method (for the non-integer plan) and the Monte-Carlo method (for integer plan) to solve the linear programming problem.
Results We built two complex portfolios based on bull and bear structured collars for falling and rising price of asset. The optimum plan and the objective function value were obtained under the Simplex method and the Monte-Carlo method.
Conclusions and Relevance The Simplex method allows us to find the non-integer optimum plan, therefore, it is necessary to round the obtained result and check all restrictions. To eliminate this deficiency, we applied the Monte-Carlo method. The optimum value of the objective function of the bull collar portfolio under the Monte-Carlo method is 1.63 times more than the corresponding value under the Simplex method. The optimum value of the objective function of the bear collar portfolio under the Simplex method in 1.06 times more than the corresponding value under the Monte-Carlo method.

Keywords: call option, put option, integer linear programming, Simplex method, Monte-Carlo method

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