Why should you never exercise a call option before maturity?
It's not quite true that you never would. With a stock option on a share that pays a dividend, it can be worth exercising a call in order to collect the dividend; the call doesn't give a right to the dividend but owning the shares does. The decision to exercise is made when the dividend is expected to exceed the extrinsic value of the call option, so it is more normal for this to be the case for deep in-the-money call options.The main reason however to not exercise a call option before maturity is that it forfeits the extrinsic value of the option. If the spot is trading at $100, the $99 strike call will be worth $1 intrinsically and if exercised this is the only 'profit'. But the call will be worth at least $1 in the market; if they have any extrinsic value left then they will be worth more than $1. So it would be better to sell the options for more than $1 rather than exercise them and only collect $1.
Why is the value of an American call option equal to that of a European one?
It's not. I'm not sure why you think it is. An American option is like a European option with an additional option to early exercise, which may in some cases be worth very little, but can't be worth zero.EDIT after clarifying comment: This question already exists here, with one answer: For a non-dividend paying stock, why does an american call option have the same value as an european call option? I answered it as well over there.
Why an american call on a dividend pating stock is always worth at least as much as its intrinsec value ?
An American-style settlement call on a dividend paying company is always worth at least as much as the intrinsic value because you can immediately exercise the option. For example, if a stock is trading at $50.00 per share, a call with a $40 strike price has an intrinisc value of $10. If the option could be purchased for $9 you could buy the option for $9 per share, immediately exercise it (paying at additional $40 per share to buy the stock) then sell the stock for $50 per share, giving you a risk-free profit of $1 per share. Similarly, for a European-style settlement call on a stock that does not pay dividends the call will always be worth at least its intrinsic value unless the stock cannot be sold short. If the stock can be sold short, using the same dollar amounts as in the previous example, you could buy the call option for $9 per share, short the stock for $50 per share, giving you a net credit of $41 per share. At expiration you would exercise the option if the stock was still trading over $40 per share, once again giving you a risk free profit of $1 per share. (If the stock was below $40 per share you would simply cover the stock by purchasing it on the open market and letting the option expire, giving you a larger profit.) However, for a European-style call on a stock that does pay a dividend, the price of the call may be less than the intrinsic value. For an example, use the same values as before but assume prior to expiration the stock will pay a $3 per share dividend. If you shorted the stock for $50 you would also have to pay an additional $3 per share for the dividend, reducing your total proceeds from the short stock position $47 instead of $50. Since your cost for the stock is $49 ($40 per share plus $9 per share for the option) you will lose $2 per share unless the stock drops below $40 per share at expiration, allowing you to cover your short stock position at a lower price.
Why does it sometimes make sense to exercise a put option prior to its maturity, contrary to a call option (assuming American options)?
Your question can be adequately answered by the understanding the concept of intrinsic value of a put option. In mathematical sense,Intrinsic value of Put (P)= max [0, X-S]. Here X is the strike price of the option that you have bought, S is the current stock price.Consider that you have bought a put option on a stock that has a strike price of ₹1,000. If the stock price is currently ₹1,050 then the value of your option is zero. If the stock price falls below ₹1,000 then you are in business and bound to make profit.Say the stock price is currently at ₹950, then the intrinsic value of your Put option is max[0, 50]=₹50. Your actual profit is ₹50 minus the premium paid on the put option. Say, due to favourable market sentiments, you expect the price to overshoot beyond ₹1,000. You would definitely be in loss if it actually does so. Your judgement call therein would be to exercise your put option to book your profits. This is the basic concept behind exercising a put option. Several other factors also need to be taken into account likeTime value of the optionThe premium paid on the put optionIn the case of a put option the maximum profit is X which can be achieved if the stock price falls to zero. However, the maximum losses are infinite. Say the stock price rises to ₹10,000 (losses = ₹9,000). In the case of a call option, the maximum loss is finite and the value is X. But, the maximum profit that can be booked is infinite. Hence to mitigate your losses, when the stock price would supposedly increase exponentially, you need to exercise put option prior to maturity. The losses from a stock may not be that high, and any upturn in the growth of the company may bring the stock price to the optimum level.
Why shouldn't you exercise a call option early?
To preface, I mean no offense here - just trying to explain some common aspects of behavioral psychology:So, in asking this question, you exhibit a classic trait of human psychology called "loss aversion." In other words, you are discouraged more by losing $1 than you are encouraged by gaining $1. This is inherently irrational since both of those outcomes are equally good or bad. In the case of a call option that's already "in the money", unless you know something about the underlying stock (e.g., they are declaring Chapter 13 in a week, AKA you have insider information, which is illegal to trade on), it is actually slightly more likely that the stock will be higher by the time the option expires rather than lower. I could elaborate further but you can simply google "S&P 500 historical returns" to see what I mean.You mention the "risk" of the stock losing value, and this is a common misconception amateur investors have about risk or "volatility." The "riskiness" of the stock is also affected by large gains in its price, not just losses. By exercising early, you are ignoring upside potential despite respecting downside risk. Also, it is worth noting that your downside is limited to the price you paid for the option. Your downside is capped while your upside is potentially unlimited. These reasons are why you do not pay $0 for an option that has a strike price that is equal to the current stock price.With all that being said, this is completely different from buying the option and then exercising it at a pre-calculated "ceiling" price determined from disciplined research of a company's fundamentals. Perhaps you think that the company's stock price will revert if it hits a certain price/earnings ratio. In this case, you at least have a theory as to why the stock might lose value as opposed to exercising your option early "just because."Disclaimer: I am not an options trader nor have I dabbled in options. I am speaking from the experience of completing a Master's degree in Financial Engineering in which a third of the curriculum is dedicated to accurately pricing options based on optimal exercise dynamics.
Why is the value of an American call option on non-dividend paying stock the same as that of a European call option?
An American style option allows the holder of the option to exercise on any business day up to and including expiration day. A European style option can only be exercised on expiration day.The value of an American style call option on a non-dividend paying stock is the same as that of a European style call option because there is no economic reason to exercise the option early.Hope this answer is helpful. Enjoy your day.
Is it possible to exercise stock options at any time prior to the expiration, or must one wait until the expiration date?
When Fischer Black and Myron Scholes wrote their famous option pricing paper in the early 1970s, they had trouble getting it published. One problem is that options at the time could be exercised any time up to expiry, and their formula only priced options that could only be exercised at expiry.To finesse that problem and help get editors to consider the paper seriously, Fischer found some Swiss options from the early 1900s that could only be exercised at expiry. So he labeled them “European options” and wrote that the formula could price them. That meant all the options actually available for buying and selling were “American options.”Occasionally someone will write an over-the-counter European option, but they are rare. There are also “Bermudan” options (halfway between European and American) that can only be exercised at specified times.So the answer is nearly always, and for exchange traded options always, the holder can exercise at any time up to maturity. That’s true in the US, Europe and everywhere else. But there are a few other schemes that you might run across now and again.
For a non-dividend paying stock, why does an american call option have the same value as an european call option?
An american call option has the same value as an european call option because it is never optimal to exercise an american option before maturity.The intuition behind this is that if we exercise an American call early, we lose 1) the benefit from the time value of money of paying strike K in the future v.s. now, and 2) the value of the right to exercise the option in the future.Now for a more “mathy” explanation:Imagine if you could sell an american call option before maturity (we can assume that S>K).If you sell the call, you will receive the value of the call, CIf you exercise the call, you will receive the payoff of the call, S-KThis might not mean much, until we realize that C>S-K. There are two ways to see this:1. You can plot the payoff diagram of a long call option against that of a portfolio containing long stock and short bond (i.e. borrowing K) and you will see that the call option payoff is always higher.2. If C