Options and the concept of volatility are heavily intertwined thanks to underlying asset price relations. Volatility is easy to define: The amount of changes in an asset’s price and the rate changes occur in a period of time. The volatility of the underlying asset and the value of the option are interrelated.
Remember that an option’s strike price has to be exceeded by its market price to be exercised. This means above the strike price if a call or below the strike price if a put. An underlying asset with frequent wide price swings is more likely to move past the strike price than a calmer underlying asset. Underlying assets that have high price volatility are, all else equal, more desirable for option holders. Options with underlying assets that have lower volatility are more desirable for writers. This is especially true with American Style options which can be exercised at any point, as long as the option is in the money.
Higher volatility has higher chances to be exercised, and it is not forgotten when paying premiums. You will pay high premiums on options that have higher underlying asset volatility. This offsets the risk of the writer being more likely to encounter financial losses due to price swings. There are two volatility measurements: historical volatility and implied volatility.
Historical volatility (HV) measures the previous rate of change in underlying asset’s pricing. This is calculated at the end of every trading day, typically by using standard deviation. They measure the deviations from the average price, and then create an average of those deviations. The bigger the historical volatility, the more the option is worth if the underlying option’s behavior continues. Note that historical track records do not guarantee that future behavior will reenact the past. There is never an assurance the future will mirror the past, but changes in historical volatility measures may indicate whether volatility is calming or worsening in the underlying asset’s price.
The differences between historical volatility and implied volatility are an indicator of potential option miss pricings. If the option’s historical volatility and implied volatility have a large distance between them, the price of the option may not be in line with the underlying asset. This can reveal a miss pricing opportunity to attentive investors, especially if a trend is widening.
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