Иммунизация несбалансированных денежных потоков на основе расстояния Монжа – Канторовича

Экономический журнал Высшей школы экономики. 2024. Т. 28. № 3. С. 412–426.

Kurochkin S. V., Rodina V.

One of the key techniques in the fixed-income portfolio management is immunization which involves a managed change in the portfolio value under interest rate fluctuations given a similar pattern in a portfolio of liabilities. Since the classic work by Redington, scholars have developed a variety of immunization models. Yet, these models are built on restrictive assumptions that a stream of liabilities is constrained to a single payment while the yield curve and/or its possible shift have a certain shape (a flat yield curve and a parallel shift, respectively, in early works). In their previous paper, the authors obtained a solution to the optimal immunization problem for the case when a stream of liabilities and the shape of and a shift in the yield curve are of arbitrary structure. In this paper, the results are first generalized to the case when the present values of the streams of assets and liabilities are not equalized. The optimization problem is formulated as an unbalanced optimal transport problem. The authors have developed an algorithm for constructing an optimal immunization portfolio which is practically feasible and has a straightforward financial interpretation. The solution is based on the proximity measure between payment streams, which is known by multiple terms (Earth Mover's Distance, the Wasserstein distance, the Monge-Kantorovich metric) and is widely used in modern machine learning. Additionally, the authors have established a set of relationships that relate the Wasserstein distance between payment streams to their Fischer-Weil durations.

Keywords: immunization, процентный риск, Wasserstein distance, interest rate risk, иммунизация, расстояние Вассерштейна