*Mrinal K Ghosh and his collaborators came up with an easy-to-use model to calculate loan defaults*

A major challenge that banks face is the non-payment of loans by defaulters. It is therefore in the interest of the banks to be able to predict the likelihood of loan default by companies which borrow money, called credit risk, for which they rely on mathematical models. But the current models employed to determine credit risk are complicated.

It is in the interest of the banks to be able to predict the likelihood of loan default by companies which borrow money, called credit risk, for which they rely on mathematical models. But the current models employed to determine credit risks are complicated

A simpler and easy to use model has now been developed by Mrinal K Ghosh (Professor, Department of Mathematics) and his collaborators to predict whether a borrower will be able to repay the loans in a given time period. He elaborated on the model – in an Institute Colloquium on 22 February 2017 – based on a principle called *Options. *

Consider the following example. A person agrees to sell a piece of real estate to a potential buyer at a pre-determined price, called strike price, to be paid back within a given time period (maturity). The deal is sealed after the buyer pays an initial amount called premium to the seller. The premium given to the seller is the price of an option.

The premium given to the seller is the price of an option

At the end of maturity, depending on the market price, the buyer can either choose to complete the payment or decline purchase of property. If the market price goes down, the buyer may not buy the property, and therefore loses the premium already paid to the seller. On the other hand, if the market price goes beyond the agreed value, then the seller incurs a loss.

Given the volatility of financial markets, what should the price of the option be? This problem was addressed back in 1973 by Fisher Black, Robert Merton and Myron Scholes, who together formulated the Black-Scholes theory of option pricing, which continues to be used even today. For their work, they won the Nobel Prize in 1997. This formula gives a fair estimate of the price of an option by taking into account the current price, strike price and the maturity period.

Ghosh and his team have applied the Black-Scholes theory of option pricing to predict the credit risk for a bank lending money to a company. As a company’s shares are traded in the market (equity), it can be treated similar to the price of an option. This enables the calculation of equity by using the Black-Scholes formula.

In the course of their research, however, Ghosh’s team encountered obstacles which arose while computing debt price because it depends on unobservable parameters involving the asset price. They estimated these parameters using sophisticated mathematical tools which included Non-linear filtering and Expectation-Maximization algorithm.