Monday, January 14, 2013

How SPX Vega changes with volatility and prices

I had studied how Vega (and other Greeks) changes with time in a previous post. Now I'd like to analyze how Vega changes with volatility and stock prices, since I'm using Vega to hedge the Delta in my monthly income portfolio selling high probability options, such as the Feb portfolio consisted of iron condors. With the help of TD Ameritrade's ThinkOrSwim analyzer, I captured the following image today to analyze my Vega changes with volatility and prices.
A picture is worth one thousand words. I have to digest this picture later when I have more time. For now, it looks to me the following is generally true in this picture. Note this is about the portfolio Vega, not the Vega of straight options.
  • When IV increases 1%, 
  •           Absolute(Vega) changes (decreases) about 7.5% at current price and VIX levels;
  •           Absolute(Vega) changes (reduces) relatively larger at far far OTM strikes;
  •           Vega changes little around break-even points;
  • Vega is most negative at the center of the portfolio P&L chart.
The changes of portfolio Vega with volatility depend on price of the SPX as well. The absolute value of Vega is largest at the center of the P&L zone (Vega is largest ATM for straight options). For near the money strikes/zone, the abs(Vega ) decreases as volatility increases. This is similar to short options (short calls or puts) which profit when volatility decreases. If volatility increases, the short options lose value, meaning the Vega become smaller for the short option position.

The change of portfolio Vega described in this post also shows its conformance to the Vega changes of the straight options of calls and puts. For straight options, the Vega has the following characteristics in general.

  • Vega vs time: Vega is higher when option has more time (shown in volatility skew of expiration cycles or Vega has time decay too!).
  • Vega vs price: Vega (All Greeks except Delta) is highest for ATM options.
  • Vega vs volatility: The higher the volatility, the higher the Vega? Not necessarily! 
    • Vega is the option's sensitivity to its implied volatility and not directly proportional to volatility. Although the volatility values are higher for OTM put option strikes (shown in volatility skew of strikes), the option's sensitivities to IV for OTM options are lower, i.e. the Vega of OTM options is lower than that of the ATM options. However, for the same option strikes, Vega is higher if IV is higher.

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