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Defining the boundaries of premium options
Determination of fair option premium the main task of the investor in the derivatives market. It is generally known that the options and have an internal time value. Intrinsic value is the positive difference between the price of the option Strike and spot price of the shares for an existing type of an option to buy or to sell. These options are called "options in the money", because they bring a buyer to profit. All options have to term expiration time value, t. E. Component of the option premium minus the intrinsic value. Options are "out of the money", which are unprofitable for the buyer, composed entirely of time value, their intrinsic value is zero.
Call option value of the top border should be of the essence of Call option - it is the right to buy shares at Strike price at the date of expiry. This option can not cost more than the price of the action itself, because such an expensive purchase rights are not promised to any investor any advantages over the usual purchase of shares on the spot market. But even if such a situation arises, arbitrageur (player dizbalansah) will buy shares in the spot and sell the appropriate amount of Call Option on them. In this case, he will receive a guaranteed income equal to the difference between the option price and the stock Call. With the definition of the lower boundary Call option on shares without dividend situation is more complicated. If an investor decides to buy the right to such a purchase in the future, the premium for this right will take into account the value of money, which in the second case, the investor saves on the market instead of buying shares, as will not pay the entire amount at once. For example, if Gazprom shares worth 34,000 rubles per 100 pieces, you can buy them today and to pay 34,000 rubles. But also, you can buy a Call option on the shares of Gazprom with the performance in half a year, and pay for them only the option premium Call. The price of the future purchase of 100 shares of Gazprom will be determined Strike option, its exercise price. Consider the price of money, ie, 34000 Strike, the discounted purchase price of the shares of Gazprom with the performance in half a year -.. Must be today for rates 10% 32 342 rubles. Thus, according to the option premium shall not be less than the difference between the share price and the discounted price Strike.
With the option Put the situation is slightly different. The lower limit of the European option premium on the sale will be equal by analogy with an option to Call, the difference between the present value of the exercise price of the option Strike and the value of shares on the spot.
In the event that the shares will be paid dividends in the formulas for calculating option prices lower boundary of Call and Put should also take into account the present value of dividends, which will reduce the number of Call option value and therefore increase the value of Put Option. So, the main rule for calculating the option premium on the shares on which the dividends are paid is as follows - the Award of the European option Call shall not be less than the difference between the spot price of shares and the sum of present values of price performance and dividends, and the European option Put premium should be less the difference between the sum of the present value of the exercise price and dividends, which are planned to pay the price, and the stock SPOT.
The relationship between the option premium
Price, or premium options, especially by Strike or exercise price. For options on the same asset with the same due date, but different Strike, t. E. Execution price on the expiry date, there is a definite relationship. Call options with lower strike prices are more expensive options Call higher Strike. This is thanks to the premium for the right to buy an asset cheaper. Options Put, with higher strike prices are more expensive options Put lower Strike, as the premium for the right to sell the asset more expensive should be higher.
For example, take the board options on the shares of Gazprom. It is clear that the right to sell shares at a price of 32,000 rubles is cheaper than the right to sell those same shares at 33,000 rubles for the same date of expiry. What will be different price options on one kind of the same assets, the same Strike, but with different dates of execution? For example, two or three-month US Call options on the shares of Gazprom. For prostate we assume that dividends during these periods will not be paid, then the three-month option will cost more than two month, as the present value of the exercise price at a greater investment period will be smaller, and therefore the premium on an option anymore. When dividend payments on shares should make adjustments in the calculation, so for example, if the dividend payment is expected after two and a half months, the European Call option with the execution will cost more in two months than the same Strike option on the same stock, but with the performance in three months. the ratio of one type of option prices should be considered, on the one asset with the same expiration date with different values of the volatility of the underlying asset markets. Logically, one can assume that in the conditions of high market volatility of the underlying asset for options and Put Call premium American and European style need to be higher than that, ceteris paribus, but in a state of low volatility of the underlying asset markets.
The relationship between the premiums for Call and Put options is called "Parity Options Call and Put», understanding of parity allows investors to operate in the options market in a wider range. For example, at the beginning of the emergence of the options market in the Chicago Stock Exchange traded only Call Options and Put Options constructed synthetically - in combination Call options and shares. That is, knowing the value of Call options, you can determine the price of the option Put the same Strike. Conversely, if the parity conditions are not met, then there is an opportunity to profit from arbitrage.
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