We conclude here our comprehensive survey on how “Greeks” affect Structured Products and Derivatives pricing and hedging. In the first part (published here), the concept of the Greeks (also known as sensitivities) was introduced and how they give precise information about price changes of a structured product from movement in the underlying parameters. This piece will look at remaining pricing parameters and sensitivities.

The use of the Greeks serves two important complementary functions. The first is for the trading desk of the issuing bank to understand how to risk manage the structured product through its lifetime. Any structured product is a contractual obligation to deliver a certain defined return depending on the performance of the underlying assets. In order to meet that requirement, risk management performs a precise role akin to that of an investment manager tracking an index or algorithm by taking into account the changes in the product’s price when market conditions change. The second group that finds the Greeks useful will be those who have bought structured products, such as a private bank or financial adviser. Greeks help them understand how the product’s value will likely move in different scenarios and will indicate aggregate risk and concentrations in a portfolio of such instruments.

In the first part, we looked at “Delta” and “Gamma”, two important quantities that govern price changes caused by movements in the underlying asset or assets. This second piece will examine the remaining major Greeks: Vega (Volatility), Rho (Interest Rates) plus sensitivities to dividend yield and correlation. Other quantities do also get examined by trading desks in particular but these tend to be more obscure or second order (such as the delightfully named Vomma and Vanna) and so we will not consider them here.

** Product payoff **

For all structured products the payoff is usually defined in terms of direct performance of the underlying assets, such as upside return or fixed returns that come from satisfying Auto-call or barrier conditions. It is clear therefore that the secondary market price or fair value of the structured product will move when the underlying moves. This is because the price reflects the previous performance of the underlying asset together with the range of likely outcomes that may happen during the remaining life of the product. As the product approaches maturity, the in-life price will converge to the final payoff of the product.

** The importance of other variables **

However, many other variables will contribute to the array of Greeks even though they are not explicitly in the product’s payoff formula. These include the parameters we will consider of volatility, dividend yield, interest rates and correlation. Option pricing models as used by investment banks take into account all relevant market variables that affect the cost of the required hedging strategy. This in turn will change the product price because of the dual relationship between the price and hedging.

In most standard equity option models these parameters are assumed constant or deterministic. Volatility is the main exception and can have different treatments depending on the modelling approach of a bank and the complexity of the product being valued. However despite this assumption, parameters constantly change in value and so the sensitivity to them must be considered.

** Volatility sensitivity**

One of the most important Greeks is the sensitivity to volatility (“Vega”). Any product which has a long option position such as a protected growth product will have positive sensitivity to volatility whereas those where the investor has capital at risk (for example a reverse convertible) will generally have negative sensitivity. The value of Vega reflects the direction that the product price will take if volatility changes. From a trader’s perspective these sensitivities translate into practical consequences because as volatility increases the trader will generally have to do more rebalancing of the underlying as it moves around more. If those rebalances happen in a way that the trader will incur cost (because of being forced to buy the underlying when it goes up and selling when it goes down) then the trader is exposed to volatility increasing and the value of the Vega will indicate that. This is known as being short Gamma and short Vega - two related concepts. The reverse would be true for a long Vega position.

Volatility levels in the market can change significantly and quickly, as measured by quantities such as the VIX series and other indicators of both implied and historic volatility. If a trader has sold a product which will increase in price when volatility goes up then it will often be desirable to reduce risk either by entering into a transaction with opposite risk or by buying options on an exchange or from another bank. Both methods are often used.

Those acting on behalf of investors will also need to be aware of the Vega of different products as they can lead to significant short-term price swings. Today, capital at risk products are the most common and these lose value when volatility increases. In the early part of 2020, nearly all Equity markets witnessed large falls in index and stock levels accompanied by sharp increases in volatility.

** Combined Greeks effects **

Most capital at risk products therefore suffered from “Delta” related price falls exacerbated by an additional “Vega” component. This can be unsettling and counterintuitive - for example in situations where the product does not fall below its barrier level. When these two contributions to price changes are added it is possible that some structured products show falls bigger than the index to which they are linked. A 20% fall in the index might give rise to a delta related price move of 16% and a Vega loss of 6%, combining to 22%. These swings are often short lived as was indeed experienced later in 2020. They can only be anticipated and understood by monitoring the Greeks carefully.

** Changing interest rates, dividends and correlations **

Rho is the usual name given to price sensitivity to Interest rates, and this tends to give the fewest problems to traders because of the easy availability of hedging instruments such as bonds and the fact that the value of Rho does not usually change as quickly as other Greeks.

The two final sensitivities that we will examine are those relating to dividend yields and correlation. Both of these caused major issues in 2020 because of big moves and because both can be very hard to hedge.

** Influencing risk management**

Nearly all structured products are long their respective underlyings in some way whether they be capital protected or capital at risk. Part of the associated long delta hedge involves dividend exposure if the product is linked to a stock or an index on a price return basis. If dividend values fall the product will increase in value and expected dividend payments to be received by those running the hedge will not materialise. Historically the investment banks in the market have always been very exposed to falls in dividend yields since almost all products have the risk in the same direction and external hedging instruments such as dividend futures are not always feasible. The usual phenomenon that is seen therefore is that implied dividend yields settle at a lower level than most future consensus estimates. This is intended to create a risk buffer, but in 2020 this proved to be not nearly enough. Other solutions have been sought, most notably the use of fixed dividend indices which eliminate dividend risk from a product.

Correlation sensitivity is also important for any product that features more than one underlying asset. Correlation is even harder to hedge and the market also suffers from the one way position of risk given that the two most popular product types tend to have long basket options or short worst-of puts which line up the risk in the same direction. Because of these factors, the main approach is to also mark the correlation values higher than most estimates. This also failed to prevent significant losses in 2020. Investors would have been able to measure both these effects which were in their favour this year.

In summary we see that structured product pricing, hedging and monitoring depends on many factors and it is very important to give the Greeks full attention in any portfolio particularly during times of market turmoil.

**Tags:**Valuations Stress testing

*A version of this article has also appeared on www.structuredretailproducts.com*

*Image courtesy of:*Alex Blajan / unsplash.com