Question

Seven months European call and put options on palladium are trading at 9￥ and 13￥, respectively, with the same exercise price of 190￥. The spot price is 179￥ and the interest rate is 7%.

Is there any arbitrage opportunity? Justify your answer.

If yes, calculate the arbitrage profit in this case.

Answer 1

Answer-

The arbitrage opporunity can be calculated by Put-call Parity equation.

S + P = C + PV(X)

Where
S = Spot price = S = 179 ¥
Put Option = P = 13 ¥
Call Option = C = 9 ¥
Exercise Price or Strike Price = X = 190 ¥
PV (X ) = X / ( 1+ R)
Risk free rate = R = 7 % = 0.07

Substituting the values andequating the equations we get

S + P = 179  ¥ + 13  ¥
S + P = 192  ¥

C + [ X / (1+R) ] = 9 ¥ + [ 190 ¥ / ( 1+ 0.07) ]

C + [X / (1+R)] = 9 ¥ + (190 ¥ / 1.07)

C + [ X / (1+R) ] = 9 ¥ + 177.57 ¥

C + [ X / (1+R) ] = 186.57 ¥

Since the value of S + P = 192  ¥ is greater than the value of  C + [ X / (1+R) ] = 186.57 ¥ , the arbitrage opportunity exists .

The arbitrage profot is equal to difference in above obtained value = 192  ¥ - 186.57 ¥ = 5.43 ¥