How to calculate option price
Options Pricing
Factors
affecting option price
How
Options Are Priced
There are many
options pricing models out there. However, options pricing is a course in
itself. You’re going to need a lot of math and a bit of physics to understand
the theory behind options pricing. Primary drivers of the price of an option:
current stock price, intrinsic value, time to expiration or time value, and
volatility. The current stock price is fairly straightforward. The movement of
the price of the stock up or down has a direct, though not
equal, effect on the price of the option. As the price of a stock rises,
the more likely it is that the price of a call option will rise and
the price of a put option will fall. If the stock price goes down, the reverse
will most likely happen to the price of the calls and puts. However,
don’t be scared. We’re going to focus on the basics here and look at the
factors affecting an option’s value.
Now,
there are three major factors affecting stock option prices:
Intrinsic
Value
The
underlying stock’s price
Time
to expiration date
Volatility
The
“less” important factors affecting options prices:
Short-term
interest rates
Dividends
Keep
in mind that interest rates would matter if they’re constantly changing. That said;
let’s take a look at how these factors affect an option’s price.
Intrinsic Value
Intrinsic value is a measure of
what an asset is worth. This measure is arrived at by means of an objective
calculation or complex financial model, rather than using the currently trading
market price of that asset.
Intrinsic value of a stock is its
true value. This is calculated on the basis of the monetary benefit you expect
to receive from it in the future. Let us put it this way – it is the maximum
value at which you can buy the asset, without making a loss in the future when
you sell it. Before you wonder how complicated this sounds, let us assure you
we will look at this in detail further.
Intrinsic value is the value
any given option would have if it were exercised today. Basically, the
intrinsic value is the amount by which the strike price of an option is
profitable or in the money as compared
to the stock's price in the market. If the strike price of the option is not
profitable as compared to the price of the stock, the option is said to be out-of-the-money.
If the strike price is equal to the stock's price in the market, the option is
said to be at-the-money.
Formula and Calculation of Intrinsic Value
Below
are the equations to calculate the intrinsic value of a call or put option:
Call Option Intrinsic Value = USC − CS
USC - Underlying Stock Current Price
CS
- Call Strike Price
Put Option Intrinsic Value
= PS – USC
USC - Underlying Stock Current Price
PS
= Put Strike Price
Underlying
Stock’s Price
Underlying Stock’s Price is a current price of stock. The market price or spot price of the underlying security is independent of the option. For call options, when the underlying stock’s price rises, the option’s price should increase. The opposite is true when the stock drops. On the other hand, as the underlying price rises, put option premiums fall. When the underlying stock’s price rises, put option premiums would rise. Pretty simple right? If you recall earlier, you could clearly see how your PnL would change when the stock’s price changes.
Time Value and Expiration
When
there is a lot of time remaining until the options expiration date, the premium
would be higher. In other words, an option with six months until its expiration
date would have a higher premium than one with one month until expiration, all
else being equal.
Since options contracts have a finite amount of time before they expire, the amount of time remaining has a monetary value associated with it—called time value It is directly related to how much time an option has until it expires, as well as the volatility, or fluctuations, in the stock's price.
The
more time an option has until it expires, the greater the chance it will end up
in the money. The time component of an option decays exponentially.
The actual derivation of the time value of an option is a fairly complex
equation. As a general rule, an option will lose one-third of its value during
the first half of its life and two-thirds during the second half of its life.
Formula and Calculation of Time
Value
The formula below shows that time value is derived by subtracting
an option's premium from the intrinsic value of the option.
Volatility
Volatility
is the underlying stock’s tendency to fluctuate in price. This means volatility
reflects the price change’s magnitude and does not have a bias toward price
movement in one direction or another. You need to understand that the higher
the volatility, the higher the option premium should be. The lower the
volatility, the lower the premium.
Option's
time value is also highly dependent on the volatility the market expects
the stock to display up to expiration. Typically, stocks with high
volatility have a higher probability for the option to be profitable or
in-the-money by expiry. As a result, the time value—as a component of the
option's premium—is typically higher to compensate for the increased chance
that the stock's price could move beyond the strike price and expire
in-the-money. For stocks that are not expected to move much, the option's time
value will be relatively low.
The
effect of volatility is mostly subjective and difficult to quantify.
Fortunately, there are several calculators to help estimate volatility. To
make this even more interesting, several types of volatility exist, with
implied and historical being the most noted. When investors look at volatility
in the past, it is called either historical volatility or statistical
volatility.
Interest Rates
Generally, interest rates do not affect premiums as much as the time value, the underlying stock price, and volatility. However, when interest rates experience a high degree of fluctuations, rates matter. An increase in interest rates typically increases call prices and decreases put prices, based on the famous Black-Scholes pricing model. There are flaws with this model, but it’s an industry standard. However, we won’t get into all the details of this pricing model.
Dividends
Options are often priced assuming they would only be exercised on the expiration date. That means if a stock issues a dividend, the call options could be discounted by as much as the dividend amount. However, put options would be more expensive since the stock price should drop by the dividend amount after the ex-dividend date.
Before you move on, you should clearly understand these factors and how they affect option prices. Next, we’re going to look at an extremely important topic: intrinsic and extrinsic value.
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