Question

A European call option on a stock with a strike price of $50 and expiring in six months is trading at $14. A European put option on the stock with the same strike price and expiration as the call option is trading at $2. The current stock price is $60 and a $1 dividend is expected in three months. Zero coupon risk-free bonds with face value of $100 and maturing after 3 months and 6 months are trading at $99 and $98, respectively. Identify the arbitrage opportunity open to a trader.

Answer #1

According to put-call parity,

Cash Investment + Call Option Premium = (Stock Investment - Dividend) + Put Option Premium

{For put-call parity to hold, strike price of call and put options must be same and cash investment must be equal to present value of strike price}

Cash Investment + Call Option Premium = 50 x 98/100 + 14

Cash Investment + Call Option Premium = $64

Stock Investment + Put Option Premium = (60 - 1x99/100) + 2

Stock Investment + Put Option Premium = 59.01 + 2

Stock Investment + Put Option Premium = $ 61.01

Since Stock Investment + put Option have same future cashflow as cash investment call option, I would buy stock & put option and short call option & cash investment

Therefore, Arbitrage Gain = $64-$61.01

Therefore, Arbitrage Gain = $ 2.99

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