Question #71231

Current price of a non-dividend paying stock is $2600. E[R] = 9%, and σ[R] = 20%. The term structure of interest rates is flat with r = 2%. For this question, consider options

with a maturity T of one year and a strike price X = $2650.

(a) Assuming that the assumptions underlying the Black-Scholes formula holds, compute

the no-arbitrage prices of a European call option and a European put option

on the stock.

(b) What is the expected return of the following trading strategy: (i) buy two call

options on the stock, (ii) sell two put options on the stock, (iii) buy $5300/(1+2%)

of 1-year zero coupon bonds?

(c) You observe the following market prices for the call and the put options priced in

(a): C = 210, and P = 203 . Assume that trading in option markets entails a cost

of $z per transaction, i.e., trading in the stock and the risk-free bond bears no

transaction costs but each time a an option is bought or sold, a cost z is incurred.

What minimum value for z guarantees the absence of arbitrage?

with a maturity T of one year and a strike price X = $2650.

(a) Assuming that the assumptions underlying the Black-Scholes formula holds, compute

the no-arbitrage prices of a European call option and a European put option

on the stock.

(b) What is the expected return of the following trading strategy: (i) buy two call

options on the stock, (ii) sell two put options on the stock, (iii) buy $5300/(1+2%)

of 1-year zero coupon bonds?

(c) You observe the following market prices for the call and the put options priced in

(a): C = 210, and P = 203 . Assume that trading in option markets entails a cost

of $z per transaction, i.e., trading in the stock and the risk-free bond bears no

transaction costs but each time a an option is bought or sold, a cost z is incurred.

What minimum value for z guarantees the absence of arbitrage?

Expert's answer

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