# Trying to get my head around how options work

A stock X is trading at \$215. I bought a put at a strike price \$195 for \$2.55 premium(paid \$255) expiring June 7.

Today the stock is down by \$15 to \$200. However, the price of my put is reduced from \$2.55 to \$2.10.

Why isn't the stock price and options price linear? For example, the price of your PUT increases with every dollar drop in the stock price?

Is the basic assumption that if you guess the direction of where the stock will move correctly, the price of your options trade increases incorrect?

How is the price premium for any stock option (\$2.55 in my case) determined.

Edit: For anyone looking for specifics, the stock was NYSE:PANW

D Stanley's answer accurately explains the behavior of a put's price in relation to the price of the underlying and his graph demonstrates its non linear behavior. However, there's more to this story.

The short answer is that the brick wall that you ran into was an implied volatility contraction.

Option price is based on 6 variables: Stock price, strike price, volatility, time until expiration, current interest rate and dividend (if any) - with dividend and interest rate being minor factors. The strike price is fixed and in the short term, day to day time decay is minimal. So that leaves two main factors, price and volatility.

When there is pending news, demand for options drives option premium up. This is reflected in the implied volatility. After PANW's last earnings report, its average IV for all options was in the high 20s where it stayed until a month ago when it started rising on its way to the high 60s. You can view this at IVolatility (free sign up) at:

https://www.ivolatility.com/options.j?ticker=PANW:NYSE&R=1&period=12&chart=2&vct=

What does this mean for you? Strap on your seat belt.

I don't know what price the PANW was when you purchased the put so all I can do is be in the ballpark. At yesterday's closing price of \$215.32, at yesterday's IV, your put was worth \$2.20. Last night PANW reported earnings and it was taken to the cleaners today (down over \$15 intraday). Average IV contracted to 34 today, most likely on the way back to the high 20s. A valuation at yesterday's price with today's IV means that your 6/07 \$195 put was really worth only 15 cents. Due to the extreme IV expansion, it was \$2.05 higher. Essentially, you paid through the nose for something worth a lot less.

Now let's factor in the price drop to today's pricing. At an IV of 34, the 6/07 \$195 put should be worth \$2.10 today at \$200.32 which is in line with your observation.

IOW, the put's price contracted \$2.05 due to IV collapse but expanded \$1.95 due to the \$15 price drop for a net loss of 10 cents.

The reason for the difference in my numbers (\$2.20 vs \$2.55) for the put is that IV is not static during the day of the earnings announcement. It was probably higher (73-ish) when you took your position.

The lesson? Buying high IV options just before a significant news release (like earnings) is an exercise in futility. IMO, if you're going to dabble, sell some inflated premium to offset the inflated premium that you buy - for example, spreads.

• An an example, a 6/07 \$205/\$195 bearish put spread would have cost about the same as your long \$195 put. With the IV contraction and PANW's price drop, the spread would have doubled in value (\$2.50 gain). May 31, 2019 at 0:15
• This is by far the best explanation I could find, Thank you. One follow up question, would it better to buy options (PUT and CALL both) which are "In the Money" during earnings ? So this way, even if the option loses its value in the IV. The option could be deep in the money due to big swings in the stock price after earnings announcement ?
– john
May 31, 2019 at 19:24
• Not sure what you mean by "Would it better to buy options (PUT and CALL both) which are In the Money?" Are you referring to buying an ITM call if bullish or an ITM put if bearish or do you mean buying both as in a strangle? Buying ITM reduces the time premium component but adds intrinsic (ITM) cost so if wrong directionally, you lose much more. There are space limitations in comments so if you want to discuss this, open a chat window (I have no clue how to do it). May 31, 2019 at 20:25
• The best way to get a feel for the effect of IV contraction on options is to analyze some data pre and post earnings announcement. AMBA and MDB have EA-s in the next few days and they have sky high IV for 6/07 options. Capture quotes about 10% on either side of current price as well as for the first 3-4 weekly expirations and observe to dispersion of the IV expansion across the different weeks and strikes as well as the same after the EA. Jun 1, 2019 at 11:49
• @ Bob Baerker I tried creating a chat room. Please find it here: chat.stackexchange.com/rooms/94512/…
– john
Jun 4, 2019 at 18:30

You bought an out of the money put, meaning that if the stock had stayed at \$215, your put would be worthless at expiry. (why exercise and sell the stock for \$195 when you can sell it for \$215 on the open market?)

So the intrinsic value of the option at this point is zero. The rest of the value of the option indicates that there is some probability that the stock will get below \$195 and your option will actually have some value. The closer to the strike price, the higher that probability and the more valuable the option.

That movement is not linear, though. Here's a graph showing the value of a put option before expiry (the red line) and at expiry (the blue line)

(ignore the "exchange rate" axis label - it's the only graph I could find for a put option. It should be "stock price" instead)

As you can see, the value of the put rises slowly and accelerates as the put becomes more in-the-money (meaning the option actually has value at expiry at the current stock price).

It is surprising that your put went down in value. Unless you bought the put a long time ago (when there was a lot of time for the stock to drop below the strike) I'd expect the put to be more valuable as it gets closer to the strike price.

How is the price premium for any stock option (\$2.55 in my case) determined.

It's a fairly complex formula with several inputs: the current stock price, the strike price, the volatility (rate of change) of the underlying stock, the time until maturity, and current interest rate. Look up "Black-Scholes Option Formula for more technical detail.

• The last time that PANW was \$215 was 4 months ago so it's not a likely possibility to pay only \$2.55 for the put. And since it's a weekly option, it's an impossibility since the 6/07 weekly didn't exist then. As for the put surprisingly going down in value, it was due to a severe earnings announcement implied volatility contraction :->) May 31, 2019 at 0:02

Why isn't the stock price and options price linear?

The option has an expiration date. Every day that goes by, the date is closer and the risk is different.

How is the price premium for any stock option (\$2.55 in my case) determined.

The market. There are various pricing models to explain or estimate an acceptable price but you can never assume all market participants are using or will continue to use the same model.

The options price represents the likelihood that the stock will reach the strike price at or before the expiration date.

At the time the option was purchased, there was probably a very long time before expiration, and the models assumed that there was a certain likelihood that the strike price would be reached, even though there was a longer distance between the strike price and the current stock price.

However, now that there is only a week to go (about 5 days), the chances are much lower that it will make such a big movement during those 5 days, so the price is lower.

In general, an option only follows the price of the stock (in a 1:1 ratio) if the option is 'deeply in the money'. For example a \$100 Call on a \$200 stock, or a \$300 Put on a \$200 stock. The actual ratio is modeled and called the delta - in the case of the deep in the money options, that would be 100%. If the strike price is close to the current stock price, then the delta is about 50%. i.e. the stock would have to move \$2 for the option to move \$1. If the option is 'out of the money' then the delta goes below 50% towards zero, depending on how far out the option is.

• I don't agree with downvote. Any feedback would be appreciated.
– xirt
Jun 5, 2019 at 16:01