MATH133A California Irvine Derivative Market Problems Paper

Upon graduating from UCI, you start a job in finance earning $72,000 per year and decides to buy a home. You can afford to pay no more than $3,000 per month for the monthly payment on 30-year fixed rate home loan(mortgage) and the current conventional 30-year fixed mortgage interest rate you qualify to borrow at is 5%
What is the maximum size home loan you can afford?
Suppose you borrow the maximum loan amount found in part(a). How much total interest do you pay in the first 2 month?
Suppose black rock stock is trading at $400 and pays a discrete dividend of $3.00 to its sharebolders once per quarter, the first dividend of $3 to be paid in 0.25 years from today, the second dividend of $3 to be paid in 0.5 years from today, the third dividend of $3 to be paid in 0.75 years from today, and the fourth dividend of $3 to be paid in 1 year from today. The continuously compound risk-free interest rate that you can lend or borrow at is 8%. In this problem, you are to use continuous compounding of interest in all computations.
A)What is the fair value price for a one-year prepaid forward contract on BLK?
B)Suppose the market prices for a normal(not prepaid) 1-year forward contract on Blackrock are as follows:
a)Bid price for BLK forward contract:$520.95
b)Ask price for BLK contract: $530.95
Does an arbitrager opportunity exist? If so, specify the exact components of the portfolio you need to capture the arbitrage, and the exact arbitrage profit.
3. Your are a bond portfolio manager at Blackrock and the investment committee has asked you to buy a bond with price B1, and sell short a certain quantity N of a second bond with price B2
Bond with price B1 is a 1-year zero coupon bond with a yield-to-maturity’s of 1%
Bond with price B2 is a 2-year zero coupon bond with a yield-to-maturity of 2%
The resulting portfolio value is II = B1-N*B2
A)How would you choose N to optimally hedge the interest rate exposure of the portfolio II and thus minimize its sensitivity to interest rate changes? Find a numerical value for N.
B)Using the value of N that you found in part (a), what is your portfolio’s profit or loss if both of the yield-to-maturities of bond B1 and B2 suddenly decrease by 1%? Round your numerical answer to the nearest 4th-decimal place.
4. Consider this table of risk-free zero coupon bond (ZCB) prices:
Quarter
1
2
3
4
5
6
7
8
ZCB
0.9804
0.9612
0.9423
0.9238
0.9057
0.8880
0.8706
0.8535
A)Given the zero coupon bond prices in the table above, what is the 8th quarter interest rate swap price?
B)Suppose there is an abrupt stock market crash and resulting flight to quality which investors sell Rosalyn assets such as stocks and aggressively buy risk-free bond. Consequently all of the zero coupon bond prices in the table suddenly increase by 0.01. What os the new 8th quarter interest rate swap price?
5. An investor enters into a 2-year swap agreement to purchase crude oil at $51.25 per barrel. Soon after the swap is created, forward prices rise and the new 2-year swap price is $61.50. If interest rate are 1% and 2% on 1st and 2nd year zero coupon government bonds, respectively, what is the gain or loss to be made from unwrapping the original swap agreement?
6. An iron butterfly, also known as the iron fly, is the name of an advanced, neutral-outlook options trading strategy that involves buying and holding four different option at three different strike prices. Suppose you construct an iron butterfly position on Blackrock stock as follows, with Blackrock currently trading at $400. All options have an expiration date of one year from today and the constant a>0.
1. Long one out-of-the-money put option with premium $5 and strike price of 400-a
2. Short one at-the-money put with premium $35
3.Short one at-the-money call with premium $45
4.Long one out-of-the-money call with with premium $15 and strike price of 400+a
A) Draw the profit diagrams at expiration for the Blackrock iron butterfly, with the constant a as a free parameter, assuming the risk-free interest rate is zero.
B) For what range of values for a does an arbitrage opportunity exist.
Suppose the risk-free rate is zero and the market price for Blackrock stock option that expire in one year are as follow
Strike Price
$350
$450
Call Premium
$25
$75
Put Premium
$15
$60
A)Specify the component and present cost of a long synthetic one-year forward agreement on Blackrock stock using only the option with strike price $350 in the table. The position should have a payoff at expiration that os identical to a one-year forward agreement with a forward agreement with a forward price of $350
B)Using any of the options in the table, does an arbitrage opportunity exist? If so, specify the exact components of the portfolio you need to capture the arbitrage, and the exact arbitrage profit.
8. Consider an investment that is long ten S&P 500 index futures contracts at a price $2700.00. The initial marg