Question

suppose that P is the price of a European put option to see a security whose present price is S. Let K be the strike price of the option. Show that if P>K then there is a buying and/or selling strategy that yields risk-less profit at expiration (ie arbitrage is present)

Answer 1

Assume stock price = S = $ 10

Strike price is = K = $ 8

Price o put option at strike price $8 = P = $9

Interest rate is r = 0 (so that present value calculation are unnecessary

Option strategy should be to SELL (Write) put option

If one sells a put option , he will receive $9 as premium

Payoff for writing put option , at strike price = $8

Assume premium at expiration = E

If E>or= 8 , Payoff = 0

If E<8, Payoff = (E-8)

There will be risk less minimum profit of $1