Historic Volatility Calculation

Dynamic replication of option price requires a key ingredient, volatility. Often we get into arguments about using Implied market volatility, Expected volatility (could be forecast/ prediction) or just historic volatility.

I was just trying to calculate historic volatility of major currency pairs and the Indian and World indexes. At first I thought using daily closing prices would be the most logical method. But later wanted to see if there is significant difference between calculations done on closing prices vs. opening and day high and day close.



I was expecting more or less same volatility figures for different data. But to my surprise the volatility figures based on Day high were significantly less volatile across markets and benchmarks.



The effect is more pronounced in stock Indexes like NSE Nifty, BSE Sensex and foreign indexes like Nikkei 225 and the Dow Jones. This is something very counter intuitive because in the last year all indexes have gone down but still the market highs from one day to other are less volatile compared to Open and High data.

The volatility was calculated by using daily log returns for past 256 data points (roughly 1 yr with 5 market days and 5 holidays)

The Currrencies are Pound, Euro, Yen and Swedis Krona all against USD.