Deep treasury management for banks

Abstract

Retail banks use Asset Liability Management (ALM) to hedge interest rate risk associated with differences in maturity and predictability of their loan and deposit portfolios. The opposing goals of profiting from maturity transformation and hedging interest rate risk while adhering to numerous regulatory constraints make ALM a challenging problem. We formulate ALM as a high-dimensional stochastic control problem in which monthly investment and financing decisions drive the evolution of the bank's balance sheet. To find strategies that maximize long-term utility in the presence of constraints and stochastic interest rates, we train neural networks that parametrize the decision process. Our experiments provide practical insights and demonstrate that the approach of Deep ALM deduces dynamic strategies that outperform static benchmarks.

Keywords: Asset Liability Management (ALM); deep hedging; deep stochastic control; dynamic strategies; machine learning in finance; reinforcement learning; term structure modeling.

Figure 1

Historical CHF term structures—The optimal balance sheet structure and the interest rate exposure of a bank highly depend on the current and future states of the yield curve. Historically, the term structure featured extremely high and inverted yields in the early 90s. Since the mid 90s, there has been a long-term trend of falling yields with presumed trend reversal during the year 2022.

Figure 2

Computational flow (DSC)—This figure illustrates the order of computations made in the DSC algorithm to reach the final state x_T from the initial state x₀. The figure is largely based on Figure 1 from Han and Weinan (2016), but extended by the memory cells h₀, h₁, …, h_T−1.

Figure 3

Simulated 1m-Yields (HJM-PCA)—In the plot on the left-hand side, the solid line represents the median 1m-yield over all scenarios. The darker shaded area is enclosed by lines representing the 25% quantile and the 75% quantile. The lighter shaded area is enclosed by the 5% quantile and the 95% quantile.

Figure 4

Simulated yield curves in 5y—The left-hand side shows a random sample of the terminal term structure simulated with HJM-PCA over a horizon of 5y. We encounter a rich family of different shapes. On the right-hand side, we see a random sample generated by a Hull-White-extended Vašiček model calibrated to the recent past; e.g., see Brigo and Mercurio (, Chapter 5). We chose the long-term mean time-dependent to match the initial yield curve and left the mean reverting rate as well as the instantaneous volatility constant. Regarding Deep ALM, the encountered diversity is not sufficient to get convincing results.

Figure 5

Decision network architecture—arrows annotated with “NN” denote a forward pass through a shallow neural network, the annotation “FC” denotes a single fully connected layer. The notations scl and dist are used to indicate the scale and distribution decisions made by the model.

Figure 6

Equity ratio histogram—This chart depicts the final equity distribution of Deep ALM after 5y and 15y, respectively, compared to the most competitive benchmark strategy.

Figure 7

Constant benchmark strategies—The vertical axis denotes the scales of total investment and financing relative to the maturing positions, i.e., $\parallel a_t^B{\parallel }_1/{\pi }^{(1)}(B_t)$ and $\parallel a_t^K{\parallel }_1/{\pi }^{(1)}(K)$. The variable d above the columns specifies the duration of the portfolios.

Figure 8

Investment and financing volume—Investment volume refers to $\parallel a_t^B{\parallel }_1$ and financing volume refers to $\parallel a_t^K{\parallel }_1$. The solid line indicates the median level of $\parallel a_t^B{\parallel }_1$ or $\parallel a_t^K{\parallel }_1$ across all 1 600 validation scenarios. The darker shaded area is enclosed by the 25% quantile and the 75% quantile. The lighter shaded area is enclosed by the 5% quantile and the 95% quantile. The gray vertical lines indicate the times at which the annual step occurs, i.e., dividends are paid out and the minimum return constraint is checked. The same layout is used for all plots in this section.

Figure 9

LCR and CMR.

Figure 10

Equity/RWA—Note that the dividend payouts lead to downward jumps in the bank's equity. In the figures, this impact seems to be delayed by one period. This is because the equity value is recorded at the end of the restructure step; but the annual step is performed after the balance sheet restructuring.

Figure 11

Interest rate sensitivity—Whereas the durations in this chart only account for parts of the balance sheet (i.e., the duration structure of the balance sheet will not necessarily be inverted by the end), the interest rate sensitivity is measured holistically.

Figure 12

Yield curve scenarios (5y)—Scenarios steep on the left-hand side and inversion on the right-hand side.

Figure 13

Decisions (5y).

Figure 14

Sensitivity gaps (5y).

Figure 15

Yield curve scenarios (15y)—Scenarios incr on the left-hand side and inv_and_back on the right-hand side.

Figure 16

Decisions (15y).

Figure 17

Sensitivity gaps (15y).

Figure 18

Swap volumes—Note that the bond volume refers to the value of bonds purchased and issued in mCHF. The swap volume refers to the notional amount in mCHF of swaps entered into this period. The swap value is, aside form spreads, zero at issuance.

Figure 19

Swap decisions (5y).