Semenov M.E.National Research Tomsk Polytechnic University (TPU), Tomsk, Russian Federation firstname.lastname@example.org ORCID id: not available
Fat'yanova M.E.National Research Tomsk Polytechnic University (TPU), Tomsk, Russian Federation email@example.com ORCID id: not available
Subject Nowadays, traditional methods may hardly forecast how prices for assets will go. The scenario-based approach becomes more widely spread in various sciences, including financial mathematics. The key idea of the scenario-based approach is a scenario tree representing the hierarchical structure of data, outlining how things may unfold, and evaluating the probability. This approach helps model various scenarios of the future situation, thus allowing to make appropriate decisions. Objectives The research produces a one-period scenario tree showing how the price for the asset may develop. We also analyze the sensitivity of the parameter influencing the number of descendants of vertices. Methods The research is based on the economic-mathematic model of the geometric (Brownian) motion, which is expressed through the stochastic differential equation. The model and sensitivity analysis are implemented in MATLAB. We also applied methods of comparative and static analysis, graphic interpretation. Results We constructed a one-period scenario tree for a change in the options price. Having analyzed the sensitivity of the descendant vertex parameter, we determined the optimal range of option strike price intervals. Conclusions and Relevance We chose the geometric motion model as the basis for the scenario-based approach since it helps construct the one-period scenario tree. This approach allows to evaluate the scenario probability. However, its weakness is that it generates the unoptimal number of descendant vertex of a tree. Furthermore, the market situation requires to test the asset for liquidity through various metrics. For example, the number of deals and trading volume.
Var'yash I.Yu., Nikonov I.V. [Macroeconomic forecasting: The composition of probabilities versus the conflict of scenarios]. Finansovaya analitika: problemy i resheniya = Financial Analytics: Science and Experience, 2015, vol. 8, iss. 43, pp. 13–21. URL: Link (In Russ.)
Zubarev A.A., Sbitnev A.E. [Formation of the method of risk analysis of road-building projects based on the scenario approach]. Finansy i kredit = Finance and Credit, 2011, vol. 17, iss. 48, pp. 37–41. URL: Link (In Russ.)
Shapiro V.Ya., Shapiro N.A. [Risk assessment of portfolio investments using Markov chains]. Finansy i kredit = Finance and Credit, 2007, vol. 13, iss. 33, pp. 33–38. URL: Link (In Russ.)
Beketov N.V., Fedorov V.G. [Traditional methods for assessing the effectiveness of investment projects]. Finansovaya analitika: problemy i resheniya = Financial Analytics: Science and Experience, 2008, vol. 1, iss. 3, pp. 75–83. URL: Link (In Russ.)
Shapiro V.Ya., Shapiro N.A. [Modeling of portfolio investments in conditions of negative scenarios of the development of the stock market]. Finansy i kredit = Finance and Credit, 2008, vol. 14, iss. 15, pp. 39–51. (In Russ.)
Mitsel' A.A., Semenov M.E., Fat'yanova M.E. [A combinatorial model of option portfolio]. Finansovaya analitika: problemy i resheniya = Financial Analytics: Science and Experience, 2016, vol. 9, iss. 25, pp. 2–13. URL: Link (In Russ.)
Fatyanova M., Semenov M.E. Model for Constructing an Options Portfolio with a Certain Payo Function. CEUR Workshop Proceedings: Online Proceedings for Scientiﬁc Conferences and Workshops, MM-ITNT 2017, International Conference Information Technology and Nanotechnology. Samara, Samara State University Publ., 2017, vol. 1904, pp. 254–262.
Yashin S.N., Trifonov Yu.V., Koshelev E.V. [Using a real put option to manage risks of cluster's innovation strategy]. Finansy i kredit = Finance and Credit, 2017, vol. 23, iss. 26, pp. 1518–1532. (In Russ.) URL: Link
Gracheva M.V., Petreneva E.A. [Real options as project risk management tools]. Finansovaya analitika: problemy i resheniya = Financial Analytics: Science and Experience, 2016, vol. 9, iss. 10, pp. 2–14. URL: Link (In Russ.)
Huss W.R. A Move Toward Scenario Analysis. International Journal of Forecasting, 1988, vol. 4, iss. 3, pp. 377–388. URL: Link90105-7
Hargitay S.E., Shi-Ming Yu.S. Property Investment Decisions. A Quantitative Approach. Routledge, 1993, 352 p.
Bradfield R., Wright G., Burt G. et al. The Origins and Evolution of Scenario Techniques in Long Range Business Planning. Futures, 2005, vol. 37, iss. 8, pp. 795–812. URL: Link
Mietzner D., Reger G. Advantages and Disadvantages of Scenario Approaches for Strategic Foresight. International Journal of Technology Intelligence and Planning, 2005, vol. 1, no. 2, pp. 220–239. URL: Link
Lindgren M., Bandhold H. Stsenarnoe planirovanie: svyaz' mezhdu budushchim i strategiei [Scenario Planning: The Link between Future and Strategy]. Moscow, Olimp-Biznes Publ., 2009, 256 p.
Coates J.F. Scenario Planning. Technological Forecasting and Social Change, 2016, vol. 113, part A, pp. 99–102. URL: Link
Ponomareva K., Roman D., Date P. An Algorithm for Moment-Matching Scenario Generation with Application to Financial Portfolio Optimization. European Journal of Operational Research, 2015, vol. 240, no. 3, pp. 678–687. URL: Link
Davari-Ardakani H., Aminnayeri M., Seiﬁ A. Multistage Portfolio Optimization with Stocks and Options. International Transactions in Operational Research, 2016, vol. 23, iss. 3, pp. 593–622. URL: Link
Topaloglou N., Vladimirou H., Zenios S.A. Optimizing International Portfolios with Options and Forwards. Journal of Banking & Finance, 2012, vol. 35, pp. 3188–3201. URL: Link
Abramov A.M. [Dynamic optimization of an options portfolio based on a polynomial tree of scenarios]. Problemy analiza riska = Issues of Risk Analysis, 2012, vol. 9, no. 1, pp. 8–23. (In Russ.)
Bachelier L. Théorie de la speculation. Annales Scientifiques de l'École Normale Supérieure, 1900, vol. 17, pp. 21–86.
Eatwell J., Milgate M., Newman P. Ekonomicheskaya teoriya [The World of Economics]. Moscow, INFRA-M Publ., 2004, 931 p.
Wiener N. Differential Space. Journal of Mathematics and Physics, 1923, no. 58, pp. 131–174.
Hull J.K. Optsiony, f'yuchersy i drugie proizvodnye finansovye instrumenty [Options, Futures, and Other Derivatives]. Moscow, Vil'yams Publ., 2018, 1072 p.
Izrailevich S.V., Tsudikman V.Ya. Optsiony: razrabotka, optimizatsiya i testirovanie torgovykh strategii [Options: Development, optimization and testing of trading strategies]. Moscow, Al'pina Pablisher Publ., 2017, 339 p.