EWMA volatility

A margin depends on how volatile a contract has been. But volatility itself keeps changing. A good estimate must react to a fresh move. It must not overreact to one wild day either.

The Exponential Weighted Moving Average, or EWMA, method balances the two. It blends yesterday's volatility estimate with today's actual return. Recent data gets more weight. Older data is not thrown away — it just counts for less.

SPAN margining for Exchange Traded Interest Rate Derivatives uses EWMA. It feeds the volatility scan range, which is one input to the initial margin.

The workbook states the method directly: the volatility estimate at the end of period t (sigma-t) is built from the volatility estimate at the end of the previous period, t-1 (sigma t-1), and the return observed in the futures market during period t.

Lambda, the decay parameter that controls how quickly the volatility estimate reacts to new information, is fixed at 0.995. A lambda this close to 1 means the estimate leans heavily on its own recent history and reacts only gradually to any single day's return. Sigma means the standard deviation of daily returns, and the return itself is defined as the logarithmic return.

This EWMA volatility feeds directly into the volatility scan range used in SPAN: for Interest Rate Derivatives, that range is set at 25% of annualised EWMA volatility, subject to a minimum of 3%.

The price scan range — a separate SPAN input, based on 6 standard deviations subject to a minimum percentage of the underlying price — is set at 1.75% for cash-settled Interest Rate Derivatives on G-Sec, 0.065% for 91-Day T-Bills, and 5.50% for MIBOR contracts.

All these SPAN risk parameters are updated six times a day: at 11:00 a.m., 12:30 p.m., 2:00 p.m., 3:30 p.m., plus end of day and beginning of day.

Suppose the EWMA volatility estimate for a cash-settled 10-year GOI bond futures contract stood at an annualised 6% (sigma t-1) at the end of yesterday. Today's observed futures return feeds into the formula, using lambda = 0.995, to produce today's updated estimate, sigma t — a small nudge toward today's actual move, not a wholesale replacement of yesterday's figure, because 0.995 keeps 99.5% of the weight on the prior estimate's own persistence characteristics.

If that updated annualised EWMA volatility works out to, say, 8%, the SPAN volatility scan range for this contract becomes 25% × 8% = 2%, comfortably above the 3% floor, so the 2% figure applies as calculated. Had the EWMA volatility instead been very low — say 6%, giving 25% × 6% = 1.5% — the 3% minimum would override it, and 3% would be used as the volatility scan range instead. Separately, the contract's SPAN price scan range is fixed at 1.75% of the underlying price regardless of the EWMA figure, because that parameter is set on a 6-sigma-subject-to-minimum basis rather than the EWMA method.

Chapter 7 (Clearing, Settlement and Risk Management of IRD), section 7.10.1.1.1 (Computation of Initial Margin), states the EWMA formula, the lambda of 0.995, and the price scan range and volatility scan range tables together as SPAN margining inputs. Expect a direct-recall question on the lambda value (0.995) and on the 25%-of-EWMA-volatility-subject-to-3%-minimum volatility scan range rule.

• Lambda is fixed at 0.995 for this workbook's EWMA method — a specific, examinable number, not merely "close to 1".
• The volatility scan range (25% of annualised EWMA volatility, minimum 3%) is a different SPAN input from the price scan range (6-sigma based, with its own per-product minimum percentages: 1.75% G-Sec IRD, 0.065% T-Bills, 5.50% MIBOR). Do not merge the two tables.
• EWMA return is the logarithmic return, not a simple percentage change.
• Risk parameters update six times a day at the stated clock times, not continuously and not just once at day's end.
• EWMA reacts to recent data but does not discard history — that balance is exactly what the lambda parameter controls.