What is Volatility?

Volatility is the deviation of a stock’s annualised returns over a period. It shows a range within which its prices may increase or decrease. In short, it is considered to be the frequency and magnitude of the movement of prices.

High volatility is when there’s a rapid movement in stock prices, hitting new highs and lows. Thus, the higher the volatility, the riskier the security. When the stock market rises and falls more than one per cent over a sustained period of time, it is called a volatile market. Volatile assets are considered to be riskier as opposed to less volatile assets because the price will be less predictable.

Low volatility is when the stock price moves higher or lower more slowly or stays relatively stable.

What causes such surges in stock prices?

• Industry/sector-specific factors
• Country’s economy
• Political events
• Individual company’s performance

What is implied volatility?

The term implied volatility (IV) refers to the metric that assesses the market’s likelihood of changes in a given security price which is the market’s forecast of a likely movement in the security prices. Investors use Implied volatility (IV) to anticipate future moves and often utilise it to price options contracts. It is one of the deciding factors that decide the price of the options. It is used to estimate future fluctuations of a security’s price based on certain factors—high implied volatility for options results in options with higher premiums.

Advantages of implied volatility: 

• Gives the investors practical insight into erratic changes in stock prices.
• It helps with lock in different option prices.
• Using the IV to play a role in the trading strategy.
• It is a method to measure uncertainty and market sentiments.

Why Implied volatility (IV) is important in options trading

Options are financial derivatives that give buyers the right, but not the obligation, to buy or sell an underlying asset at an agreed-upon price and date. A call option is a right to buy an underlying asset or contract at a fixed price at a future date but at a price that is decided today. On the other hand, the put option is the right to sell an underlying asset or contract at a fixed price at a future date but at a price that is decided today. The value of an option depends on several external factors. One such influencing factor is implied volatility. IV has the capacity to move the options premium even as the price of the underlying or the time remain unchanged. IV is often used to price options contracts where high implied volatility results in options with higher premiums and vice versa. An option buyer pays a premium that is proportional to the market’s predicted volatility. Hence volatility is extremely important for every options trader. It can change the profit and loss profile of the options that you are holding. Each option has a specific sensitivity to implied volatility. Short-term options are less impacted by IV, whereas, long-term options, since more sensitive to market changes, have higher IV sensitivity quotients.

1. Mathematical models for option pricing:  

• Implied volatility can be derived from option pricing models such as Barone-Adesi and Whaley model (American options), the Black-Scholes model or its modified versions. They use the current market price of options to estimate future volatility that would correlate to the observed option prices.

2. Iterative methods: 

• The Newton-Raphson and bisection methods are 2 iterative techniques since the Black-Scholes formula does not have a definite solution for implied volatility.
•  Iterative methods make the initial guess for implied volatility and then iteratively refine the estimate until the it matches the observed option prices.

3. Volatility Index (VIX): 

• It is a popular measure of IV for bigger markets.
• It is calculated based on specific options, and it represents the market’s expectation of volatility for 30 days.
• This is predominantly used for American options.

• Traders can also trade the VIX using a variety of options and exchange-traded products, or they can use VIX values to price certain derivative products.

4. Beta:

• To measure the relative volatility of a particular stock to the market is its beta(β).
• A beta approximates the overall volatility of a security’s returns against the returns of a relevant benchmark.

5. Option Greek: Vega

• It is the Greek that measures the sensitivity to implied volatility.

• Vega is the sensitivity of a particular option to changes in implied volatility.
• To trade options, one must incorporate vega as a deciding factor.

There is no defined method to calculate implied volatility, and there is no fair value, but there are fair ways to derive the value for implied volatility. It is important to consider the different methods; each model may result in different values for implied volatility. The choice of method is crucial and may depend on numerous factors.

We will now take a closer look at the Black-Scholes model:

This mathematical model estimates the theoretical value of derivatives based on other investment instruments, taking into account the impact of time and other risk factors. It is a widely used formula for option pricing contracts. Although the model is usually accurate, it makes certain approximations that can lead to predictions that deviate from real-world, observed results. This model is used only in the European options.

C= call option price

N= Cumulative Distribution Function of the normal distribution

S= spot price of an asset

K= strike price

r = risk-free interest rate

t = time to maturity

σ= volatility of the asset

This is a complex mathematical formula that requires more domain knowledge in order to implement. However, with the help of Matlab, we can find the implied volatility. Matlab provides a toolbox, the blsimpv() toolbox, which is part of the computational finance in Matlab to find the implied volatility using the Black-Scholes model.

Vol_output=blsimpv(price,strike,rate,time,value) 

Strike — Exercise price of the option 

Price – underlying asset price 

Rate — Annualized continuously compounded risk-free rate of return over the life of the option 

Time — Time to the expiration of the option 

Value — Price of a European option from which implied volatility of an underlying asset is derived. This can either be the call option value or the put option value. 

This example from Matlab shows how to compute the implied volatility for a European call option trading at $10 with an exercise price of $95 and three months until expiration. Assume that the underlying stock pays no dividend and trades at $100. The risk-free rate is 7.5% per annum. Furthermore, assume you are interested in implied volatilities no greater than 0.5 (50% per annum). Under these conditions, the following statements all compute an implied volatility of 0.3130, or 31.30% per annum.

Volatility = blsimpv(100, 95, 0.075, 0.25, 10, ‘Limit’, 0.5);

Volatility = blsimpv(100, 95, 0.075, 0.25, 10, ‘Limit’,0.5,’Yield’,0,’Class’, {‘Call’});

Volatility = blsimpv(100, 95, 0.075, 0.25, 10, ‘Limit’,0.5,’Yield’,0, ‘Class’, true);

Volatility = blsimpv(100, 95, 0.075, 0.25, 10, ‘Limit’,0.5,’Yield’,0, ‘Class’, true,’Method’,’jackel2016′)

Volatility = 0.3130

Plot (i) is the implied volatility produced from Matlab, and Plot (ii) is the implied volatility supplied by the National Stock Exchange (NSE). We see that the 2 graphs are slightly different from each other, which is to be expected since NSE uses a different variation of the Black-Scholes model. But Matlab can help us create a benchmark or standard for which we can closely estimate the real-world value.

How Implied volatility (IV) can affect options trading negatively? 

Implied volatility depends on market sentiment, and its change is oftentimes hard to predict. If investors make their decisions solely based on IV, they may incur a loss. IV is scalar, so its direction of movement is not accurately predicted. It does indicate how the security price will move. If investors are highly dependent on IV, it can result in incorrect decision-making of strategies, resulting in a loss. Implied volatility (IV) has to be considered cautiously, or the result will be unforeseen.  Implied volatility (IV) indicates the swing of movement, but not the direction; the longer the period before expiration, the longer the stock needs to move either in or out of the trader’s favour, making it riskier and offering greater potential to prove profitable eventually.

In conclusion, the more accurate the Implied volatility (IV) value is, the better it is for making strategic changes in option prices. Making useful inferences is also a key aspect for a company or investor.  It points out the anticipated ups and downs for the option’s underlying stock and indicates good entry and exit points for all the traders. Calculating accurate implied volatility is a challenging task since there are various reasons why stock market prices fluctuate. Implied volatility is affected by a number of factors, with the most significant being supply and demand and time value.