1) Price a call option on Planetary Resources Group stock expires in two periods With a strike price of $200. The PRG stock is $215 a ton. The price either moves up with u=1.15, or down with d=1/1.15. The risk-free interest rate is 2%. What is the value of your option today in period 0?
A) Recompute the price from above assuming that the risk-free interest rate has risen to 4%. In one sentence, explain why the price changed the direction it did.
B) Recompute the price from question 1 assuming that the current price has risen to $230. In one sentence, explain why the price changed the direction it did.
C) Donets Extraction stock sells for $10. The monthly interest rate is 1%. The standard deviation of the price of this stock is 100% per year. Use the Black-Sholes equation to determine the price of a call option with a strike price of 9 that expires in 6 months? Using Put-Call parity determine the price of a put option on this stock with a strike of 9 expiring in 6 months.