# Let today be November 3, 2008. (a) Use the LIBOR rate and the swap data on November

## Question:

Let today be November 3, 2008.
(a) Use the LIBOR rate and the swap data on November 3, 2008 in Table 11.26 and fit the LIBOR curve.
(b) From the LIBOR discount curve, fit the Ho-Lee model of the interest rates, with quarterly steps. You can use the LIBOR volatility reported in the text, or estimate the LIBOR volatility yourself. Data on LIBOR are available on the British Bankers Association Web site (www.baa.org.uk).
(c) Compare risk neutral expected future interest rates to the continuously compounded interest rates. How does the difference depend on the assumed volatility of the interest rate? (For each assumed volatility of the interest rate,
Issuer...................................... HAL Corp.
Rating .................................... AAA
Pricing Date .............................. November 3, 2008
Maturity Date ............................ November 3, 2013 100
Principal.................................... 100
Coupon Frequency ....................... Quarterly
Coupon.....................................5.4% if reference rate within corridor bounds; 0% otherwise 1%
Corridor Lower Bound .................. 1%
Corridor Upper Bound ................... 5%
Reference Rate..............................3 Month LIBOR on previous fixing date
You need to refit the tree to make sure that the tree correctly reflects the forward rates. Do the exercise for 3 values of volatility).
(d) Compute the value of 1-year, 2-year and 3-year cap. Compare your value with the one in the data, in Table 11.26.

(e) Compute the value of a 5-year swap (the swap rate in Table 11.26) with quarterly payments (i.e., assume that both floating and fixed payers pay at quarterly frequency). Is the value of the swap obtained from the tree what you would expect from first principles?
(f) Use the swap tree computed in Part (e) to compute the value of 1-year, at-the-money swaption to enter into a 4-year swap.

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