Volatility

Question

Denote the formulas used to compute the log-returns and the %-returns.

Answer 1

log(Si / Si-1)

or

(Si - Si-1)/(Si-1)

both give almost the same result if there are no excessive jumps in the value of the variable of interest.

Answer 2

sigma*sqrt(T)

In this case uncertainty increases with the square root of time.

hence:

sigma_yr = sigma_day*sqrt(365). (Calendar days)

sigma_yr = sigma_day*sqrt(252). (Business days)

sigma_yr = sigma_day*sqrt(256). (Business days)

Answer 3

Traders assume 252 (business) days because the volatility on the market is much higher when the market is open.

Answer 4

The standard deviation of the return provided by the variable per unit of time. Also, the proportional change in the variable during the day

Answer 5

Calender days are all the days of the year. We observe heavy volatility during business days, and less during calendar days. Therefore we use 252 days per year, the amount of business days

Answer 6

Implied volatility is the volatility that leads to the option price equaling the market price when Black-Scholes assumptions are used. It is found by 'trial and error'. Since different options have different implied volatilities, traders are not using the same assumptions as BS.

Answer 7

The vix index is the index determining the implied volatilitie. The VIX index does this by calculating the implied volatility from a wide range of Call and Put options.