Question

A 1-month European call option on a non-dividend-paying-stock is currently
selling for $3.50. The stock price is $100, the strike price is $95, and the risk-free interest
rate is 6% per annum with continuous compounding.

Is there any arbitrage opportunity? If "Yes", describe your arbitrage strategy using a table of cash flows. If "No or uncertain", motivate your answer.

Answer 1

Prima facie there is a arbitrage opportunity as call option is at $3.5 and strike price is $95. So total cost is $98.5. The stock price is $100 so there is $(100-98.5) =$1.5 advantage. Int on $3.5 premium @6% p.a. at continuous compounding

Fv in continuous compounding =PV x e (i x t)

taking pv as 3.5 and e =2.7183, i=6/12=0.5 and t=1

fv=5.77 so total cost would be 95+5.77 =100.77 which is lesser than stock value of 100 so with continuous compounding @6 percent int rate there is no arbitrage opportunity