A stock that does not pay a dividend is trading at $73.50. A riskless bond that...

A stock that does not pay a dividend is trading at $73.50. A riskless bond that will pay $100 after a year is trading at $97. A European call option on the stock with strike price of $65 and one year to maturity is trading at $5.00. Propose an arbitrage strategy and prove that it is an arbitrage strategy.

Expert Solution

The call option with a strike price of $65 is in the money by ($73.50-$65) = $8.50

However, the call option is currently priced at only $5 (less than the in-the-moneyness of the option)

Hence an arbitrage opportunity exists.

We short 194 stocks at $73.5 each and buy 137 bonds today at a price of $97 each along with buying 194 call options at strike price $65 for $5 each

Time	Action	Cash-flow	Net cash-flow
t=0	Short 194 stock at $73.5 each (-194*73.5)	14259	0
Buy 137 bonds at a price of $97 each (147*97)	-13289
Buy 194 1-year European call option at strike price $65 (194*5)	-970
t=1	Buy 194 stocks at $65 from the call option and close out the short position	-12610	1090
The bonds will mature and will pay $100 per bond face value	13700

This is an arbitrage strategy, as at t=0, no investment is made by the arbitrageur and at t=1, the arbitrageur gains $1090 from the arbitrage strategy.

jeff jeffy answered 1 year ago

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