Financial Analytics: Science and Experience

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A combinatorial model of option portfolio

Vol. 9, Iss. 25, JULY 2016

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Received: 20 April 2016

Received in revised form: 7 June 2016

Accepted: 14 June 2016

Available online: 18 July 2016


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

Semenov M.E. National Research Tomsk Polytechnic University, Tomsk, Russian Federation

Fat'yanova M.E. National Research Tomsk Polytechnic University, Tomsk, Russian Federation

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


  1. Agasandyan G.A. Formuly pariteta i predstavleniya portfelei dlya dvumernykh optsionov. V. kn: Trudy Shestoi mezhd. konf. MLSD'2012, T. 1 [Formulae of the parity and portfolios for two-dimensional options. In: Proceedings of the Sixth International Conference MLSD'2012, Volume 1]. Moscow, Trapeznikov Institute of Control Sciences of Russian Academy of Sciences Publ., 2012, pp. 174–184.
  2. Zhukov P. Default Risk and Its Effect for a Bond Required Yield and Volatility. Review of Business and Economics Studies, 2014, vol. 2, no. 4, pp. 87–98.
  3. Selyukov V.K., Sorokin I.Yu., Barsukova O.A. [Risk management of the financial organization in the event of portfolio investment in the Russian share market]. Ekonomika i upravlenie: problemy, resheniya = Economics and Management: Problems, Solutions, 2014, no. 1, pp. 33–39. (In Russ.)
  4. Sarafanov N.S. [Strategies of option trading in the stock market under crisis]. Innovatsionnye napravleniya razvitiya APK i povyshenie konkurentosposobnosti predpriyatii, otraslei i kompleksov vklad molodykh uchenykh: m-ly mezhd. konf [Proc. Sci. Conf. Innovative Areas of Agribusiness Development and Increase in the Competitiveness of Enterprises, Branches and Complexes: The Contribution of Young Scientists]. Yaroslavl, Yaroslavl SAА Publ., 2012, pp. 260–266.
  5. Jackwerth J.C. Recovering Risk Aversion from Option Prices and Realized Returns. Review of Financial Studies, 2000, no. 2.
  6. Mysochnik V.A. [Option strategies]. Uspekhi sovremennoi nauki = Modern Science Success, 2015, no. 4, pp. 38–42. (In Russ.)
  7. Kibzun A.I., Sobol' V.R. [Modernizing the strategy of consecutive hedging of option position]. Trudy instituta matematiki i mekhaniki URO RAN = Proceedings of Institute of Mathematics and Mechanics of Ural Branch of RAS, 2013, no. 2, pp. 179–192. (In Russ.)
  8. Kurochkin S.V., Pichugin I.S. [A structured collar: creating complex options]. Rynok tsennykh bumag = Securities Market, 2005, no. 14, pp. 64–68. (In Russ.)
  9. Burenin A.N. Forvardy, f'yuchersy, optsiony, ekzoticheskie proizvodnye [Forwards, futures, options, and exotic derivatives]. Moscow, NTO Publ., 2008, 512 p.
  10. Natenberg Sh. Optsiony: volatil'nost' i otsenka stoimosti. Strategii i metody optsionnoi torgovli [Option Volatility & Pricing: Advanced Trading Strategies and Techniques]. Moscow, Al'pina Pablisherz Publ., 2011, 546 p.
  11. Kurochkin S.V. [The functions of payments implemented through option strategies]. Ekonomika i matematicheskie metody = Economics and Mathematical Methods, 2005, no. 3, pp. 135–137. (In Russ.)
  12. Sukhinin M.F. Chislennoe reshenie zadach lineinogo programmirovaniya i vychislenie granits spektra simmetrichnoi matritsy [Numerical solution to linear programming problems and calculating the spectrum boundaries of the symmetric matrix]. Moscow, Fizmatlit Publ., 2002, 160 p.
  13. Kovalev M.M. Diskretnaya optimizatsiya (tselochislennoe programmirovanie) [Discrete optimization (integer programming)]. Moscow, Librokom Publ., 2011, 191 p.
  14. Ponomarev M.V. Raschet tsen optsionov aziatskogo tipa metodom Monte-Karlo. V kn.: Sbornik trudov molodykh uchenykh i sotrudnikov kafedry vychislitel'noi tekhniki SPbNIU ITMO [Asian option pricing under the Monte Carlo method. In: Collection of works of young scientists and Computer Science Chair staff of ITMO University]. St. Petersburg, ITMO University Publ., 2012, pp. 47–52.

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