# What is the Put/Call Ratio, Max Pain, and it's usage as a Directional Indicator for the Underlying Asset

### Level 1 - Zero to Options Hero

In today’s post, the OptionsNerds will explain the concepts of Put Call Ratio and Max Pain, and what possible indications this can give us on the future direction of the underlying asset. Let’s go!

Now, if you’ve been having a look at options market commentary, you might see something similar to the below (which is an example from the cryptocurrency options market):

The Put Call Ratio and Max Pain Point are two things that options traders like to look at and are also useful for directional traders. Why is this the case?

**Put Call Ratio**

First of all, the Put Call Ratio is mathematically defined as:

The news item above, it is describing that of the options expiring on Nov 24th, the Put Call Ratio is 0.83 for BTCUSD.

This gives an indicator that option buyers have more positions expiring on Nov 24th expecting the BTCUSD price to be higher than lower. Usually the sellers of options are the option market-makers who are continuously delta-hedging their portfolios, so **if the Put Call Ratio for options expiring today is skewed towards puts, the market-maker delta-hedging activity will likely result in the spot drifting down, and vice versa for calls.**

The Put Call Ratio can also be used to look at the trading activity on any given day. This gives a sense of which side of the market (up or down) option buyers have been more excited about on any given trading day. A typical put-call ratio for equities that is considered a good basis for evaluating market sentiment would be 0.7 — that is, a ratio below 0.7 would mean that options buyers are adding to bearish positions on the day and above 0.7 would mean that options sellers are adding to bullish positions on the day. The reason that 0.7 is the typical neutral put-call ratio (in the equity markets) is that normally there are more investors buying calls than buying puts, so 0.7 is a typical put-call ratio for evaluating sentiment.

**Max Pain**

Max pain, or the max pain price, is the strike price with the most open options contracts which causes the most losses for option buyers at expiration. It is called max pain due to the idea of **maximum pain theory**, which assumes that option buyers will buy and hold the option (without delta hedging) until expiration, while option sellers are market-makers who will be continuously delta hedging their option portfolios. In this case, the max pain price is the price at which the maximum amount of financial losses would occur for these option buyers. This is because they are not delta hedging and thus their payoff is solely based on how far the underlying is at expiry from the strikes of the options that they purchased. Note, that this theory is controversial in the industry because of the assumption that only option sellers are continuously delta-hedging their option portfolios.

**Calculating the Max Pain Price**

To calculate the max pain price, one needs to sum up the difference between the current spot price and the strike price for each in-the-money strike price, multiply by the open interest of that strike, add together the dollar value for calls and puts, and repeat for each strike price. Finally, we need to determine which strike price has the highest dollar value, and this is the Max Pain Price.

In formulas, for each strike, we can define the Pain Value as:

and then find the strike that maximizes the Pain Value across all strikes with open interest.

**Important point**: The OptionNerds believe that an improved Max Pain Price metric should be scaled by the time to maturity to account for the higher gamma of shorter-dated options which would have a larger influence on the potential path of the underlying towards the Max Pain Price. We therefore define a Modified Max Pain Price based on a Modified Pain Value:

**Note:** If the Max Pain Price is being calculated for a given expiry (i.e. options expiring today, options expiring tomorrow), then the Modified Pain Value is not needed as the Gamma will be directly proportional to the Open Interest.

Let’s dive in to a numerical example of calculating the Max Pain Price!

Let’s say the Stock Price is $100, and the open interest is 10 lots of $110 calls, 20 lots of $115 calls, and 5 lots of $85 puts. The options open interest graph looks like this:

The $110 strike has a Pain Value of (($110-$100) * 10), the $115 strike has a Pain Value of (($115-$100) * 20), and the $85 strike has a Pain Value of (($100-$85) * 5). When we compare these values, it is clear that the Max Pain Price is $115.

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