Question

A stock price with no dividends is $50 and the strike price of a 1-year European put option is $54. The risk-free rate is 5% (continuously compounded). Compute the lower bound for the put option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound?

Answer 1

Lower Bound (Minimum Value) of Put Option = Max. of ( 0 , S * E-rt - C) (In Bold is PV of S)

where, C = Spot Price / Current Price , S = Exercise Price/ Strike Price, Rf= Risk free rate , t is tenure in pa, E is Exponential

= Max. of (0, 30 * E-rt - 35)

= max. of (0, 28.5 - 35) = Max of (0, -6.5)

Thus 0 is the Minimum Bound.

At below 0 say -0.1 (Impracticle Put Buyer will never receive OP)

At Above 0 say 0.1; Gain/ Loss = PV of 30 -35 - OP =28.85 -35 - 0.1 = -6.25 Loss i.e No Arbitrage Opportunity.

Step-by-step explanation: