# Understanding The Nuances Of The Volatility Index (VIX)

When you read any report on the stock markets, it is quite common to see comments that the volatility index has shifted. As we all know, the VIX is calculated by the NSE on a real time basis and is published on their website. But the questions are much larger. What exactly is the concept of VIX and how is VIX calculated? How do you interpret shifts in the VIX number and what is the ideal VIX for any market? Are there are any investment decisions that you can make purely based on the VIX? Let us examine these points.

**What is the concept behind VIX?**

VIX or volatility index is a measure of volatility that is implicit in the market. It is a measure of the perception of risk in the stock markets. A higher level of VIX means that there is more risk perception or fear in the market and vice versa if the VIX is lower. That is why the VIX is also referred to as the Fear Index. The India VIX is an index based on the Nifty index option prices. From the best bid-ask prices of Nifty option contracts the volatility figure (%) is calculated which indicates the expected volatility over the next 30 days. This method is borrowed from the Chicago Board of Exchange (CBOE), which originally used this methodology to calculate the volatility.

**How is the VIX Calculated?**

The calculation of the VIX is based on the popular Black & Scholes model for option valuation. Before getting into the mathematics of Black & Sholes, let us understand the concept underlying the model. The mathematical formula for VIX is as under:

**C = SN(d**_{1})-Ke^{(-rt)}N(d_{2})

_{1})-Ke

^{(-rt)}N(d

_{2})

C = Call premium

S = Current stock price

t = time

K = option striking price

r = risk free interest rate

N = Cumulative standard normal distribution

e = exponential term

d_{1} = ( ln(S/K) + (r + (S^{2}/2))t ) / S (SQRT)t

d_{2} = d_{1} – S(SQRT)t

S = standard deviation of stock returns

Of course, there are simpler excel sheets available and your trading terminal itself allows you to calculate the Black & Scholes options value by merely imputing the input values. Let us look at what the Black & Scholes formula calculates and the key factors that determine the value.

Black & Sholes formula calculates the fair value of the option and helps you to find out if call and put options are underpriced or overpriced. There are 5 factors that impact the calculation of the fair valuation of an option…

- Market price of the underlying stock. In case of call options, higher market prices increase the value of the options. The reverse is true in case of put options.
- Strike price of the option. In case of a call option, a higher strike price reduces the fair value of the option. In case of a put option, the reverse is true.
- Volatility of the stock price. Higher volatility higher is the value of the option. That is because if the volatility is in your favour then the option is more valuable and if the volatility is against you then you just lose the premium. Higher volatility is positive for call options and for put options.
- Time to expiry of the option. Greater the time to expiry, more the probability of you making money on the option. Longer time to expiry is positive for call options and also for put options.
- Risk free interest in the market. Why are interest rates relevant? Options strikes pertain to a future date and hence time value becomes material. Higher interest rates mean lower present value of the strike price and therefore higher option value in case of call options. The reverse is true in case of put options.

These are the 5 variables that are used to calculate the fair value of the option and then to decide whether the option is underpriced or overpriced. Now let us tweak this formula a little bit. Instead of finding the fair value of option, we assume the option price is the fair value of the option. We then use the other inputs and then calculate the missing volatility figure. This is called implied volatility (IV) as it is the volatility that is implied in the option market price. When the IVs of a series of Nifty strikes of puts and calls are combined the outcome is the VIX index. Since the VIX captures the volatility assumption in various strikes, it becomes a good and reliable gauge of the extent of risk perception in the market.

**How VIX moves with the stock market index?**

Generally, the relationship between the VIX and the market index has been negative globally and India has exhibited similar trends in the last few years. A rising market is normally accompanied by falling VIX and a falling market is normally accompanied by a rising VIX. There are the following key take-aways…

- When the Nifty has been on a long term uptrend as we saw between Feb 2016 and January 2018, the VIX has typically been at subdued levels of 10-13.
- In such cases, the intermittent corrections in the Nifty have been marked by sudden spikes in the VIX index.
- Sharp spike in VIX often acts as a lead indicator of a likely correction in the market whereas a tepid VIX is an indication that any correction will be limited
- Under normal market conditions the historical trend line of the VIX works quite effectively and can be bought or sold into within this range to get the best results in trading.

VIX has been a fairly reliable gauge of the market mood across world markets and India has been no exception. A better understanding of the underlying methodology of the VIX and its interpretation goes a long way in putting the gauge to better use.

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