Question

Two call options are written on the same stock that trades for $70 and both call options have
the same exercise price of $85. Call 1 expires in 6 months and Call 2 expires in 3 months.
Assume that Call 1 trades for $6 and that Call 2 trades for $7. Do these prices allow arbitrage?
Analyse. If they do permit arbitrage, then explain the arbitrage transactions.

Answer 1

Call 1 expires in 6 months

Call 2 expires in 3months

Since, the strike prices are same.

Call 1 should have higher price than call 1

Option Price=Intrinsic Value +Time value

Time value of Call 1 is higher than Call2

Call 1 is cheaper since it is priced lower than 3months call option(Call 2)

Arbitrage transaction will be to SELL the costlier option (Call 2) and BUY the cheaper option (Call 1)

Option Strategy:

BUY (long ) on Call 1 at $6 expiring after six months, and pay $6 per option

SELL (short) on Call 2 at $7 expiring after 3 months, and receive $7 per option.

Arbitrage profit $1 per option.

If the share price moves above $85:

There will be profit on long call and equal amount of loss on short call.

If the Share price is X, where X>85, during three months:

Gain on Long Call =(X-85)

Loss on Short Call =(X-85)

After 3 months any increase of price above $ 85 will give additional profit on long call