Approximations and asymptotics of upper hedging prices in multinomial models

TL;DR

This paper explores upper hedging prices in multinomial models, demonstrating their convergence to solutions of the Black-Scholes-Barenblatt equation as the number of rounds increases, using linear programming and game-theoretic probability.

Contribution

It provides a detailed exposition and numerical analysis of upper hedging prices, linking discrete multinomial models to continuous limit equations.

Findings

Upper hedging prices converge to Black-Scholes-Barenblatt solutions

Numerical studies illustrate the approximation accuracy

Linear programming effectively computes hedging prices

Abstract

We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to infinity, the upper hedging price of a European option converges to the solution of the Black-Scholes-Barenblatt equation.