Adapted Downhill Simplex Method for Pricing Convertible Bonds

TL;DR

This paper develops an adapted downhill simplex method to optimize pricing strategies for convertible bonds, incorporating stock price modeling, payoff calculation, and min-max optimization.

Contribution

It introduces a modified downhill simplex algorithm tailored for the complex optimization problem in convertible bond pricing.

Findings

Guidelines for choosing initial simplex size

Optimal number of Monte Carlo trajectories

Impact of problem size and initial conditions

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 min-max 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 min-max 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.