While the concept of volatility smirk is simple, the pattern itself is unstable. For example, different expiries have different shapes.
And these shapes change across days as well.
One way to keep track of these changes is by fitting a model through the implied volatilities. Here, we fit a parabola (y = ax2 + bx + c). a, the coefficient of strike_pct2, gives a measure of the narrowness/steepness of the smirk.
By sampling the curve and tracking these coefficients, you can begin to form an opinion on what is “normal” vs. a trading opportunity.
The volatility risk premium (VRP) is the difference between implied volatility and realized (or actual historical) volatility. Implied volatility is, on average, overpriced compared to realized volatility.
The VRP exists because investors are essentially “selling insurance” when they sell implied volatility.
Volatility is negatively correlated with equity returns; typically, volatility increases when equity markets decline. Therefore, a short volatility position is implicitly “long equity risk”. Since equities are generally expected to earn an equity risk premium (ERP) over the risk-free rate, strategies that are implicitly long equity risk should also be abnormally profitable. This is why short volatility strategies tend to be profitable on average.
Just like how you can get long ERP by getting long an equity index, you should be able to get long VRP by programmatically shorting options and delta-hedging them. Volatility becomes a beta that you allocate towards.
Building Blocks
An option’s value changes relative to the price of the underlying – the rate of this change is called delta.
Gamma is the rate of change of delta given a change in the price of the underlying. As the underlying price moves, an option’s delta does not remain constant; gamma quantifies how much that delta will change.
Since we are only interested in volatility and not price, we can hedge out this delta. Delta-hedging a basket of options mitigates the exposure to the directional movement of the underlying. Profitability becomes solely determined by the volatility (not direction) of the underlying.
Vega is the rate of change of an option’s value relative to a change in implied volatility (IV). If IV rises or declines by one percentage point, the value of the option is expected to rise or decline by the amount of the option’s vega, respectively.
When you short options, you have negative gamma (you don’t want large price movements) and negative vega (you don’t want IV to rise). You hope for low realized volatility and falling IV. However, you have positive theta — time works in your favor.
Theoretically, a delta-hedged short option position’s P&L = vega(IV – RV).1
Construction
Historically, NIFTY ATM option Implied Volatility across days-to-expiry, looks like this:
So, theoretically, if you shorted 30dte ATM calls and exited them at 7dte, your P&L distribution will look like this:
And the same thing with puts:
If you are willing to treat volatility as just-an-other beta, then by creating programmatic delta-hedged short ATM straddle/strangle portfolio, you can get long this beta.
Just as it is with ERP, one could build models to time VRP. Having a beta portfolio as a benchmark should help.
When you use the Black-Scholes-Merton (BSM) model, you end up with theoretical prices that assumes that volatility affects all strikes uniformly. i.e., strikes have no bearing on implied volatility (IV). This was largely true in the market as well until the crash of 1987. However, after the October 1987 crash, the implied volatility computed from option prices using the BSM model started differing between puts and calls. This is called “volatility smile“, or the smirk, given its actual shape.
The reason for this is quite simple, markets take the stairs up and the elevator down. Fat tails, if you must. So, put options sellers require a little bit of an incentive to take on that risk.
How crooked is the smirk? If you take the ratio of the IVs of OTM puts to OTM calls and plot them, you’ll notice that as you get farther away from spot, the distribution flattens out.
Notice the area below 1.0? Those are the days when the calls were trading at a higher IV than the puts.
On the left of zero are the calls with descending order of strikes and on the right are puts with ascending order of strikes. The farther away from zero, the more OTM they are.
Also, unlike the stylized charts of IV you might have seen with sweet smiles, the reality is quite different.
If this tickles your curiosity, do read The Risk-Reversal Premium, Hull and Sinclair (SSRN)
Summary: Mar NIFTY 18000 calls added 65,14,850 contracts while 17400 calls shed 44,21,500. On the Put side of the equation, the 17500 strike added 80,10,000 while the 16850’s shed 4,60,800.
MAR NIFTY OI
MAR BANKNIFTY OI
MAR NIFTY Volatility
MAR BANKNIFTY Volatility
Dotted lines indicated actual underlying volatility. Solid lines are IVs.
SEBI, in its infinite wisdom, concluded that retail investors are speculating too much with derivatives because exposures are too low. So they decided to increase the minimum exposure to Rs. 5 lakh per contract. You can read their press release in the appendix below.
Who is affected?
Anybody who trades naked derivatives will see their margin requirements go up. As you can see from the chart above, most of the exposures are below the new Rs. 5 lakh threshold. Lot-sizes of MRF, BOSCHLTD, EICHERMOT and PAGEIND will come down, but that is of little comfort.
What next?
For exposure margin, you can always buy a bond fund and pledge it with your broker. This way, your margin cash will earn something while it is with your broker.
Second, you can always use option strategies to execute the same view. For example, the total margin requirement to enter a trade in NIFTY futures is around Rs. 17,000/- right now. But when the new regulations kick in, it could go up 3x to 51,000/- Suppose you want to express a bullish view on the NIFTY, instead of buying a naked call or futures contract, you can enter a bull spread to lower the margin requirements.
Here are the numbers from the Zerodha SPAN calculator.
Nifty Futures:
Nifty 8500/8600 Call Spread:
The bull spread has lower up-front margin requirements than the naked futures contract, with the added benefit of bounded profit and loss – resulting in lower mark-to-market margin requirements. Traders can use the pledge + spread strategy to bring down their net margin requirements.
Net effect
The net effect of the new regulation could be that naked positions in the futures markets may be replaced by strategies in the options market. The total risk in the system remains constant – like a water balloon, if you squeeze it in one place, it will pop out in another.
We expect retail futures trading volumes to drop and options volumes to pick up once these changes go into effect.
