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?