Comment on the following statement: "If an interest-rate model allows the possibility of negative interest rates, then it is not useful in practice."

What will be an ideal response?

All because an interest-rate model allows for the possibility of negative interest rates does not imply it is not useful. Furthermore, allowing for the possibility of a negative interest rate does not mean the model will produce a negative interest rate. Allowing for the possibility of
a negative interest rate may even be viewed as realistic since there are documented occasions (albeit rare) where negative rates have occurred. More details are supplied below.

Our focus is on nominal interest rates. Although we know that real interest rates (i.e., a nominal rate minus an inflation premium) in an economy have been negative, it is generally thought that it is impossible for the nominal interest rate to be negative. The reason is that if the nominal rate is negative, investors will simply hold cash. However, there have been time periods in countries where interest rates have been negative for a brief time period, refuting the notion that investors would not be willing to lend at negative interest rates.

For example, during the Great Depression in the United States, financial historians have identified periods where Treasury securities traded at a negative yield. Japan provides another example. In early November 1998, Western banks charged Japanese banks interest of 3 to 6 basis points to hold 2- or 3-month yen deposits that Japanese banks were unwilling to deposit with local institutions because of the perceived instability of Japan's financial system. The yield on
3-month Japanese Treasury bills during one trading day in November 1998 fell to minus 5 basis points, although the closing yield was positive.

It is fair to say that although negative interest rates are not impossible, they are unlikely. The significance of this is that one might argue that an interest-rate model should not permit negative interest rates (or negative rates greater than a few basis points). Yet, this may occur in a model where volatility is measured in terms of basis points—as in the normal model. In contrast, if interest-rate volatility is measured in terms of the percentage yield change (i.e., logarithm of the yield ratio), interest rates cannot be negative. Hence, a stated advantage of using an interest-rate model whose volatility is dependent on the level of interest rates is that negative returns are not possible.