Questions from Business Statistics

Q: Calculate the price of an option that caps the 3-month

Calculate the price of an option that caps the 3-month rate, starting in 15 months’ time, at 13% (quoted with quarterly compounding) on a principal amount of $1,000. The forward interest rate for the...

Q: If the yield volatility for a 5-year put option

If the yield volatility for a 5-year put option on a bond maturing in 10 years’ time is specified as 22%, how should the option be valued? Assume that, based on today’s interest rates the modified du...

Q: Explain whether any convexity or timing adjustments are necessary when:

Explain whether any convexity or timing adjustments are necessary when: (a) We wish to value a spread option that pays off every quarter the excess (if any) of the 5-year swap rate over the 3-month LI...

Q: a) What is the second partial derivative of P(t

a) What is the second partial derivative of P(t,T) with respect to r in the Vasicek and CIR models? (b) In Section 31.2,
is presented as an alternative to the usual duration measure, D. What is a sim...

Q: Observations spaced at intervals t are taken on the short rate.

Observations spaced at intervals t are taken on the short rate. The ith observation is ri (1 ≤ i ≤ m). Show that the maximum-likelihood estimates of a, b*, and  in Vasicek’s model are given by maxi...

Q: Suppose that the risk-free zero curve is flat at 6

Suppose that the risk-free zero curve is flat at 6% per annum with continuous compounding and that defaults can occur at times 0.25 years, 0.75 years, 1.25 years, and 1.75 years in a 2-year plain vani...

Q: Suppose that a =0:1 and b=0:

Suppose that a =0:1 and b=0:1 and in both the Vasicek and the Cox, Ingersoll, Ross model. In both models, the initial short rate is 10% and the initial standard deviation of the short-rate change in a...

Q: Calculate the price of a 2-year zero-coupon bond

Calculate the price of a 2-year zero-coupon bond from the tree in Figure 32.4.

Q: What does the calibration of a one-factor term structure model

What does the calibration of a one-factor term structure model involve?

Q: Use the DerivaGem software to value
,
,
, and
European

Use the DerivaGem software to value
,
,
, and
European swap options to receive fixed and pay floating. Assume that the 1-, 2-, 3-, 4-, and 5-year interest rates are 6%, 5.5%, 6%, 6.5%, and 7%, res...