Question

Let the six-month interest rate be 5% semi-annual. To satisfy no-arbitrage, assume the six month rate moves up or down by 25 bp each six-month period with equal probability. Build an interest rate tree and value a two-year, 5.5% callable bond that can only be called at six-months or one-year for par ($100). What is the value of the embedded option?

Answer 1

Up by 25 bp each six-month for 2 years

Interest Rate	Year	Carry Forward Amount	Interest	Principal +Interest
5.00%	0.5	100.000	5.000	105.000
5.25%	1.0	105.000	5.513	110.513
5.50%	1.5	110.513	6.078	116.591
5.75%	2.0	116.591	6.704	123.295

Down by 25 bp each six-month for 2 years

Interest Rate	Year	Carry Forward Amount	Interest	Principal +Interest
5.00%	0.5	100.000	5.000	105.000
4.75%	1.0	105.000	4.988	109.988
4.50%	1.5	109.988	4.949	114.937
4.25%	2.0	114.937	4.885	119.822