A six-month European call option's underlying stock price is $86, while the strike price is $80 and a dividend of $5 is expected in two months. Assume that the risk-free interest rate is 5% per annum with continuous compounding for all maturities.
1) What should be the lowest bound price for a six-month European call option on a dividend-paying stock for no arbitrage?
2) If the call option is currently selling for $2, what arbitrage strategy should be implemented?
1) theoretical price = $2.85
1) theoretical price = $3.02
1) theoretical price = $3.67
1) theoretical price = 1.98
arbitrage strategy: Buy the call and short the stock.
2) arbitrage strategy: Buy the call and buy the stock.
2) arbitrage strategy: Short the call and buy the stock
2) arbitrage strategy: Short the call and sell the stock
Spot = 86, Strike = 80, Time = 6 month = 0.5 years , Dividend = 2 , Time = 2 months = 2/12 years
Present Value of dividend = 5 * exp ( -0.05* 2/12 ) = 4.958
Future value after month = (S -pot - present value of dividend ) * exp ( interest rate * time)
= (86 -4.958) * exp ( 0.05* 0.5 )
Quest 1 )
Since strike price is 80 so minimum call price so that there is no arbitrage opportunity = 83.093 - 80 = 3.093
Quest 2 )
If call option price is $2
Then there exists an arbitrage opportunity because theoretical call price comes out to be 3.093
So current call option priced at $2 is cheaper so we buy it and short the stock
Buy the call option and short the stock
If theoretical call option price is greater than $2 then buy the call and short the stock
If theoretical call option price is lower than $2 then Short the call and buy the stock
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