The price of an American put option on a non-dividend paying stock is $2.00. The underlying stock
Question:
The price of an American put option on a non-dividend paying stock is $2.00. The underlying stock price is currently at $28.00, the strike price of the option is $26 and the expiration date of the option is 8 months. The risk-free rate of interest is 8% p.a. continuous compounding for all maturities. Assume that traders can borrow or lend at the risk-free rate, can buy and short-sell shares of the underlying stock if necessary, and do not face any transactions costs.
(i)Derive upper and lower bounds for the price of an American call option on the same stock with the same strike price and expiration date using the put-call parity condition for American options.
(ii) If the American call option in part (i) trades in the market for $6.00, state how you would exploit any arbitrage opportunity (if any). Also, explain why it is an arbitrage by showing the initial and future cash flows from the strategy
