# ABN Amro – The fair value of a mortgage #SWI2017

ABN AMRO is a retail bank and mortgages are an important part of the core business model. The balance sheet covers over EUR. 150 billion in residential mortgages, which is about 40% of the total assets. In order to properly steer the balance sheet and manage the banks risks it is essential to correctly estimate the cash flows resulting from mortgages. During this case we will challenge the banks complex models for modelling mortgages and try to come up with a better approach!

On first sight residential mortgages seem like simple collateralised loans: The bank loans the customer the money to buy a house; And the customer pays back the mortgage over a period of 30 years by monthly instalments, which include interest. The value of such a mortgage as of today could simply be determined by discounting the monthly payments with today’s interest rates. However, mortgages have embedded optionality’s for a client which makes them much more complex. Two common examples of these optionality’s are:

- The prepayment option: This option allows the client to early repay (part of) the loan at any point in time. Prepayments result in a loss of interest for the bank and decrease the value of the mortgage.
- The take-along option: If a client decides sell the house, the client can either use the money to pay-off the mortgage or the client can take along the mortgage to finance a new house.

The client behaviour regarding these options is strongly influenced by many factors such as interest rates, legislation and economic factors. To give an example: In 2006 mortgages were offered at an interest rate of 6% and clients would get about 4% interest on their savings account. Legislation in the Netherlands allows a customer to deduct the payed interest for a mortgage from his or her taxes, lowering the effective interest rate on the mortgage from 6% to 3% (if the customer pays 50% taxes over its income). In 2006 it was, therefore, logical for the client to keep his or her money on the savings accounts (earning 4%) instead of pre-paying the mortgage (saving 3%). As of today (2016) the same customer, however, earns 0.7% on his or her savings account because of the historically low interest rates. The rate on the mortgage has remained unchanged (effectively still 3%) because the client fixed the rate for 20 years in 2006. Therefore, today the same rational client will use savings to pre-pay the mortgage, which is the exact opposite behaviour as compared to 2006.

So what does this mean for the bank? In order to have valued the mortgage and manage its risk properly back in 2006, the bank should have considered that client behaviour in 2016 is significantly different due to a low interest rate environment. The bank has complex mathematical models in place in order to make such predictions on future client behaviour. The development of such models typically includes numerous mathematical techniques including stochastic calculus, regressions on historical data and Monte Carlo simulations over future interest rate paths.

During this case we plan to challenge the banks current models. We will focus on a limited number of optionality’s and see if we can come up with a better way of pricing them than we currently do. We will start by using logical thinking to determine how a rationale customer would behave. Then we will see if this rational can be applied to develop a model based on actual data.

In order to challenge the banks current models we are looking for candidates who have a strong analytical background, who think in a structured and logical way, and who can inspire other people!