Question

•A European call option and a European put option with the same maturity of 1 year, as well as the same underlying asset, are priced respectively at $0.50 and $0.75. If the strike is $50, the spot $51, and the risk-free interest rate with continuous compounding 2.25%; how could an investor benefit from this arbitrage opportunity?

Answer 1

As per put call parity,

Cash investment + call premium = stock price + put premium

{Note that strike of call and put option should be same and cash investment should be present value of strike of call or put}

Cash investment + call premium = 50 / e^2.25% + 0.50 = 48.89 + 0.50 = $ 49.39

Stock price + put premium = 51 + 0.75 = $ 51.75

Both the above positions will have same future cashflow

However, present value of cash + call < stock + Put

Therefore

buy call @ 0.50 and invest in risk free 48.89

and sell put @ 0.75 and sell stock @ 51

Future cashflow from above position will be nil. since we bought (cash + call) and sold (stock + put)

Therefore, arbitrage gain = 51.75 - 49.39 = $ 2.36