# 31

# Application to Banking Book Activities

*Qui ne peut moissonner, qu'il se contente de glaner*.

In this chapter, we will see through examples how the optimization programme can be applied to Banking Book activities:

- demand deposit hedging;
- prepayment hedging;
- Capital Book hedging;
- credit risk hedging.

## 31.1 DEPOSIT ACCOUNTS: VALUATION AND HEDGING IN AN ECONOMIC CAPITAL APPROACH USING THE GRID METHODOLOGY

We will start by introducing the optimization programme for a bank constituted only with demand deposits.

We will exclude the perequations from the modelling since our optimization programme will be based on a one period optimization. Indeed, we will consider just the economic value of the existing clients.

### 31.1.1 Definitions

We denote by K(t) the total amount of deposits without maturity at time t. We assume that no interest is paid to the deposit holders. The total amount of deposits associated with the existing clients (excluding new production) follows a diffusion process under the real historic probability Q_{REAL}:

where W_{K} is a Brownian motion.

We denote by r(t) the spot interest rate at date t and B(t, T) the discount factor between t and T. Under risk neutral probability, this factor follows:

### 31.1.2 Valuation formula

Our first goal is to calculate the market value of ...