Financial Engineering and Risk Management

1.

Lottery payments

A major lottery advertises that it pays the winner $10 million. However this prize money is paid at the rate of $500,000 each year (with the first payment being immediate) for a total of 20 payments. What is the present value of this prize at 10% interest compounded annually?

Report your answer in $millions, rounded to two decimal places. So, for example, if you compute the answer to be 5.7124 million dollars then you should submit an answer of 5.71.

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point 2.

Sunk Costs (Exercise 2.6 in Luenberger)

A young couple has made a deposit of the first month's rent (equal to

$1,000) on a 6-month apartment lease. The deposit is refundable at

the end of six months if they stay until the end of the lease.

The next day they find a different apartment that they like just as well,

but its monthly rent is only $900. And they would again have to put a

deposit of $900 refundable at the end of 6 months.

They plan to be in the

apartment only 6 months. Should they switch to the new apartment? Assume

an (admittedly unrealistic!) interest rate of 12% per month compounded monthly.

Stay

Switch

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point 3.

Relation between spot and discount rates

Suppose the spot rates for 1 and 2 years ares1=6.3%ands2=6.9%with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified. What is the discount rated(0,2)?

Please submit your answer rounded to three decimal places. So, for example, if your

answer is 0:4567 then you should submit an answer of 0:457.

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point 4.

Relation between spot and forward rates

Suppose the spot rates for 1 and 2 years ares1=6.3%ands2=6.9%with annual compounding. Recall that in this course interest rates are always quoted on an annual basis unless otherwise specified. What is the forward rate,f1,2assuming annual compounding?

Please submit your answer as a percentage rounded to one decimal place so, for example, if your answer is 8.789% then you should submit an answer of 8.8.

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point 5.

Forward contract on a stock

The current price of a stock is $400 per share and it pays no dividends. Assuming a constant interest rate of 8% per year compounded quarterly, what is the stock's theoretical forward price for delivery in 9 months?

Please submit your answer rounded to two decimal places so for example, if your answer is 567.1234 then you should submit an answer of 567.12

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point 6.

Bounds using different lending and borrowing rate

Suppose the borrowing raterB=10%compounded annually. However,

the lending rate (or equivalently, the interest rate on deposits) is

only8%compounded annually. Compute the difference between the upper

and lower bounds on the price of an perpetuity that paysA=10,000$per

year.

Please submit your answer rounded to the nearest dollar so if your answer is23,456.789then you should submit an answer of23457.

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point 7.

Value of a Forward contract at an intermediate time

Suppose we hold a forward contract on a stock with expiration6

months from now. We entered into this contract6months ago so that when we entered into the contract, the expiration wasT=1year. The stock price$6months ago wasS0=100, the

current stock price is125and the current interest rate isr=10%

compounded semi-annually. (This is the same rate that prevailed6months ago.) What is the current value of our forward contract?

Please submit your answer in dollars rounded to one decimal place so if your answer is42.678then you should submit an answer of42.7.