Forward Variance and Volatility Spikes

One of the strengths of variance swaps is the ease of pricing and constructing forwards.

Forward variance can be used to trade the future volatility of an underlying.

- before the forward date --> P&L entirely driven by changes in expectations of volatility --> mvmts in IV term structure.

- once forward date reached --> P&L is exposed to realised volatility.

Forward variance can be an attractive vehicle to be long volatility without accruing realised volatility losses.

Below we introduce the fixed income concepts of slide and carry as applied to volatility.

Volatility Carry:

In Fixed Income

Carry is the cost of funding a spot position and reflects the difference between short and long term interest rates.

Example:

An investor wants to take a view the LT IRs will rise --> short sell a bond or short a long-dated swap.

To fund this position --> pay the difference between long and short rate --> usually positive spread --> negative carry.

In Variance Swap

The holder of a long VS position will have to pay the spread of IV over RV every day he holds the swap.

Since this spread is usually positive --> negative carry.

For both FI and VS, forward starting instruments have no exposure to carry until the forward starting date is reached.

Volatility slide

Slide occurs because once a trade is implemented the maturity is fixed, so that relative maturity diminishes over time.

Slide measure the impact of diminished relative maturity assuming shape of term structure remains unchanged.

For upward sloping variance term structure --> long VS will lose out through time as VS ‘slides’ down the term structure.

Both spot and forward starting variance swaps have exposure to slide.

Principal component analysis

The behaviour of changes in the implied variance curve can be analysed using principal component analysis (PCA).

PCA decomposes moves in the volatility curve into its major components, or factors.

Figure 68 shows the two most important components of weekly changes in the SX5E volatility curve.

First factor illustrates how the dominant curve move is to increase/decrease much more at the short-end of the curve.

Short dated IV tends to move about twice as much as longer dated maturities during a shift in the term structure:

increases in volatility tend to flatten the curve
decreases in volatility tend to steepen the curve

Second factor: twist factor, with vol decreasing (increasing) at short-end of curve and increasing (decreasing) further out.

Pca

Pca analysis 2

PCA analysis is useful in calculating expected gains/losses for different parts of the implied variance curve following a general increase/decrease in volatility.

In conjunction with carry and slide analysis, they can help identify the best part of the curve to be long/short volatility.

Volatility Spikes

Below we use carry, slide and PCA analysis to help decide which long variance position (spot/forward, long/short-maturity) is likely to perform well as a hedge against a volatility spike. Factors to consider include:

The likely magnitude of a volatility spike and its effect across the variance term structure
The likely timing of a volatility spike
The cost of holding the position until the spike occurs
The possibility of term structure flattening, which could adversely affect the mark-to-market of fwd starting variance

Forecasting when a spike in volatility might occur is well nigh impossible.

However, by decomposing a long history of realised volatility into periodic components using Fourier transforms, one of higher weighted components of the transform suggests that there is a bias for a spike to occur about every six months.

If shift up in vol immediately -> likely greatest impact at short end of curve -> best strategy likely to be spot short-dated VS.

Whilst it is important to consider the likely time of arrival of any spike and the effect such a spike is likely to have on the variance term structure, the behaviour of volatility, both implied and realised, after a spike is also an important consideration.

Our analysis of spikes (in realised volatility) on major indices since the 1950’s suggests the following results:

There is not a strong pattern of reduction in volatility in the first month following a spike.
In the second month after the spike, there is a clear bias for volatility to decrease, on average by about 4.5 vegas.
For those spikes with a reduction in vol within 2m, the reduction in vol is ~ same size as the increase seen in its spike.

That is, short-lived spikes tend to subside to pre-spike levels within 2 months.

For those spikes which have not subsided within 2m, it is likely that there has been a significant further increase in volatility, and although these kind of spikes tend to eventually subside, they take longer and typically subside to a significantly higher base level than the previous spike (on average 5.5 vegas higher after 6 months).
The short lived spikes tend to outnumber the longer-lived spikes by about 3 to 1.

Volatility spikes

Given that we can make an assumption on the likely timing of a spike and have a reasonable idea, from PCA, on how it will affect the curve, we can estimate the likely P&L from holding different maturity variance swaps. We can then gauge which variance swap offers the best cost/benefit profile given the prevailing variance term structure.

Example

Graphes example 1

Graphes examples 2

Thus for investors expecting a rise in volatility even within the next few months, the forward starting maturities can be a better place to position for this than the spot maturities. Moreover, the forward starting maturities can provide some cushion against the precise timing of any spike, which by their very nature are difficult to predict. Note though that entering and exiting a forward-starting variance swap can be more costly than running a spot variance swap to maturity, because the forward has to be traded twice and because it has a (slightly) wider bid-offer spreads.

Other example

Graphs other example

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