Question

Problem 12. A European call and put option on a stock both have a strike price of $30 and an expiration date in three months. The price of the call is $3, and the price of the put is $2.25. The risk free interest rate is 10% per annum, the current stock price is $31. Indentify the arbitrage opportunity open to a trader.

Answer 1

According to Put call parity theorum,

If

[ Call Price + PV of STrike Price ] = [ Put Price + CUrrent price of share ], else there exist arbitrage profit.

[ Call Price + PV of STrike Price ] = $3 + PV of $30 for 3 Months

= $ 3 + $ 30 * e^-0.025

^{= $ 3 + $ 30 * 0.9753}

^{= $ 3 + 29.26}

^{= $ 32.26}

^{Put Price + Price of Share = $ 2.25 + 31}

^{= $ 33.25}

As 32.26 not equal to 33.25, there is arbitrage profit.

Technique:

. Hold a call, Shore sale a share and Write a put option

using the above technique, we can gain the difference amount [ 33.25 -32.26 ] as arbitrage gain.

Pls comment, if any further assistance is required.