Introduction to Options Pricing and Implied Volatility (IV)

When first introduced to options it can be easy to brush over the subject of pricing or volatility without realising it’s importance, after all with futures once your position is open all you really need to worry about is whether the price moves in your favour or not. So with this article I hope to plant the seed in the minds of anyone new to options that it’s an extremely important variable to be aware of.

The mathematics behind option price modeling is quite a long and complex subject so we’ll save the intricate details for another time, and today we will simply introduce the idea of implied volatility, explain how it relates to options prices and why they are both important when planning which option strategies to use.

What is Implied Volatility?
Implied volatility is a forward looking figure that tells you what the current price of an option implies about the expected size of future price movements of the underlying asset.

If the market has a view that the future price movements of the asset will be small, then option prices and therefore the corresponding implied volatility figure (IV) will be lower. If the market has a view that the future price movements of the asset will be large, then option prices and therefore implied volatility will be higher.

It is important not to confuse implied volatility with historical volatility (aka realised volatility) which is a measure of how much the asset has actually moved in the past. Whereas implied volatility is the market’s current estimate of future moves (based on the options pricing). It can however be useful to compare these two.

If you only ever looked at the numerical cost of an option it would be quite difficult to tell if it was relatively cheap or expensive as there are several other variables that affect an option’s price other than just the current price of the underlying asset.

With so many different strike prices and expiry dates on offer how can you possibly compare different option prices to one another? The answer is with the corresponding implied volatility figure, and because it is an annualised figure it also allows comparison between options with different expiry dates.

The Effect of Supply And Demand
When market participants are expecting a big move in price, buyers of options will be willing to pay a higher price as they expect the larger move to make up for the larger initial cost. Sellers will also want to charge a higher premium for the options they are selling to account for the (perceived) increased chance of a big move. This will push up option prices which leads to a higher implied volatility figure.

Similarly when future moves in price are expected to be smaller there will be less demand to buy and more participants willing to sell and collect premium, driving down option prices and therefore implied volatility.

Where IV Is Displayed On Deribit
Below we have an example of the current prices of Bitcoin options expiring on 29th March 2019 (in ~19 days at time of screenshot).

Highlighted in green is the 4000 call. The current bid is 0.0365 BTC which equates to 48% IV displayed to the left. The current ask is 0.037 BTC which equates to 48.5% IV displayed to the right. We will move on to what parameters affect these figures shortly.

Notice also, highlighted in red, that the bid on some of the options has an IV of 0%. This is because these options are in the money and the current bid is less than the intrinsic value.

Intrinsic vs Extrinsic Value
An options value is comprised of it’s intrinsic value plus it’s extrinsic value.

The intrinsic value is how much the option would be worth if it was exercised immediately, or to put it another way how far in the money it is. So for example if the underlying price of BTC is $3500, then a put with a strike price of 4000 would have an intrinsic value of $500. Any put with a strike price under 3500 would have an intrinsic value of zero.

An option’s extrinsic value is calculated as the current option price minus the intrinsic value. For example if the put with a strike price of 4000 was priced at $700 and the current BTC price was still $3500, it’s extrinsic value would be $700 — $500 = $200. Extrinsic value is also sometimes known as the time value of the option. As the option gets closer and closer to the expiry date this time value decreases towards zero until at expiry the only value an option has is it’s intrinsic value.

Black Scholes Option Pricing Model
By far the best known options pricing model is called the Black Scholes model, and indeed this is what is used on Deribit. There are several parameters that are entered into the Black Scholes model to generate the total option price. These include the underlying price, time to expiry, strike price and implied volatility.
(There are also interest rates and dividend yield parameters, however for the Bitcoin options on Deribit these are both assumed to be zero)

The mathematics behind this model is quite complex so we won’t go into it in this article, however thankfully there are a multitude of free options calculators available online (like this one) that allow you to enter the parameters above and generate the theoretical price for that option.

Why Option Pricing and IV Matters For Profitability
When buying options, or anything for that matter, you of course want to get them for the best (lowest) price possible as this will mean you lose less capital when you’re wrong and make more profit when you’re right. And of course the opposite is true when selling, you want to charge the highest price possible. All other things being equal it is better to be buying options when implied volatility is relatively low, and selling options when implied volatility is relatively high.

First let’s look at a general example of how different values of implied volatility affect the price of a single call option. In the chart below we have an asset with a current price of $100 and we’re looking at call options with strike prices in $10 increments (70, 80, 90 etc).
The y axis is the total call option premium for each strike, and the x axis is the strike price. Each coloured line represents a different value of implied volatility.

The other values used to calculate the prices with the Black Scholes model are included on the chart.

As you can see the higher the IV percentage the more expensive the options are for every strike price. The chart above is the total option price so also includes the intrinsic value for the in the money options. So now let’s take that out to see just the extrinsic value as you’ll notice something interesting.

The above chart shows that at the money options have the most extrinsic/time value, and this decreases the further away you get from the current price of the asset (in this case $100).

All other things being equal the lower the IV the closer option prices will be to their intrinsic value. As the expected move is smaller, so is the extrinsic value.

Bitcoin Example
Let’s take a look at an example of buying a strangle on Bitcoin on the 28JUN19 expiry on Deribit. We’ll buy the 3500-P and 4000-C, which at time of writing has ~115 days to expiry. (Bitcoin price at time of writing was ~$3800)
The option prices are currently the equivalent of just under 60% IV, so let’s compare how a difference in IV of +/-20% would affect the possible profit of this strategy. On the chart below we have:

• Orange — 40% IV — Which equates to a combined price of 0.121 BTC
• Blue — 60% IV — Which equates to a combined price of 0.208 BTC (roughly the current prices)
• Red — 80% IV — Which equates to a combined price of 0.2955 BTC

It’s clear to see that the higher the implied volatility percentage, and therefore the higher the cost to purchase the options, the further down the chart the profit line is pulled. Meaning at every price point this strangle purchase makes less money at expiry.

Also notice how the breakeven points (the points at which the profit line crosses the x axis) move further away the higher the option prices and IV are. This means when IV is higher you need a larger move just to get to breakeven. This should be intuitive as the more you pay for something the more you need to receive back to turn a profit.

So all other things being equal it makes sense to try and buy when IV is as low as possible because:

• The price you pay to open the position is lower so you lose less if you’re wrong
• The breakeven points are closer, so you don’t need as big of a move for the position to profit as you would if IV was higher

And you might be thinking at this point ‘well I can’t choose what the current IV level is, the price is what it is!’ and you’d be right. However you can track both historical and implied volatility over time.
By tracking an asset’s volatility over time you can get a much better sense of when to use strategies that are long volatility (for example a long strangle as above) and when to use strategies that are short volatility (for example a short strangle).

To understand whether a particular position is long or short volatility you just need to understand how a change in implied volatility will affect the value of the position. In general when buying options you want implied volatility to increase after you have opened the position. This is because all other things being equal this will increase the extrinsic value of the options you have purchased. Conversely when selling options you ideally want implied volatility to decrease after you have opened the position, as this will decrease the extrinsic value of the options you have sold.

This article has very much just scratched the surface of options pricing and implied volatility, but I hope if you’re new you’ve now got a sense of how this variable needs to be something you pay attention to when trading options.

If you have any questions at all feel free to comment on here, hit me up on twitter @cryptarbitrage or in the Deribit telegram chat here: https://t.me/deribit

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