FC 323 Quiz 3

subject Type Homework Help
subject Pages 2
subject Words 462
subject Authors John C. Hull

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1) A binomial tree prices an American option at $3.12 and the corresponding European
option at $3.0 The Black-Scholes price of the European option is $2.98. What is the
control variate price of the American option?
2) The spot price of an investment asset that provides no income is $30 and the risk-free
rate for all maturities (with continuous compounding) is 10%. What, to the nearest cent,
is the three-year forward price? Assume that the asset provides an income of $2 at the
end of the first year and at the end of the second year.
3) You sell one December gold futures contracts when the futures price is $1,010 per
ounce. Each contract is on 100 ounces of gold and the initial margin per contract that
you provide is $2,000. The maintenance margin per contract is $1,500. During the next
day the futures price rises to $1,012 per ounce. What is the balance of your margin
account at the end of the day?
4) An American put futures option has a strike price of 0.55 and a time to maturity of 1
year. The current futures price is 0.60. The volatility of the futures price is 25% and the
interest rate(continuously compounded) is 6% per annum. Use a four time step tree to
value the option.
5) A one-year call option on a stock with a strike price of $30 costs $3; a one-year put
option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two
call options and one put option.
i. What is the breakeven stock price, above which the trader makes a profit?
ii. What is the breakeven stock price below which the trader makes a profit?
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6) It is May 1 . The quoted price of a bond with an Actual/365 day count and 12% per
annum coupon in the United States is 105 . It has a face value of 100 and pays coupons
on April 1 and October 1 . What, to two decimal place accuracy, is the cash price?
7) Suppose that ABSs are created from portfolios of subprime mortgages with the
following allocation of the principal to tranches: senior 75%, mezzanine 20%, and
equity 5%. An ABS CDO is then created from the mezzanine tranches with the same
allocation of principal. Losses on the mortgage portfolio prove to be 16%. What, as a
percent of tranche principal, are losses on
i. The equity tranche of the ABS
ii. The mezzanine tranche of the ABS
iii. The senior tranche of the ABS
iv. The equity tranche of the ABS CDO
v. The mezzanine tranche of the ABS CDO
vi. The senior tranche of the ABS CDO

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