Volatility for BSM Model

Summaries

Historical Volatility:

1. Find the change of price (return) in each time slot

Ri = (P_i-P_i-1)/P_i-1

2. Compute continuously compounded return:

R_ci = ln(1+R_i)

3. Find the standard deviation of R_ci

_­­Implied Volatility:

This is the volatility found when the BSM model is used by matching the market price:

Market price = BSM(S0, X, T, rf, volatility)

Compared definition of yield volatility:

1. Yield Change = Xt = 100 ln (yield2/yield1)
2. Yield Volatility = standard deviation of Yield Change
3. *** Since this is sample (Historical Volatility), remember to use T-1 in the calculation
4. Annualized Yield Volatility = Daily Volatility X sqrt (days)
5. Implied Yield Volatility = Calculated using observed prices for interest rate derivatives and option pricing models
6. Forecasting Yield Volatility just like historical volatility
1. Can assign different weight to different time slot
2. Assume the average yield change is zero