FC 323 Quiz 3 | Course Paper

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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?

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