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Adapted downhill simplex method for pricing convertible bonds
Kateryna Mishchenkoa, Volodymyr Mishchenkob, Anatoliy Malyarenkoa a Department of Mathematics and physics, Mälardalen University, Box 883, SE-721 23 Västerås, Sweden
b Master student graduated from Royal Institute of Technology,
Stockholm, Sweden
Abstract:
The paper is devoted to modeling optimal exercise strategies of the
behavior of investors and issuers working with convertible bonds.
This implies solution of the problems of stock price modeling, payoff
computation and minimax optimization.
Stock prices (underlying asset) were modeled under the assumption
of the geometric Brownian motion of their values. The Monte Carlo
method was used for calculating the real payoff which is the objective
function. The minimax optimization problem was solved using the
derivative-free Downhill Simplex method.
The performed numerical experiments allowed to formulate recommendations for the choice of appropriate size of the initial simplex in
the Downhill Simplex Method, the number of generated trajectories
of underlying asset, the size of the problem and initial trajectories of
the behavior of investors and issuers.
Keywords:
Convertible bonds, Monte Carlo simulation, optimal strategies, Downhill Simplex method, minimax optimization problem.
Citation:
Kateryna Mishchenko, Volodymyr Mishchenko, Anatoliy Malyarenko, “Adapted downhill simplex method for pricing convertible bonds”, Theory Stoch. Process., 13(29):4 (2007), 130–147
Linking options:
https://www.mathnet.ru/eng/thsp239 https://www.mathnet.ru/eng/thsp/v13/i4/p130
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Abstract page: | 96 | Full-text PDF : | 39 | References: | 15 |
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