In: Finance
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.
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.