Volatility is a frequently misunderstood but undoubtedly powerful force shaping financial markets, and a particularly pertinent source of both risk and opportunity for option market makers.

# What Is Volatility?

Volatility is defined as the measure of the variability of an asset’s price measured as the annualised standard deviation of daily returns on the underlying asset. More generally, it can be viewed as quantifying the speed of the market as exemplified by the Chicago Board Options Exchange VIX index.

The definition may be referring to one of two types. Realised volatility refers to the volatility of the stock in the past derived from historical prices measured at regular intervals. Its applicable variant is future realised volatility which aims to describe the future distribution of price changes for the option estimated through considering both the historical realised volatility observed for the option and additional factors through employing forecast models.

On the other hand, implied volatility is derived from the quoted stock price of the option on an exchange, which represents the market’s opinion of what future realised volatility will be over the option’s lifetime. This is attained through the Black-Scholes-Merton model, widely accepted as the optimal way of finding an option’s theoretical value. The assumption that all other inputs such as the risk-free interest rate, exercise price, time to expiration, and underlying price are constant must be made in order to find the implied volatility value resulting in the theoretical value being equivalent to the option’s price.

# Trading Volatility

The fundamental challenge of trading option contracts relies on interpreting the gap between the estimated realised volatility, which represents their value, and implied volatility, which reflects their price. Therefore, if implied volatility is less than expected future realised volatility, a trader would go long on an option, and short for the opposing scenario.

Many option strategies such as the straddle, which combines a long position in a call option and short position in a put option based on the same underlying at identical strike price, base their profitability entirely on the share price volatility itself and are effectively independent of the direction in which the change takes place.

# Relationship Between Price And Volatility

The volatility skew shape shown to price equity options suggests that a higher strike price decreases the implied volatility. This relationship is due to the leverage effect whereby a company’s reliance on debt increases as its common stock decreases in value, making it a riskier investment and thus introducing volatility.

The strike price chosen depends on and will generally follow the expected performance of the underlying stock. The equation describing the skew represents an additional input into the theoretical pricing model used to calculate an option’s theoretical value.

# Managing Risk

The sensitivities of option characteristics to various parameters influencing their price are referred to as ‘Greeks‘ and correspond to the derivative of an option’s value with respect to one of the parameters affecting it. Option traders must be constantly aware of how these parameters change and affect their overall position.

For volatility the relevant risk measure is Vega, a derivative expressing the degree to which the option value changes with respect to the implied volatility measured for the underlying stock. Ultimately the higher this quantity, the more substantial the impact of the stock’s fluctuations on the option’s price.

Vega will increase for a higher strike price and as the time to expiration is extended. Its function is to identify the position of the probability distribution for the option’s price. Since risk parameters must be estimated accurately to obtain a correct probability distribution for the options price, correctly calibrating for volatility risk is a significant determinant of a volatility trade’s success.

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