Assume Annual Compounding $\sigma = 0.30$ What Is the Price of a One-Year Maturity Cap

question 3

Multiple Choice

Assume annual compounding. The one-year and two-year zero-coupon rates in the BDT model are 6% and 7%. The volatility is given to be $\sigma = 0.30$ . What is the price of a one-year maturity cap on the one-year interest rate at a strike rate of 8% and a notional of $100?

• A) 1.000
• B) 1.025
• C) 1.050
• D) 1.075

---

Definitions:

Exponential Density Function

A probability density function used to model the time between events in a process where events occur continuously and independently at a constant average rate.

Density Function

A mathematical function that describes the probability distribution of a continuous random variable, indicating the likelihood of a variable taking on a particular value.

Exponential Distribution

A probability distribution used to model the time between events in a process where events occur continuously and independently at a constant rate.

Parameter

A measurable feature or characteristic that helps to define or classify a system, often a constant in mathematical models and statistical analyses.