Problem 7 (6 points): Find the price of a six-month European put option with a strike $970 on a six-month 1,000 face zero-coupon bond (i.e., on a bond that will have 6 month till maturity left at the time when the option matures). Assume 1-year spot rate is 6.2%, six-month rate is 6%, and 6 months from now the six-month rate can be either 8% or 4%. Keep at least 6 decimal digits for all calculations!!!

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Problem 4 (7 points): By using risk-neutral probabilities, find the price of a six-month European call option with a strike $975 on a six-month 1,000 face zero-coupon bond. Assume f(1) = 5.1%, r(.5) = 5%,and r(1) can be either 6% or 4%. Solution: 970.8738 (0) 950.88655% $1,000 6% $1,000 4% ^$1,000 1-p 980.3922 (5.3922) Possible prices of the underlying bond in six months: 1000/1.03=970.8738 or 1000/1.02=980.3922 Price of the underlying bond today: 1000/1.02552=950.8865 (p*970.8738+(1-2)* 980.3922)/(1+0.05/2) = 950.8865 allows to find p: (970.8738-980.3922)p =-9.5184 p = 974.6586-980.3322=-5.6735, so p=0.596 So, the value of call today is c=(0.596*0+0.404*5.3922)/(1+0.05/2) =2.1781/(1+0.05/2)=2.125 Answer: 2.125 Grading: 1 point for bond price in 6 months (0.5 for each node), 1 point for bond price today, 1 point for correct option value in 6 months, 1 point for correct equation for p, 1 point for correct value of p, 1 point for correct equation for c, 1 point for correct value of c