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1) Three-month European put options with strike prices of $50, $55, and $60 cost $2,
$4, and $7, respectively.
i. What is the maximum gain when a butterfly spread is created from the put options?
ii. What is the maximum loss when a butterfly spread is created from the put options?
iii. For what two values of the stock price in three months does the holder of the
butterfly spread breakeven with a profit of zero?
2) A company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year
zero-coupon bond. What is the duration of the portfolio?
3) 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 is the value to the
nearest cent of a three-year forward contract with a delivery price of $30?
4) What, to the nearest cent, is the lower bound for the price of a six-month European
put option on a stock when the stock price is $40, the strike price is $46 and the
risk-free interest rate with continuous compounding is 6%?
5) At the end of Thursday, the volatility of asset A is 2% per day and the volatility of
asset B is 1% per day. Also the covariance between the assets is 0.0001. During Friday
asset A produces a return of 3% and asset B produces a return of zero. An EWMA
model with = 0.9 is used.
i. What is the estimate of the correlation between the asset returns at the end of
Thursday?
ii. What is the estimate of the volatility of asset A at the end of Friday?
iii. What is the estimate of the volatility of asset B at the end of Friday?
iv. What is an estimate of the correlation between asset A and asset B at the end of
Friday?
6) What, to the nearest cent, is the lower bound for the price of a two-year American
call option on a stock when the stock price is $20, the strike price is $15, and the
risk-free interest rate with continuous compounding is 5% and there are no dividends?
