Question

Let the six-month interest rate be 5% semi-annual. To satisfy no-arbitrage, assume the six month rate...

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?

Homework Answers

Answer #1

Up by 25 bp each six-month for 2 years

nterest 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
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let the six-month interest rate be 5% semi-annual. To satisfy no-arbitrage, assume the six month rate...
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?
A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual compounding) has...
A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual compounding) has a remaining life of nine months.  The six-month LIBOR rate observed three months ago was 4.85% with semi-annual compounding. Today’s three and nine month LIBOR rates are 5.3% and 5.8% (continuously compounded) respectively. From this it can be calculated that the forward LIBOR rate for the period between three- and nine-months is 6.14% with semi-annual compounding. Can anyone explain the steps to calculate the forward...
Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that...
Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that can be locked in for the period between six months and nine months using an FRA is 7%. What arbitrage opportunities are open to investors? All rates are continuously compounded.
Consider six months as one period. Assume that the six-month and one-year spot rates are 2%...
Consider six months as one period. Assume that the six-month and one-year spot rates are 2% and 2.5%, respectively. Assume that six months from now, the six-month spot rate will be either 1.8% or 2.2% with equal probability. What is the price of a security that pays $100 six months from now if the six-month spot rate then is 1.8% and pays $20 otherwise? Semi-annual compounding
A stock price is currently $100. Over each of the next two six-month periods, it is...
A stock price is currently $100. Over each of the next two six-month periods, it is expected to go up by 10% or down by 10%. The risk-free interest rate is 10% per year with semi-annual compounding. Part I. Use the two-steps binomial tree model to calculate the value of a one-year American put option with an exercise price of $101. Part II. Is there any early exercise premium contained in price of the above American put option? If there...
There is a six month European call option available on XYZ stock with a strike price...
There is a six month European call option available on XYZ stock with a strike price of $90. Build a two step binomial tree to value this option. The risk free rate is 2% (per period) and the current stock price is $100. The stock can go up by 20% each period or down by 20% each period. Select one: a. $14.53 b. $17.21 c. $18.56 d. $12.79 e. $19.20
An interest rate swap where the annual fixed rate is 6.00% has a remaining life of...
An interest rate swap where the annual fixed rate is 6.00% has a remaining life of one year. Both floating and fixed rates are paid every six months. The floating payments are indexed on the six-month LIBOR rate. The six-month LIBOR rate observed today is 7% with semi-annual compounding. Today’s LIBOR rates for 6-month and 12-month deposits are 7.5% and 8.0%, respectively. These two rates are annual and continuously compounded. a) Calculate the forward LIBOR rate for the period between...
A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 5% and...
A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that can be locked in for the period between six months and nine months using an FRA is 9%. What arbitrage opportunities are open to the bank? All rates are continuously compounded.
A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 5% and...
A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that can be locked in for the period between six months and nine months using an FRA is 9%. What arbitrage opportunities are open to the bank? All rates are continuously compounded.
A 15-year callable bond is currently issued at market interest rate of 7.67%. Annual coupon rate...
A 15-year callable bond is currently issued at market interest rate of 7.67%. Annual coupon rate is 10.5%. The callable bond will be called in 4 years at $1,100. What is YTC? (Assuming the bond is semi-annually compounding.) 1. 13.15% 2. 8.12% 3. 6.32% 4. 10.50% 5. 5.69%
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT