Options Trading Greek Interactions

Volatility Smile is an intriguing idea that I think to be something worth knowing. Therefore, instead of exploring further, I prefer simply grazing the topic.

Theoretically, all options of the same underlying expiring on the same date should show comparable Implied Volatilities. Nevertheless, in practice this is not always the case.

The option chain of SBI on 4th September 2015 has the 225 strike as ‘At the money’ and this is highlighted in blue. The two green bands depict the implied volatilities of other strikes. Moving away from ATM, you will notice that both Calls and Puts have higher IVs. This pattern holds true for all stocks/indices and the ATM option has the lowest implied volatility.

 – Volatility Cone

Up until now, we have refrained from discussing the ‘Bull Call Spread’ strategy. I will proceed under the assumption that you are already familiar with it.

As an options trader, implied volatility of the options has a great impact on your success. With a Bull Call Spread, if you purchase when volatility is high, you will face greater costs and smaller potential rewards. If, however, you enter into the position when volatility is low, then it will cost less but you could earn more.

As of today, Nifty is trading at 7789 and the implied volatility of option positions is 20%. With that in mind, a 7800 CE and 8000 CE bull call spread would cost 72 and has a potential profit of 128. Alternatively, if the implied volatility were higher at 35%, this same position would require 82 to purchase and would only yield a potential profit of 118. It’s worth noting that with an increased volatility level, not only do prices rise but the prospective gains diminish significantly.

The crux of option trading lies in assessing volatility levels to time transactions accurately. In addition, a trader must select the underlying and strike appropriately (especially if their strategies are dependent on volatility).

Given that Nifty ATM options have an IV of ~25%, and SBI ATM options having an IV of ~52%, should you trade the former due to its low volatility or opt for the latter?

The Volatility cone is a useful tool for Option traders, as it helps them to ascertain the costliness of an option, whether it be in different strikes of the same security or across different securities. This gives the trader greater flexibility and decision-making options.

Let’s figure out how to use the Volatility Cone.

This chart shows the last 15 months of Nifty’s performance, with vertical lines marking derivative contract expiries and boxes indicating price movements 10 days beforehand.

If you calculate the Nifty’s realized volatility in each of the boxes, you will get the following table –

The realized volatility of Nifty has varied significantly, with February 2015 seeing 56% as its highest and April 2015 noting the least at 13%.

We can calculate mean and variance of the realized volatility, as demonstrated below.

By repeating this exercise at 10, 20, 30, 45, 60 and 90-day intervals, we can compile the data into a table.

Graphically, the table is represented by a cone – hence the name ‘Volatility Cone’.

The way to read the graph is to start by locating the ‘Number of Days to Expiry’ and examining the values plotted above it. If the number of days is 30, for instance, take a look at the data points (representing realized volatility) right above it to identify the ‘Minimum, -2SD, -1 SD, Average implied volatility etc’. It is important to bear in mind that the ‘Volatility Cone’ illustrates historical realized volatility.

Having created the volatility cone, we can map Nifty’s near month (September 2015) and next month (October 2015) implied volatility onto it. The graph below clearly illustrates this.

Each dot on the chart is an indication of the implied volatility for a corresponding option contract. Blue dots represent call options, while black dot show put options.

Take the first set of dots from the left for example; there are 3 within it, two being blue and black. Each spot stands in for an option contract’s implied volatility – as such, the lowest blue one could be 7800 CE while over it lies 8000 CE and 8100 PE respectively.

Note that the first set of dots, stating from the left, represent options for the near month (September 2015), and are plotted 12 days from today. The next set on the x-axis are for middle month (October 2015) and will expire 43 days from now.

Interpretation

Examine the second set of dots on the left. One in blue is just above the maroon-coloured +2SD line and might represent 8200 CE expiring on October 29, 2015. This position indicates that the stock is experiencing an elevated implied volatility level, which surpasses its average volatility when there are 43 days to expiration over the last 15 months. Consequently, it has a high IV and correspondingly prices will be significant – implying traders may wish to consider a strategy of shorting volatility with expectations of reduced movement.

A black dot near -2 SD line on the graph is indicative of a Put option with low IV, and thus a low premium. This could make this put option attractive for trading purposes, if one wanted to buy it.

The trader can utilize the volatility cone to analyse a stock’s past realized volatility and its current implied volatility. This helps them gain an understanding of the relationship between the two.

Options close to the +2 SD line are expensive, whereas those near -2 SD line are less costly. Traders can take advantage of this mispricing of IV by taking a short position in pricier options and looking to go long on more affordable ones.

Please note: Use the plot only for options which are liquid.

We have now acquired a thorough grasp of Volatility through our conversation concerning the Volatility Smile and Volatility Cone.

– Gamma vs Time

In the following parts of this discussion, let’s direct our focus on the relationships between Greeks.

Let us now focus a bit on greek interactions, and to begin with we will look into the behaviour of Gamma with respect to time. Here are a few points that will help refresh your memory on Gamma –

• Gamma measures the rate of change of delta

• Gamma is always a positive number for both Calls and Puts

• Large Gamma can translate to large gamma risk (directional risk)

• When you buy options (Calls or Puts) you are long Gamma

• When you short options (Calls or Puts) you are short Gamma

• Avoid shorting options which have a large gamma

The last point suggests that it is not prudent to short an option with a large gamma. However, if you decide to proceed with shorting one having a small gamma value, the goal would be to keep it till expiry and gain the entire option premium. In this case, how can we guarantee that the gamma will stay low during the entirety of the trade?

To gain a clear insight into this, we should consider the changes in Gamma over time.

This graph illustrates how the gamma of ITM, ATM, and OTM options varies as ‘time to expiry’ decreases. The Y axis shows gamma while the X axis displays time to expiry. It is essential to reverse the usual direction when reading the X axis; 1 at the extreme right means there is ample time to expire, whereas 0 on the far left implies no time remaining. This timeline can be for any duration – 30 days, 60 days or 365 days – but the behaviour of gamma will remain constant.

The graph above drives across these points –

• When ample time remains until expiry, Gamma is low for all three options—ITM, ATM and OTM. However, ITM option’s Gamma tends to be less than that of ATM or OTM options.

• The gamma values for all three strikes (ATM, OTM, ITM) remain fairly constant till they are half way through the expiry

• ITM and OTM options race towards zero gamma as we approach expiry

• The gamma value of ATM options shoots up drastically as we approach expiry

From these points it is quite clear that, you really do not want to be shorting “ATM” options, especially close to expiry as ATM Gamma tends to be very high.

Realizing that we are dealing with three variables – Gamma, Time to expiry and Option strike – it is logical to visualize how changes in one variable impact another.

The graph depicted is known as a ‘Surface Plot’, which can be employed to determine the behaviour of three or more variables. On the X-axis, ‘Time to Expiry’ is represented, with the Y-axis providing ‘Gamma Value’. The third variable, ‘Strike’, is featured on the final axis.

Red arrows are plotted on the surface plot to indicate that each line corresponds to different strikes. The outermost lines show OTM and ITM strikes, while the one at the centre represents an ATM option. As expiry draws nearer, the gamma values of all strikes except ATM approach zero, with highest values for the line in the centre.

From an alternate viewpoint, we can still appreciate the notable spike in Gamma for ATM options. Conversely, Gamma remains constant across other option strikes.

 – Delta versus implied volatility

It’s clear that 6800 is 1100 points below the current level of Nifty at 7794. Interestingly, the 6800 PE is trading at 8.3 which suggests a lot of traders anticipate a drop in the market over the next 11 trading days (noting the two trading holidays during this period).

It is unlikely that the Nifty will go down 1,100 points (14% lower than its current rate) in 11 trading sessions. However, why is the 6800 Put Option at 8.3? Could something else be pushing up the asking price besides predictions?

The graph represents the movement of Delta with respect to strike price. Here is what you need to know about the graph above –

• The blue line represents the delta of a call option, when the implied volatility is 20%

• The red line represents the delta of a call option, when the implied volatility is 40%

• The green line represents the delta of a Put option, when the implied volatility is 20%

• The purple line represents the delta of a Put option, when the implied volatility is 40%

• The call option Delta varies from 0 to 1

• The Put option Delta varies from 0 to -1

• Assume the current stock price is 175, hence 175 becomes ATM option

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

• Beginning from the left – examine the blue line (CE delta when IV is 20%), with 175 being the ATM option, 135, 145 and so on are all Deep ITM. Evidently, Deep ITM options have a delta of 1

• When IV is low (20%), the Delta flattened at the tips of the wings (deep OTM and ITM options). This means Delta moves slowly, as does option prices. To put it another way, very deep in the money options behave similarly to futures contracts when volatility is low; out of the money options will have close to zero prices.

• You can observe similar behaviour for Put option with low volatility (observe the green line)

• We can observe that the end of the red line (delta of CE when volatility is 40%) does not flatten; it appears to be more reactive to underlying price movement. In other words, the premium on the option will change significantly with respect to any changes in spot price, when volatility is high. This means a wide range of options around ATM will react noticeably to spot price movements, when volatility increases.

• It follows that Put options tend to be more valuable when volatility is high, as demonstrated by the purple line.

• When the volatility is low, the delta of OTM options drops to close to nothing (blue and green lines). On the other hand, even at high volatility, the delta of OTM will remain above zero and maintain some level of value.

Now, going back to the initial thought – why is the 6800 PE, which is 1100 points away trading at Rs.8.3/-?

The 6800 PE is a highly out-of-the money option, as one can tell from the delta graph above that implies in an environment with high volatility the deep OTM options will have a not null delta.

Draw your attention to the Delta versus IV graph, particularly at the Call Option delta when implied volatility is high (maroon line). We can see that it doesn’t come close to zero like the CE delta when IV is low (blue line), which explains the premium not being too low. Additionally, with sufficient time value, the OTM option still has a respectable premium.