Questions from Business Statistics

Q: Suppose that all risk-free (OIS) zero rates are

Suppose that all risk-free (OIS) zero rates are 6.5% (continuously compounded). The price of a 5-year semiannual cap with a principal of $100 and a cap rate of 8% (semiannually compounded) is $3. Use...

Q: Show that
, where V1 is the value of a swaption to

Show that
, where V1 is the value of a swaption to pay a fixed rate of
and receive LIBOR between times T1 and T2, f is the value of a forward swap to receive a fixed rate of
and pay LIBOR between...

Q: Suppose that risk-free zero rates and LIBOR forward rates are

Suppose that risk-free zero rates and LIBOR forward rates are as in Problem 29.17. Use DerivaGem to determine the value of an option to pay a fixed rate of 6% and receive LIBOR on a 5-year swap starti...

Q: Explain why a swap option can be regarded as a type of

Explain why a swap option can be regarded as a type of bond option.

Q: Describe how you would (a) calculate cap flat volatilities

Describe how you would (a) calculate cap flat volatilities from cap spot volatilities and (b) calculate cap spot volatilities from cap flat volatilities.

Q: Explain carefully how you would use (a) spot volatilities

Explain carefully how you would use (a) spot volatilities and (b) flat volatilities to value a 5-year cap.

Q: LIBOR zero rates are flat at 5% in the United States

LIBOR zero rates are flat at 5% in the United States and flat at 10% in Australia (both annually compounded). In a 4-year diff swap Australian LIBOR is received and 9% is paid with both being applied...

Q: A bank uses Black’s model to price European bond options. Suppose

A bank uses Black’s model to price European bond options. Suppose that an implied price volatility for a 5-year option on a bond maturing in 10 years is used to price a 9-year option on the bond. Woul...

Q: Calculate the value of a 4-year European call option on

Calculate the value of a 4-year European call option on bond that will mature 5 years from today using Black’s model. The 5-year cash bond price is $105, the cash price of a 4-year bond with the same...

Q: What other instrument is the same as a 5-year zero

What other instrument is the same as a 5-year zero-cost collar where the strike price of the cap equals the strike price of the floor? What does the common strike price equal?