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Calculate the price of a call and a put option with exercise price $10 and two
periods on a stock whose initial price is $13. The stock can go up by 1.1 (u = 1.1), or
down by 0.8 (d = 0.8), the risk free rate is 0.2% per period.
2. Find the number of future contracts required to hedge a $ 2 MM face value of the
127?17 cash value, 5 yr bond with 7% coupon and CF 0.8317. You hedge using
the 6.5% coupon, 5 year bond with CF = 0.7488 and cash value of 121?07.
Use the face value hedge, the CF hedge, and the BPV hedge.
3. Calculate the gains or losses for the long and short position in a Eurodollar futures
contract if the initial settlement price is 98.355 and the final settlement price is
97.9350. Use the standard Eurodollar futures contract of 1 million dollars at 90
4. Easy questions:
a. Explain the effect on the prices of call and put options of a change in the
risk free rate.
b. If a firm decides to increase dividends, what will happen to the price of the
call and put options whose underlying asset is the firm stock?
q = (1 + r ? d)/(u ? d)
c = (Cu*q + Cd*(1-q))/(1+r)
p = (Pu*q + Pd*(1-q))/(1+r)
ln(S / K ) (r 0.5 2 )T
d 2 d1 T
C Se T N (d1 ) Ke rT N (d 2 )
r p w1 r1 w2 r2
2p w12 12 w22 22 2 12 w1 w2 1 2
2p w12 12 w22 22 2w1w2 cov(r1 , r2 )
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