This Learning Curve explains how the large amount of capital associated with structured products exaggerates movements in long-dated implied volatility. The sellers of structured products are short long-dated skew and short long-dated vega convexity. The hedging of these structured products causes banks to buy long-dated volatility when it rises, and sell when it falls. As there are no natural counterparties and all structured product sellers have the same position, this hedging exaggerates any move in long-dated implieds.
Vega is the sensitivity of an option price to volatility and skew is the difference in the implied volatility of options of identical maturity but different strike. We define being long skew as having greater exposure to lower-strike options' implied vol than that of higher-strike options. If a trader is long EUR1 million vega though buying options at the 110% strike, and short EUR1 million vega through buying options at the 90% strike, then the position is therefore short skew but has no sensitivity to the overall level of volatility.
We take the above example and assume volatility surfaces remain stable, i.e. a fixed strike and at expiry the option's implied volatility does not change. Should markets decline 10% then the original short EUR1 million vega at 90% position is now at-the-money. As the vega of ATM options is greater than for out-of-the-money options, the short position will increase in vega. Similarly, the original long EUR1 million vega at 110% position declines in vega as it is now approximately a 120% strike option. Chart 1 shows how the originally vega neutral position is now short 160,000 vega due to the 10% stock price decline. It demonstrates that being short skew leads to a short volatility position if equity markets fall, but the reverse is also true, i.e., should equity markets rise, then being short skew would lead to a long volatility position.
The effect of a short skew position leading to a short volatility position as equity markets decline is due to the change in value of an option due to a moving equity price, i.e. an ATM option having greater time value than an OTM option. It is not due to the fact lower strike options tend to have a greater implied than higher strike options as the same effect would be seen for a flat or inverted skew. As this effect is completely independent of skew, another measure for this risk is needed. The rate of change in vega for a given change in spot (dVega/dSpot) is measured by vanna.
The sale of capital-guaranteed structured products causes investment banks to be short long-dated skew. The above example is not the actual position of structured products sellers, but is a simplified example of how being short skew causes investment banks to be long or short long-dated volatility should there be a movement in equity markets. For more details of the actual position held by structured products sellers, and why this causes them to be short long dated skew and vega convexity, please see the appendix.
As similar products are sold by all banks, all participants have the same position, causing an imbalance in the market due to the lack of natural counterparties. The maturity of these products can be up to 10 years, but they tend to be concentrated around the five-year mark. Although hedge funds are comfortable removing any imbalance in short maturity implieds, they are more reluctant to do so for maturities longer than two or three years due to the lack of visibility and hence greater risk. Covering of these long or short implied volatility positions therefore causes a large movement in long-dated implied volatility. The longer-dated end of volatility surfaces suffers more from the technical pressures of structured products, whereas the shorter-dated end is more driven by fundamentals due to greater hedge fund participation.
An option has approximately constant vega only if it is ATM, for OTM options the vega increases as volatility increases. This is known as vega convexity and is demonstrated in the graph below. Vega convexity is measured by the rate of change of Vega for a given change in volatility (dVega/dVol) and is called volga (or vomma). If someone is short vega convexity, an increase in implied volatility will cause an increase in the amount of vega they are short or long. Being short vega convexity is problematic as the magnitude of the vega position moves to your detriment, i.e. if you are short vega and volatility increases, the size of your short increases and vice versa. The principal protection feature present in most structured products ensures their vendors are short long-dated skew and short long-dated vega convexity.
Let us assume the sellers of structured products want to be or are forced to be implied volatility neutral. A decline in equity markets causes them to be short volatility or vega, due to their short skew position. They begin to cover their short vega position by buying volatility, causing an uptick as everyone has similar positions. Due to increasing volatility, the vega of their short positions increases due to vega convexity. This increase in their short positions prompts structured product sellers to buy volatility again, starting a vicious circle of increasing implieds.
Because of the above effect for long-dated volatilities the large amount of capital associated with hedging structured products could lead to an implied volatility overshoot to the upside when markets collapse, and an implied volatility undershoot to the downside when markets soar.
As an example of the effect structured products can have in the volatility market, the recent April 2005 decline in equity markets, which was the largest two-day fall for two years, caused significant hedging problems for some investment banks. As the short skew position had to be hedged dynamically, such a sudden movement left some traders exposed. The subsequent hedging of these products appeared to lift longer-dated implieds and hence also term structure, the difference in implied volatility of options with identical strike but different expiry.
Conversely, the sudden collapse of implied volatilities in early 2003 can be attributed to structured products reacting to the impressive rise in stock markets at that time. Although implieds subsequently continued their fall, the magnitude of the initial steep decline is more likely to have been caused by technicals rather than fundamentals.
Appendix
As structured products are often capital guaranteed, the seller can be thought of as effectively short an OTM put as this provides similar downside protection. Being short an OTM put leads the structured products seller to be short long-dated skew and short long-dated vega convexity.
We recognise that this description is simplified. In practice, structured products cause the seller to be long ATM volatility and short OTM volatility at both wings. As OTM options are more convex than ATM options, this leads structured products sellers to be overall short vega convexity. Due to the capital protection feature in structured products they are usually hedged with a zero coupon bond plus an embedded option bought from an investment bank. The embedded option in structured products is floored, i.e. cannot go below zero as this would prevent the capital from being protected. This floor leaves the seller short skew in a similar way to being short an OTM put as both offer downside protection.
This week's Learning Curve was written by Colin Bennett, head of derivatives research at Dresdner Kleinwort Wassersteinin London.
