Reading 43/44 - binomial interest option pricing

CFA Level II Fixed Income
#1

I’m having a bit of trouble how to calibrate a binomial interest rate tree. I know that iH = iL[e^2σ]. But how do you get the lowest number (iL)? All the book says is it uses Excel Solver to calculate it but it doesn’t teach you how to do it manually. Can you calculate it from the par yields given?

Pg 358 Ex 8

A three-year floating-rate bond pays annual coupons of one-year Libor (set in arrears) and is floored at 3.00%. The Libor swap curve for one-year, two-year and three-year par yields are 2.5%, 3.0% and 3.5%, respectively, and interest rate volatility is 10%. The value of the floored floater is closest to:

A 100.000

B 100.488

C 103.000

#2

You calculate it based on the spot rates, one year forward rates, volatility, and the current market price, given a binomial scenario of equal probability, and the paths within 95% confidence interval for a logarithmic distribution.

You could use the Ho Lee model to derive them.

The value of a floater is always par. But in the first year, it pays more than the market interest rates because there is a floor. The difference between par and the new market price is 103/1.025 = $100.48