To build a term structure I need different volatilities; as I don't get them at every strike, I use interpolation technique to calculate the rest and plot. This is how I calculate the implied vols. How is the Newton-Raphson method used to calculate the implied vols? Is it another way to calculate like I calculate with interpolation techniques? Is my understanding correct? Now what ae actual vols and how are they calculated?

Edit: Basically I want to understand how the Newton-Raphson method is used to calculate to implied volatility and what is the difference between the Newton-Raphson method and interpolation methods?

What is the difference between implied volatility and actual/local volatility?

  • $\begingroup$ From your question I cannot quite understand what you are aiming to achieve - can you offer a more precise description of what you are doing? As to your last question - there are at least two concepts of deriving volatility: implied volatility, which is derived from option prices and realised volatility, which uses past returns of an asset. Perhaps the latter is what you refer to as "actual vols"? $\endgroup$ – Martin Georg Haas Sep 8 '20 at 15:37
  • $\begingroup$ edited the question $\endgroup$ – syed tabrez Sep 8 '20 at 16:52

Newton-Raphson is not an implied volatility calculation method, it's just a way to minimize (above a certain threshold) the difference between traded options prices and BS prices, the volatility at which this minimization happens is called implied volatility. You cannot have said options for all maturities trading in the market at the time of calculation, so you need to create an interpolation curve. E.g you may have an option with 1m to maturity and 3m to maturity but not 2m, you'll calculate the iv for 1m and 3m and try to interpolate between these values (linear or otherwise). The interpolation curve should be such that the implied vol surface is arbitrage-free.

As for actual volatility, we don't know what actually volatility is, we can estimate it for example by standard deviation of return, as for the difference between the two, IV is dependent upon the valuation model i.e. Black Scholes while the other is just a statistical estimate. IV is also widely used to quote options, instead of prices.

  • $\begingroup$ when you say you'll calculate the iv for 1m and 3m,do you use newton raphson method to arrive at a value with minimum error and then with these values you interpolate for 2m, is my understanding correct? $\endgroup$ – syed tabrez Sep 11 '20 at 7:54
  • $\begingroup$ Yes, it is correct. $\endgroup$ – Dhruv Mahajan Sep 11 '20 at 8:27
  • $\begingroup$ to calculate iv for 1m and 3m, i can use the BSM and get the IV right?, then what is the use of newton raphson here? I can get the iv's from BSM and then interpolate to get the iv for 2m. $\endgroup$ – syed tabrez Sep 13 '20 at 10:13
  • $\begingroup$ To get the IV from BSM you need Newton Raphson $\endgroup$ – Dhruv Mahajan Sep 13 '20 at 10:27
  • $\begingroup$ I can directly equate the BSM to market price and I know every parameter except the IV, wont i get by just solving it? $\endgroup$ – syed tabrez Sep 13 '20 at 13:57

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