Liquidity costs: a new numerical methodology and an empirical study

TL;DR

This paper introduces a new numerical method using stochastic gradient algorithms to optimize hedging strategies for rate swaps considering liquidity costs, validated through numerical experiments and algorithm variants.

Contribution

The paper presents an efficient stochastic gradient-based algorithm for approximating optimal hedging strategies in the presence of liquidity costs, avoiding complex stochastic control solutions.

Findings

The proposed algorithm effectively computes near-optimal strategies.

Numerical experiments validate the algorithm's accuracy and efficiency.

Different algorithm variants show robustness across parameter settings.

Abstract

We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error. We here propose an efficient algorithm based on the stochastic gradient method to compute an approximate optimal strategy without solving a stochastic control problem. We validate our algorithm by numerical experiments. We also develop several variants of the algorithm and discuss their performances in terms of the numerical parameters and the liquidity cost.