In the Black-Scholes Framework,return Volatility Is Assumed to Be Constant

question 6

Multiple Choice

In the Black-Scholes framework,return volatility is assumed to be constant over the life of the option.This is not theoretically appropriate for pricing options on (default-risk-free) bonds because

• A)Empirically,interest rates are known to change over time,so bond volatility will change over time.
• B)Even if interest rates are constant over time,the duration of the bond will change over time,and duration is a measure of volatility.
• C)Constant return volatility on a zero-coupon bond is possible only if the bond price does not change over time.
• D)The bond price at maturity is known for certain,so volatility must go down as maturity approaches.

---

Definitions:

Graph Equations

A visual representation of the solutions to an equation, typically plotted on a coordinate plane.

Hyperbola

A type of conic section that appears as two symmetrical curves, defined mathematically as the set of points where the difference of the distances to two foci is constant.

Standard Form

A way to write numbers using the digits 0-9, where each digit is given a place value, or for equations, a specific arrangement, such as \(Ax + By = C\) for linear equations.

Method of Substitution

A technique used to solve systems of equations where one equation is solved for one variable in terms of the others, and then substituted into another equation.