Is it ever optimal to early exercise the put option

I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it. If you think the stock is going to continue going up, just wait. If you think the stock has reached its peak, then short it in the open market.

If the shorted stock continues to climb, you can always cover with your call option. If however the stock falls below your strike price, then let the option expire and cover at the market price. It's this very ability to choose the buying price strike vs market when covering a short sale that makes the option valuable.

But of course, you can do the same thing with a European option! That's why the American option gives you no added value over the European option. There is no benefit to exercising an American call option early. And the American is worth at least as much as the intrinsic so it's never sensible to early exercise. The transaction has a net 0 cashflow at time 0 and at expiry you will be long a share of stock and have to pay the bond off.

If the stock is less than the strike price, you can exercise you call to get the strike price. You cannot short the stock or sell the option and believe it has peaked.

If you believe that the stock has reached it's highest point before the expiration date and you are unable to hedge by shorting the stock including using a synthetic shortyou should exercise early. The market is not efficient and you have an opportunity for arbitrage. There are a couple different ways this could happen, but if you can construct a series of purchases that give you risk free profit, congratulations, you have found a rare opportunity for arbitrage and should take advantage of it.

You will lose the option. If the option is conditional on some external factor eg. The risk-free interest rate is negative. If for some strange reason, interest rates are negative, then the interest on the strike price is negative. If this is larger than the implicit put, buy the put and exercise the option. You wish to be subtly charitable to the seller of the call. If exercising early is disadvantageous to you and if it is a zero-sum game, then your loss will be their gain.

You could subtly donate to them by exercising non-optimally. They can simply sell another call, which will more than pay for the money they owe you or else you are in situation 3 above and they have made money. If you can dynamically hedge then you can monetize the value of your option without prematurely exercising it. Before writing about Randomness and Black Swans, Taleb wrote a book on the topic. The short version of the story is find the DV01 of your position, and take an opposite position with the same DV If you can't dynamically hedge for whatever reason, then the "Don't exercise early" rule is not so black and white.

For example, executives have is it ever optimal to early exercise the put option restrictions on their companies. In these cases, they may be restricted to exercising options early rather than dynamically hedging. Because you would make a higher profit if you sold the option on the open market at that point in time, rather than exercising it at that point in time due to the time value of money.

Because if you sell, you will get a higher value than 20USD per share. You can think of the reason behind this added value is that having a deep ITM option is better than having a stock: Therefore your option is worth more on the market than it's exercise value. This is why you are better off by selling it in your case if you know that the price will drop to 25USD.

The theoretical answer is: So rather than exercising just sell the option and let someone else hold it. But then practically there are transaction costs etc. You can only make a decision africa brokers in list stock whether to early exercise an American call option on an equity underlying with current information.

In your question you anticipate a movement in the underlying higher in the future. This has no economic bearing on whether to exercise early.

Early Exercise

There will be no early ato foreign exchange rates china. Back before the OCC starting adjusting strike prices for large dividends you would exercise early to capture the dividend. I think this is a common problem for a beginner in QF.

The holder has two ways to treat the stock if he exercises the call option earlier:. The second case is free money making sites online work iamnotacommonman little tricky. Suppose the stock price is 50, and the strike price is Selling the stock will give you However, a better choice is to short the stock borrow and sell the stock gives you 50 and close the short position at maturity use money equal or less than 40 because you have the call option, you at most pay 40 for the stock.

Then you can make a profit more than So you see in either case, we have a better solution than just exercising it. For more details, please check Hull's book: By posting your answer, you agree to the privacy policy and terms of service. By subscribing, you agree to the privacy policy and terms of service.

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Join them; it only takes a minute: Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top. Exercising an American call option early.

Would it not be more optimal to exercise early, in this case? A genuine question isn't it? Basically you'd make more money by selling the option than exercising. I am surprised no one actually gave a proof here Loving the answers here learning new information about stuff I thought I already knew!

Exercising an American call option early - Quantitative Finance Stack Exchange

But my example describes a profit that wouldn't be possible if the option was European, why isn't that a benefit? What are you talking about?! It's foolish to exercise now if you believe the stock will go higher.

The market price could be lower than the exercise price, which is why you'd be giving-up money to exercise now if you believe it's going to fall further. But had I exercised when the stock price was higher than the exercise price not necessarily highest I'd have made a profit.

Isn't that more optimal than the loss that has been made by holding onto the option until expiry? Do you know what short selling is? I've mentioned it twice because it's the classic textbook argument against early exercise. The rationale I read only gave the reason that you'll lose interest on the cash you spend to exercise the call option. Note that this does not require dynamic hedging. I discuss this question at length in my book Concepts etc.

Mark Joshi 4, 10 Cases where exercising a call early makes sense: Kalev Maricq 51 1 1. Could you please post a quote from the book by Taleb? This is already stated in a previous answer.

Alexey Kalmykov 2, 11 Piczak 1, 4 17 The holder has two ways to treat the stock if he exercises the call option earlier: In the first case, the holder lost the interest from the cash and also the stock price may fall.

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