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.

Rupee Depreciating!

In the latter half of the year Rupee has weakened against the Dollar significantly. Black line in the graph is USD/INR which has appreciated from close to 40 Rs for a Dollar in April to about 50 Rs.

At the same time it is argued by some that USD has strengthened across all currencies. Implying that INR has not weakened much its just USD showing lot of strengthening. The red like shows USD index which is trade weighted index of USD against major currency pairs. This like shows performance of USD against other major currencies like Euro, Pound and Yen etc.

There is a close association in the upward movement of Dollar against Rupee and against all other major currencies (in other words the black and red lines)

Bull Everywhere !

Globally almost all asset classes are again touching new highs. Just recently few days ago there were talks of crude oil staying above the $100 per barrel mark. Gold is also heading towards its all time high of $850, last time I checked it was around $830 per ounce. India being the largest consumer of Gold in the world is the major source of the increasing demand for this metal.

The price of gold in India per 10 gram is clearly above Rs. 10,000. The market analysts earlier had predicted that the gold will not touch the 10,000 level because the consumers would move away from gold due to the high price. Infact it was speculated that the gold prices will stay below Rs. 9,700 when the prices were touching the levels of Rs. 9,300.

Another main reason for the increase in the Gold and crude oil is due to depreciation of US dollar. The dollar has weakened in terms of Euro from the June levels of 1.34 to the levels of 1.45 now.


Year on year gold as an investment in India has not done extremely well with returns below 10%. But in the last few months it has made good return of close to 25% to 30%. Infact it makes more sense to invest in the gold overseas in dollar terms particularly in order to best capture the depreciation of dollar. The Gold ETF’s that were recently started in the county were a good example of this. Gold ETF’s have gone up by almost close to 30% in the last six months.