Volatility is a prime indicator of the risk inherent in a portfolio. The primary risk for a fixed income portfolio arises out of movements in interest rates.

Interest Rate Vols have two main uses:

• Pricing interest rate options
• Measurement of risk and calculation of Value at Risk

As part of our efforts to facilitate the development of the market, we have provided a volatility calculator. This calculator enables you to compute interest rate volatility using different methods.

Historical Volatility

This is a simple standard deviation calculation that gives the volatility based on returns from the past n days, where n is user-specified.

Exponentially Weighted Moving Average

This method gives the maximum weight to the most recent data on returns. The weights go on decreasing exponentially. We have used the limiting case of the EWMA formula, which has only one parameter (the decay factor) and two factors: the previous day’s EWMA volatility and the previous day’s returns. The formula for the limiting case is as follows:

s2 t+1 = l. s2t + (1-l).r2t

• Where t and t+1 represent days
• s is the volatility
• And r is the return on a particular date.
• Notice that st itself will have information about the previous day’s volatility.

This formula can also be used for forecasting the next day’s volatility. Intuitively, this method is more elegant because volatility does tend to have a recency effect. Thus the volatility for a day becomes conditional to the previous day’s returns and volatility.

As a basis of all calculations, we use the zero coupon yield curve released by FIMMDA on all days except Saturdays and Holidays (Since the Indian Market works on Saturdays, this is likely to introduce an approximation). The calculator uses the following standard maturity buckets: 1 Year 2 Year 3 Year 4 Year 5 Year 7 Year and 10 Year

Volatility can be computed on the basis of:

• Zero Coupon Yield Returns
• Discount Factor Returns

Volatility of yield returns is a useful input to many interest rate options pricing and VaR models.

Volatility of discount factors returns is closely linked to the volatility of portfolio value. This is because the economic value of a portfolio is simply the summation of cash flows multiplied by their respective discount factors.

Disclaimer

The volatility calculator is meant for information purposes only. It is not meant for use as a Value at Risk Model, or for pricing options, because of the approximations made. Users are encouraged to use more sophisticated models, which use actual security prices on all trade-days, for these purposes.

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