How option writers had an easy ride in February 2018

Karthik Rangappa

The month of February 2018 was a very interesting month for trading options. This was the kind of month which favored option traders with knowledge of Option Greeks. Here is the background data for you –

Date: February 6, 2018

Nifty Spot - 10498

Option - 9500 PE

Option Premium - Rs 20.35

Number of trading days to expiry - 9

Consider this, the 9500 Put option, which was 1,000 points away was trading at Rs 20.35 or in other words, there were few market participants, who were willing to pay a premium as high as 20.35, for this option.

The buyers of these Put option would be profitable only if the market fell 10 percent in a matter of nine days. The question to ask – what is the probability of Nifty falling 10 percent in a matter of nine days?

Well, as you can imagine, the probability of this event occurring is low. Fair enough, but given the low probability, why was the premium so high for this option?

Is there something else which is driving the price of these options apart from the option buyer’s irrational expectations?

The answer to these questions lies in the following graph –

This graph represents the movement of Delta with respect to strike price and volatility. Here is what you need to know about the graph above:

➢ The blue line represents the movement of the delta of a call option, when the implied volatility is 13 percent

➢ The red line represents the movement of the delta of a call option, when the implied volatility is 25 percent

➢ The green line represents the movement of the delta of a Put option, when the implied volatility is 13 percent

➢ The purple line represents the movement of the delta of a Put option, when the implied volatility is 25 percent

➢ The call option Delta varies from 0 to 1 and the Put option Delta varies from 0 to -1

➢ Nifty is at 10498, hence 10,500 becomes the ATM strike

With the above points in mind, let us now understand how these deltas behave:

➢ Starting from left – observe the blue line (CE delta when IV is 13 percent), considering 10,500 is the ATM option, strikes such as 9,500, 9,700, etc are all Deep ITM. Clearly, Deep ITM options have a delta of 1

➢ When IV is low (13 percent), the delta flattens at the ends (deep OTM and ITM options). This implies that the rate at which Delta moves (further implying the rate at which the option premium moves) is low. In other words, deep ITM options tend to behave exactly like a futures contract when volatility is low.

➢ You can observe similar behavior for Put option with low volatility (observe the green line)

➢ Look at the red line (delta of CE when volatility is 25 percent) – we can notice that the end (deep ITM/OTM) is not flattened, in fact, the line appears to be more reactive to underlying price movement. Or in other words, when the volatility is high, the deep OTM and ITM options tend to display faster delta changes

➢ A similar observation can be made for the Put options when volatility is high (purple line)

➢ Interestingly, when the volatility is low (look at the blue and green line) the delta of OTM options goes to almost zero. However when the volatility is high, the delta of OTM never really goes to zero and it maintains a small non zero value.

Now, going back to the initial question – why is the 9500 PE, which was 1000 points away, trading at Rs 20.3?

Well, that’s because 9,500 PE was a deep OTM option, and as the delta graph above suggests, when the volatility is high, deep OTM options have non zero delta value. In fact, the volatility of Nifty had shot up to 24 percent, as opposed an average value of 13-15 percent.

Given the high volatility, Delta does not really collapse to zero (like the blue/green line). This should explain why the deep OTM option commanded a premium.

Further, add to this the fact that there was some time value, the OTM option tends to have a ‘respectable’ premium, much to the option writers delight.

(Disclaimer: The author is VP, Educational Services, Zerodha. The views and investment tips expressed by investment expert on moneycontrol.com are his own and not that of the website or its management. Moneycontrol.com advises users to check with certified experts before taking any investment decisions)