Perceived Market Uncertainty over the Financial Crisis:

Measuring the Implied Volatility Function

The implied volatility shows the market perception of the level of uncertainties of the rate level over different time horizon.  The annualized volatility of one month forward rate at different time horizon is called the implied volatility function. We use the quotes of at-the-money swaptions with expiration 1, 2, 3, 4, 5, 7, 10 years and tenor every year from 1 to 12, in addition to 15 and 20 years to calibrate the Ho-Lee implied volatility function over the period March 31 2007 to March 31, 2009.  For details of the estimation procedure see Ho and Mudavanhu (2007).

The results below show the dramatic increase in the implied volatility of the swap curve starting mid 2007 with volatilities less than 20%. The volatility reaches a peak in the first quarter of 2008 and spiked in November 2008, exceeding 100%, at the time of Lehman bankruptcy. The implied volatility has increased first quarter of this year suggesting the market is concerned with the earnings announcements of early 2009.

Applications of the implied volatility function

·         Pricing of swap curve based options, such as the swaptions or the embedded options in structured products and corporate securities

·         The dynamics of the implied volatility function can lead to trading opportunities in buying and selling straddles

·         The implied volatility can be used as a market benchmark in measuring market risks. For example, inputs to the Value-at-Risk (VaR) calculation