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The Greeks Part II

Theta - Θ

Theta is the measure of how Time Decay affects the option premium.  We already know that the shorter the time to expiration, the lower the Time Value of an option, therefore the lower the time value portion of the option price will be.

4 ways to combat Theta (Time) Decay

  1. sell off any ATM or OTM options with 30 days left to expiration - do not hold options into the last month
  2. sell options as an adjustment to existing positions
  3. sell options you don't own as an adjustment to existing positions
  4. buy short-term DITM options, which have plenty of Intrinsic Value and virtually no Time Value - if there is no Time Value, then it can't decay any further, can it?!

Theta Picture Summary

Vega - Κ (also known as Kappa or Lambda)

  • When you trade stocks, you must be aware of volatility.  Volatility is also recognised as risk.
  • Higher volatility is predicated by larger price fluctuations, which translates into greater risk.
  • The greater the volatility and risk, the higher the options premiums will be.
  • Volatility is expressed as a percentage, reflecting the average or expected price change (regardless of the direction).
  • If a stock is currently priced at $100 and has a (Historical) Volatility of 20%, then that stock will be expected to trade within the range of $80 - $120.
  • Vega measures an option's sensitivity to Historical Volatility (measured by standard deviation) of the underlying asset price.
  • Vega is always positive and is identical for both calls and puts.

Implied and Historical Volatility

There are two types of Volatility that you need to understand for options trading: Historical Volatility and Implied Volatility. 

Remember that there are 7 variables that affect an option's premium.  Six of these variables are known with certainty: (1) stock price; (2) strike price; (3) type of option; (4) time to expiration; (5) interest rates; (6) dividends.  The final variable is not known with certainty and is the expected volatility of the stock.  This expected volatility figure is expressed as an annualised standard deviation and, working back from the option premium itself, is an "implied" figure, hence Implied Volatility.  Historical Volatility is the annualized standard deviation of past price movements of the stock.  We use Historical Volatility as a reference figure for calculating what the Fair Value of the option should be, given the stock's Historical Volatility.  In the real world, option premiums frequently trade away from their fair values.

Historical (or Statistical)
  • Based on the underlying asset volatility over past (20-23 trading days is popular)
  • Expressed as a % reflecting the average annual range (ie standard deviation)
  • Based on the option's actual price (premium), expressed as a % and based on the perception of where market will be in the future
  • This is the volatility figure derived from the Black-Scholes options pricing formula

Look for Comment
Implied > Historical Options prices could be overvalued as a result of higher implied volatility (look to sell options)
Historical > Implied Options prices could be undervalued, indicating good buying opportunities, particularly if you anticipate asset price movement

Generally, Implied Volatility will veer towards Historical over the medium to longer term - this is known as the "Rubber Band Effect"

Bollinger Bands are a good visual representation of volatility

About Volatility

  1. What does Historical Volatility mean?
  2. It is a reflection of how the underlying asset has moved in the past (often 20-23 trading days)


XYZ = $200 and has Historical Volatility of 10%

Volatility Smiles and Skews

Volatility Smile

  • A Volatility Smile occurs where the Near the Money options have lower Implied Volatility than the Deep ITM and Deep OTM options.  When plotted on a chart, the Implied Volatility against strike price graph appears to be in the shape of a smile. 
  • It is not always clear why this occurs, but factors can include illiquidity leading to mispricing for Deep ITM and Deep OTM options.

Volatility Skew

  • A Volatility Skew occurs where there is a difference in Implied Volatility between OTM calls and puts.  The reasons for Volatility Skew are not always obvious, however, factors include market sentiment and supply and demand. 

Vega Picture Summary

Rho - Ρ

  • Rho is the measure of an option's sensitivity to a 1% move in the Risk Free Interest Rate.
  • Call Rho is always positive (helpful) and Put Rho is always negative (unhelpful).
  • Even large changes in interest rates have relatively little effect on options prices.  Rho is generally considered to have the least impact of the options Greeks, particularly in a low interest rate environment.

Rho Picture Summary