Blog #29 - Significance of Delta, Gamma, Theta, Rho & Vega.

Delta vs Gamma vs Theta vs Rho

  

What is Delta?

Delta deals with most important determinant of an option price namely the price of the underlying. Personally, I consider delta to be the most important Greek letter of all. As we would all remember from the class XII math, delta of an option is the first derivative of option value with respect to change in the price of the underlying.

 

 

We will not delve into mathematics of delta but instead focus on its concept and utility. Delta is an estimate of the likely change in an option’s value given a one unit change in price of the underlying instrument assuming other factors remains constant. Deltas can vary from +1 to -1.

 

Delta vs. Gamma vs. Rho vs. Theta vs. Vega In Share Market

 

In simple language, in case of higher delta option, the change in optimum premium would be more for each rupee of change in underlying stock or index, whether upward or downward. In case of lower delta option, on other hand for each rupee of change in the underlying, the change in option premium would be lesser. In other words, the correlation of an option’s premium to its delta is positive. As a trading strategy I always trade higher delta option because for each unit of move in the underlying , the higher delta option premium moves more relative to a lower delta option. 

 

 

Now what is high delta option?

The more in the money an option is, the higher is its delta. The less in the money an option is, the lower is its delta, everything else being constant. The other way I look at it is that the more in the money option you buy, the higher is the intrinsic value in its premium. As we know by now, the time value part of the option can evaporate very fast. So the option which has greater intrinsic value is one that I like to buy, since I want to pays as low a time premium as possible. Such an option behaves more like a future and my downside remains limited.

 

 

The Calls Have Positive Delta While Puts Have Negative Delta.

 

What is Gamma?

Gamma is an estimate of the change in delta for a one unit change in price of the underlying instrument, assuming other factors remains constant. Mathematically gamma is second derivative of the option pricing formula with respect to change in price of the underlying. The importance of this factor is captured by delta.

 

 

What is Vega?

Vega is change in option value that results from a one per cent change in volatility, assuming other factors remaining constant. Vega answers the questions: if the volatility changes by one percent, how much does the option value change. Mathematically Vega is first derivative of option price with respect to change in its volatility. Since first derivatives are theoretically “instantaneous rate of change”, and since Vega estimates the impact of one per cent change, there will be frequent rounding errors.

 

 

What is Theta?

Theta is an estimate of the change is option value give a unit change in time to expiration, assuming other factors to remain constant. Now, this is the all important time factor that we have been discussing. Time factor is critical in India because we are really talking only about the near month options as the others do not have sufficient liquidity to be relevant.

 

 

What is Rho?

Rho is an estimate of the change in option value given a one per cent change in interest rates, assuming other factors to remain constant. Rho is not important from  a short term trading perspectives as interest rates don’t change very often.

 

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