RUS  ENG
Full version
JOURNALS // Theory of Stochastic Processes // Archive

Theory Stoch. Process., 2007 Volume 13(29), Issue 4, Pages 130–147 (Mi thsp239)

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.

MSC: 62P05, 65K10, 91B28, 90C47

Language: English



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024