# PROBLEM SET 11 1) Consider the data in the table below. St 132 X 100 T t 1.5 35% r 3% (a) What is the price of a European call option with properties…

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1) Consider the data in the table below

(a) What is the price of a European call option with properties as describedin the table?

(b) What is the price of the corresponding European put option?

(c) How would you expect the put and call prices to change if the risk-freeinterest rate increased to 4%?

(d) Show that, in general, the price of a European put option ispt = Xe−r(T −t)N(−d2) − SN(−d1)

(e) You hold 100 put options. What position would you have to take in theunderlying stock in order to be delta neutral?

(f) You hold 100 put options. What position would you have to take in thecall option in order to be delta neutral?

(g) The market price of the call option is \$42.60. What is the impliedvolatility?

(h) Suppose you would estimate the historical volatility of S to 30%. Whatimplications would that have for the volatility and/or the Black-Scholesmodel.

(i) If we accept the assumptions underlying the Black-Scholes model, whatshould the implied volatility of a European call option written on Swith a time to expiration of 1.5 years and a strike price of \$150?

(j) Suppose you find that the implied volatility for the option is actually40%. What implications would that have for the volatility and/or theBlack-Scholes model

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