Исследование модифицированной стратегии последовательного хеджирования с наклонной полосой нечувствительности

Abstract

In this article The stop-loss start-gain strategy modification with tilt deadband is studied. The top line of this band is tilted. During the research mathematical model with discrete pricing process was examined. The increments of this process have a normal distribution with a constant nonzero mean and constant dispersion. The article considers the distribution of the number of intersections of a nonrectilinear strip by a discrete Gaussian walk. Formulas that allow to specify the distribution of the number of intersections of the strip in the directions “bottomup” and “top-down” were deduced. An algorithm was developed to calculate the number of these intersections and evaluate the conditional probability of the transition. In addition, the dependence of the average hedger losses while using this strategy on the slope coefficient of the upper boundary of the dead band and the band width was considered. Using the Monte Carlo simulation, an algorithm was developed to find the optimal width and slope of the strip. During the numerical experiments, the dependence was revealed and the optimal slope coefficient was determined for the given parameters. Experimental work confirmed the correctness of the proposed algorithms and proved the effectiveness of this modification in comparison with the use of a strategy with a straight strip.