For a call option, the option price is convex and decreasing with increasing strike price, assuming a fixed maturity and same underlying price.
Exercising an option means exercising your rights to buy or sell the underlying asset in accordance to the parameters of the option. When you exercise a call option, you will get to buy the underlying stock at the strike price no matter what price the stock is trading at in the market. When you exercise a put option, you will get to sell the underlying stock at the strike price no matter what price the stock is selling at in the market. In both cases, the option you own disappears from your account.
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If the spot price of the stock exceeds the "strike price" in the call option, the option is in-the-money and you can exercise it. But if you have a choice, wait to exercise it until the stock's spot price exceeds the strike price enough to cover the premium. Example: the strike price is $40 and the premium was $2. In order to make money on this option, the stock price needs to be over $42--enough to pay for the stock and replace the money you spent buying the option.
The vesting schedule determines when the employee gets control over his options. Once vested, the employee still has to exercise the options at the exercise price during the exercise period in order to become the owner of the shares. The vesting schedule, exercise price and the exercise period are all specified in the stock option plan.
The Payoff i.e. profit for a Call Option is St-X where St is the market price at time t and X is the exercise price. Assuming that it is an American Style option where it can be exercised at any time, If St is significantly greater than the exercise price,X, (the agreed price to buy an option at) then if the option holder exercises it immediately they will be 'in-the-money.' This means it has a high intrinsic value which causes a rise in value for the option. The Payoff for a Put Option is X-St where X=exercise price and St equals market price at time t. If the market price increases the gap between X and St (Payoff or Profit) reduces or if X<St then they will be making a loss. This will mean it will have a low intrinsic value (value if exercised immediately) therefore the value of the option will fall.
Stock options allow you to buy stock in a company at a certain price, no matter what the price of the stock is currently. There is usually a time period associated with the offer. Sometimes this could be a sweet deal (if the stock is currently higher than the option) to worthless (if the option price is higher that the current stock price). You also don't have to have the funds to exercise the option, you can have a brokerage company exercise the option, then sell the stock at the higher price, with the difference being your profit.
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You certainly should not exercise a call option when the stocks price is above the strike price. If you really want the stock, go and buy it at the market price. For example, if you own an option with a strike price of $15 and the stock is trading at $9, why would you pay $15 to buy a stock that you could only buy or sell for $9. That would be irrational.
An in-the-money option is one that makes financial sense to exercise. In-the-money puts are ones where the security's open-market price is lower than the option's strike price. In-the-money calls are ones where the security's open-market price is higher than the option's strike price.
What is the exercise price of the put?
I think it's the same
In both cases, you will have to provide the stocks to the counterparty if the option is exercised. There are two differences. First is the nature of the option. Calls are exercised when the stock spot price exceeds the call's strike price. Puts are exercised when the stock spot price is below the put's strike price. The other is, if you write a call you don't get to decide whether it gets exercised--the buyer does. If you buy a put, the choice to exercise it is yours.