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## A combinatorial model of option portfolio

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 )

Journal: Financial Analytics: Science and Experience, #25, 2016

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.

## The Scenario-Based Approach to Trade in Option Contracts

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

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

Journal: Digest Finance, #1, 2019

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.

## The use of the scenario-based approach for trade in options contracts

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

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

Journal: Financial Analytics: Science and Experience, #1, 2019

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.

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