A RISK MANAGER IS PRICING A 10-YEAR CALL OPTION ON 10-YEAR TREASUR...

16.

A risk manager is pricing a 10-year call option on 10-year Treasuries using a successfully tested pricing model.

Current interest rate volatility is high and the risk manager is concerned about the effect this may have on

short-term rates when pricing the option. Which of the following actions would best address the potential for

negative short-term interest rates to arise in the model?

a.

The risk manager uses a normal distribution of interest rates.

b.

When short-term rates are negative, the risk manager adjusts the risk-neutral probabilities.

c.

When short-term rates are negative, the risk manager increases the volatility.

d.

When short-term rates are negative, the risk manager sets the rate to zero.

Correct Answer: d

Rationale:

Negative short-term interest rates can arise in models for which the terminal distribution of interest rates

follows a normal distribution. The existence of negative interest rates does not make much economic sense since

market participants would generally not lend cash at negative interest rates when they can hold cash and earn a

zero return. One method that can be used to address the potential for negative interest rates when constructing

interest rate trees is to set all negative interest rates to zero. This localizes the change in assumptions to points in

the distribution corresponding to negative interest rates and preserves the original rate tree for all other observa-

tions. In comparison, adjusting the risk neutral probabilities would alter the dynamics across the entire range of

interest rates and therefore not be an optimal approach.

When a model displays the potential for negative short-term interest rates, it can still be a desirable model to use in

certain situations, especially in cases where the valuation depends more on the average path of the interest rate,

such as in valuing coupon bonds. Therefore, the potential for negative rates does not automatically rule out the use

of the model.

Section: Market Risk Measurement and Management

Reference:

Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 9, “The Art of Term Structure Models:

Drift.”

Learning Objective:

Describe methods for addressing the possibility of negative short-term rates in term structure

models.

2015 Financial Risk Manager (FRM®) Practice Exam