Question

‘static hedging strategy’ to prove that early exercising a nondividend paying call option is never optimal. The argument only says that early exercising is not in the best interest of the option holder. Argue that if such early exercisers exist, then an arbitrage opportunity is there for you to make a risk-free profit. Assume you only know that such early exercisers exist, but you do not know when they would exercise. Explain how, why and when you can make a risk-free profit. Please explain your trading strategy clearly. Make all the standard assumptions.

Answer 1

Static hedging is more of the investment strategy that doesn’t need the security to be re-balanced as the price of other characteristics or market drivers (such as volatility) of the securities it hedges the change, in contrary to a dynamic hedging strategy that requires constant re-balancing with Market drivers. Static hedging can be much more complex when there has to statically hedge a barrier option with vanilla options a number of vanilla options may be required to hedge one barrier option.
Early exercising of a non-dividend paying call option for underlying equity may not be optimal or profitable as the non-dividend Call option doesn’t pay the dividends or interest income over the holding period or upon exercising, and as such early exercising of such call option may result in a loss by a way of paying margin over it. Early exercising is indeed not in the best interest of the option holder and, but if such early exercising happens, then an arbitrage opportunity may arise to make a risk-free profit. Early exercising may involve the strategy where the market price of the underlying Equity is considerably higher so that there is a net profit making opportunity upon exercising the call option, and at the same time foreseeing the reciprocal effect of the market in near time during the holding period.

Also, exercising the non-dividend paying Call option during the holding period may provide an additional opportunity to buy the underlying security at market price which is relatively lower than the Exercise price and that can be held to benefit from the arbitrage in due course of time.