How are Options Priced?

Option pricing (Option Valuation), the two basic components of option value are: embedded value and time value.

Option pricing

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Option pricing (Option Valuation), the two basic components of option value are: embedded value and time value.

Embedded value, also known as intrinsic value, is the income realized by option holders by acquiring stocks through exercise, rather than buying stocks directly. For example, an employee is allowed to purchase options with a price of 300 shares at a life of 100 per share. Options with a strike price equal to or exceeding the stock market price have an embedded value of zero.

The reason why options have time value is that
Option holders do not have to pay the exercise price before exercising.
Over time, the stock market price may rise, creating additional embedded value. As long as it expires, all options have time value. When other conditions such as the risk factor are the same, the longer the time to maturity, the greater the time value.
Time value is based on two components of its formation: the time value of money and the value of volatility. For example, before expiration, an option with an embedded value of $ 200 as described above may have a fair value of 280. The difference of $ 80 represents the time value of the option.

Option holders can invest their capital elsewhere while waiting for exercise. For example, the return on risk-free T-bills. The higher the time value of money, the higher the value of being able to defer payment of the exercise price.

The volatility value represents the possibility that the option holder can obtain profits from the market value appreciation of the corresponding stock of the option, or lose the option value at the same time instead of losing the entire market price of the stock. For example: Stock volatility refers to the amount of previous or expected future stock price volatility. Generally speaking, the greater the volatility of a stock, the greater the potential return, the risk reward. Stock fluctuations are usually measured by the standard deviation of a statistical distribution. From a statistical perspective, if the volatility in the first year is expected to be 25%, the probability that the stock price at the end of the year will fluctuate 25% from the beginning of the year is about 67%. That is to say, the probability of year-end stock price movement outside this range is about 33%.
The option pricing model assumes the statistical distribution of the future stock price by considering the fluctuation of the expected stock price, thereby estimating various possibilities of the future stock price. For example, the Black-Scholes model assumes that stock prices follow a log-normal distribution. The assumption is that small fluctuations in stock prices are more likely than large fluctuations. The greater the volatility of the stock, the higher the possibility that the market price will have a large increase. Because the cost of a sharp drop is limited by the current value of stock options, the profits from a sharp rise in stock prices are unlimited. Options on stocks with large volatility are more likely to generate greater profits than options on stocks with low volatility.