Aug 15, 2022
An Introduction to Implied Volatility and Options Pricing
Implied Volatility
An option’s price is influenced and determined by a variety of factors. Assumptions about how these factors change, affect the decision making process for investors. Understanding how they relate is also important. Commonly referred to as the “Greeks”, following the usual nomenclature from calculus (which itself means “small pebble” in Latin, and based on the study of continuous change) these computations follow the breakthrough work of Fischer Black and Myron Scholes in the 1970’s (the eponymous “Black Scholes” option model for which they won a Nobel Prize and which modern options pricing is predominantly based).
These calculations are based on assumptions of a log normal distribution of returns (prices bounded at zero), no arbitrage, dividends or market frictions, and no transaction limits with a given risk free rate.
Factors that contribute to an options price include:
Theta, which measures the changes of an options price over time;
Implied Volatility, which is a market derived measure reflecting expectations of the asset’s probable price range over a set period;
Delta, which reflects the sensitivity of an option’s price to price movements of the underlying security, asset, etc. and;
Vega (which is not a Greek letter!), measures how an options price reacts to changes in implied volatility.
How all 4 of these directly affect options pricing are crucial in options trading to manage risk and derive the highest return. For example, implied volatility, the subject of this short vignette, may be trending higher or lower; these changes profoundly affect the price of related options, i.e. if the market believes that the future price movements of an asset will be more narrowly distributed around its mean, ceteris paribus, the option’s price and implied volatility will be lower and vice versa if higher. It is important to note that implied volatility is not the same as historical volatility, which is a statistically derived number based on historical returns.
Implied Volatility in Options Pricing Models
IV can be determined by utilising options pricing models, with one example being the Black-Scholes Model:
Where:
And
C is the option premium
S is the spot price of the asset
K is the option’s strike price
r is the risk-free interest rate
t is the option’s time to maturity
e is the natural log
𝜎 is the standard deviation of the underlying asset’s return
N(d) is the value of the cumulative normal distribution at d1 and d2
The Black-Scholes Model uses the asset’s spot price, options strike price, time to option’s expiration, and the risk-free interest rate to determine implied volatility and an option’s premium. Implied volatility is the one factor in the pricing model that cannot be directly observed in the market. We can, however, perform reverse engineering on the Black-Scholes Formula by inputting the current price of the option and working backwards to calculate the IV of an option. As long as we know the price of an option we can determine the implied volatility and if we know the implied volatility we can get a price.
While implied volatility can assist one in quantifying the market’s sentiment on an asset’s future volatility, we see that the calculations for IV are based solely on price and current market factors. It can give us an estimate of the size an asset’s price movement will make but cannot provide any indication of the direction in which said movement will take. Thus, IV will react to unexpected factors such as news or events that might affect a market’s sentiment which will in turn affect the price of the option.
Implied Volatility and How it Helps to Understand Options Pricing
Let’s take a look at the price of an option. It is not trivial to tell if the option’s price is relatively low or expensive, as we know several variables affect the price of an option besides the spot price of the underlying asset (which is easily referenced). With so many options with different strike prices and expiry dates, how does one compare the prices of contracts? The answer is with an option’s corresponding implied volatility.
In times of heightened volatility in markets, the values of implied volatilities increase. This translates to a rise in the premiums for options, as the likelihood of an option expiring in the money is higher. This is because option writers are only willing to sell their options at higher premiums to offset the increased probability of these options expiring in the money, resulting in them paying a settlement to the option buyer.
Following is a graphical representation of how call options prices relate to differing IV levels.
Taking a strike price of 100, we observe that the premiums for an option vary for different values of IV. The higher the IV, the more costly the premium.
Capitalising on Implied Volatility
Implied volatility is an indication of the market’s view on the future volatility of an asset based on the current market price. However, one can bet on rising or falling volatility by purchasing or selling delta hedged options.
Over time, implied volatility correlates highly with historical volatility, which is the realised volatility of an asset. This is of course logical. If the IV of an asset is higher than the historical realised volatility, the market is pricing a greater possibility that an upcoming event will affect the asset’s price or some structural or market driven situation is causing an elevated price. On the other hand, if the observed implied volatility is below the realised volatility, one could assume that the market is stabilising and might be heading into times of lowered volatility, or there’s been a greater selling pressure on the options. Market-driven demand and supply factors can heavily affect the market pricing of options causing significant deviations from “fair” prices derived from models. Recognising and profiting from these will be the subject of a future note.
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