Option Pricing

Now you understand what options are, the next thing to understand is how are they priced. It’s clear that a contract giving me the right to buy or sell something at a set price in the future could be really valuable, but how valuable?  

Option pricing is a tricky area- it can be a real minefield and a complicated mathematical minefield.  You can fall down many holes of different models (Black Scholes etc) but fortunately in reality you don’t have to have a maths PhD to understand and make money in options, in reality it is far simpler than many would have you believe.

Firstly, remember that options are derivatives- so they themselves have no inherent value- their value is derived from the underlying asset to which they relate. At any point in time, the value of an option is largely made up of two separate things:

Time Value: Time value represents the fact that you own something today that gives you the right to transact in the future at a set price. The longer in the future your right extends, the more it’s worth, because there is a higher likelihood of your option being ‘in the money’ and worth something. Example: let’s say you own the UPS $200 Call that expires on June 2023.

If UPS is trading at $180 in January, even though your option is out of the money, your option still has lots of time value, because you’re 6 months from expiry- so there’s a good chance the price could reach above $200 by June. If you fast forward to May and the price is still only $180, well your time value is going to be a lot lower as you’ve now only got one month for the price to rise above $200.

Time value erodes every single day- which is good news for whoever wrote (sold the option), it is bad news for whoever bought it.   

Intrinsic Value: Intrinsic value relates to whether your option is in the money, or out of the money. It is simply the difference between the current stock price and your strike price. If the option is in the money that’s a positive number, if the option is out of the money, there is no intrinsic value. If you’re holding a call option with a strike price lower than today’s market price, let’s say your option has a strike of $150 vs today’s price of $180, then you’re holding an option with $30 of intrinsic value.

But if the stock is trading at $180 and your call option has a strike price of $200, your intrinsic value is $0, because your strike price is above the current market price.

Now while both time value and intrinsic value are fairly intuitive, you can see that for time value in particular, it’s hard to attach a real monetary value to it. How much is 5 months of opportunity worth compared to 1 month?

The way this is calculated for options is based on something called volatility- which is a calculation of how much the stock price moves up and down. The more volatile a stock is (the more it’s price is expected to move over the term of an option) the higher the likelihood of it changing enough for your option to be worth something at expiry- so more volatility equals more time value.

It makes logical sense- if you own an option that is currently 10% out of the money, expiring in one month, but the price of the stock hardly ever changes (low volatility), then your out of the money option probably isn’t worth much as it’s not likely to be in the money on expiry. On the other hand, if the stock is hugely volatile and the price moves a large amount every day, then you’ve got a good chance your option will be in the money in a months time. As a result, for the same distance in/ out of the money, time value is worth different amounts depending on what the underlying stock is.

For some context, volatility itself (known more commonly as ‘vol’) is calculated based on the historical price movements of a stock- depending on how much a stock has moved each day in the past, some not so clever calculations use standard deviation to predict how much it will move each day in the future. In reality the volatility calculation is quite heavily flawed- it is based on historical data (so whatever happened to a stock in the past is assumed to happen in future), and it relies on standard deviation for the calculation.

In real life, stocks are not standardly deviated- they tend to tick up gradually and crash down hard. But the flaws in the calculation needn’t be a concern- you simply need to understand the intuitive principle that the more volatile a stock is, the more expensive the option will be.

(Extra comment: technically just to confuse even further- volatility in the world of options is actually split into two types: realized volatility (what’s actually happened historically) and implied volatility (what is implied in the future)- for our purposes here it really isn’t necessary to make these distinctions, I mention them simply for context.

One final point to note on valuation, that while intrinsic value and time value look like separate things, they are in fact interdependent. For example, the amount of time value in an option is also affected by how far in or out of the money it is. An option that’s deeply in the money will react little to changes in vol and react little to time value.

The reasoning is intuitive- if it’s really deep in the money then its also really likely that option will expire in the money (with intrinsic value), so the passage of time or changes in vol don’t really matter- you’re likely to make money anyway.

If an option is trading very close to your strike price, then you’ll see that time value erodes more quickly, as each passing day increases the chance of that option ending out of the money, and therefore worthless. This is good for whoever wrote the option, bad for whoever owns it. This loss of time value is also often called ‘decay’.

The final impact on option pricing is old fashioned supply and demand. If lots of people are trying to buy calls, that will squeeze prices up and make them more expensive. The reverse is also true.  While a lot of option pricing is mathematical and formulaic, prices are not immune from these traditional market forces.

Dividends 

Dividends or lack thereof will impact options prices. As the holder of an option, you don’t actually own the stock itself, so you are not eligible to receive any dividends that may be due. The fact that dividends may be paid during the term of your option can reduce the price of a call option, and increase the price of a put, as stocks typically (and theoretically should) fall in price by the same amount as the dividend that’s just been paid out.

So we should expect a fairly mechanical price decline at the time of dividends. This will be reflected in the option prices.

Holders of long call options may sometimes want to exercise their option early (buying the stock), giving up any remaining time value if they really want to be eligible to receive the dividend. You need to own the stock before the ex dividend date to be eligible to receive the dividend.