Question

Explain why a European call on a stock that pays no dividends is never exercised early. What would you do instead to eliminate the call option position?

Answer 1

It seems you want the answer why 'American call' on a stock that pays no dividend is never exercised early. Theoretically it is simple to understand that value of option prior to maturity comprises of time value and intrinsic value . The instrinsic value is the difference between the underlying security price minus the strike price (for call options) and is positive for in the money options. The time value is the difference between the option price and the intrinsic value. In a way time value encompasses the interest rates and the premium investors are willing to pay for the probability of the option to become profitable. In case an option is exercised early, the option holder will only receive the intrinsic value of the option (anyways there is no point in exercising out of money options) and will have to let go of the time value of the option since the option seller is only obligated to pay option holder the intrinsic value as per the option contract. On expiry, the option's time value will be zeroised and it will only have intrinsic value which can be zero is worst case or positive. Hence it will make sense to delay exercise of option till expiry otherwise the option holder looses out on the time value of the option. ANother to way to look at this is that the option holder istead of paying the strike price to purchase the underlying stock can keep that money in an interest bearing deposit till expiry and on expiry use the strike price to exercise option and keep the interest earned with themself.

Instead the option holder can do the following:

a. For traded options, the option holder can sell the call option at market traded price which will include benefit of both intrinsic value and time value

b. Otherwise, the option holder can short the underlying security at current market levels which will be akin to exercise of call option at current market price level but at the same time with the option being live. In this case if the expiry price of the underlying stock increases then the option holder's option pay off will cover for the loss on the short position and if the price falls the option holder would make profit on the short stock position which will cover for any loss that the possible early exercise could have conferred