P&L Explained on Equity Index Derivatives

by Lucido Group

Dividend Yield Changes Lead to Unexplained P&L

An important input to the pricing of an equity index derivative is the dividend yield. We have written twice previously about difficulties Findur has capturing equity index derivatives, including how to import the dividend yield, and how to see the dividend yield used in pricing. This paper describes an additional challenge for users wanting to explain the P&L on a portfolio of equity index derivatives.

P&L Explained is a native simulation result in Findur to explain the daily P&L on a position as a result of changes in market data and lifecycle events. The result supports many instrument types in Findur, although we will write in the future about problems that remain for fixed income derivatives.

Depending of course on the instrument type, most of an instrument’s P&L is explained as a result of first order sensitivity to interest rates and market prices, and volatilities. Pricing of equity index derivatives is also sensitive to the dividend yield. When the dividend yield changes, Findur reports high residual (unexplained) P&L.

The Right Way to Explain the Impact of Dividend Yield Changes

The P&L explained by first order interest rate sensitivity of a vanilla swap is explained by the Impact of Delta (or Impact of Output Delta) result. The simulation engine uses the prior day’s delta result, and the changes in rates from the prior day to the current day, to estimate the daily P&L that is explained by the change in rates. To be consistent, an Impact of Dividends result would need to have the same inputs available.

Findur has no native feature or result that allows us to bump the dividend yield and derive the dividend yield price sensitivity. Findur also does not track the prior day dividend yield. As a result of these gaps, it is difficult to calculate the sensitivity of the instrument to a change in dividends without reimplementing the pricing model.

Let’s look at pricing model customizations for a moment. The OpenComponents API is used to implement custom pricing models. It has powerful features that allow a financial engineer to override only one part of a calculation. For example, if you are satisfied with a particular pricing model used for a swaption, but would like to override the way that the model resolves the instrument’s volatility, you may implement only the volatility lookup method. This allows you to extend an otherwise suitable model, and significantly reduces the complexity of a customization. This is one of the many features that makes OpenComponents the API of choice over OpenJVS. It’s simply no contest.

Unfortunately, the OpenComponents pricing model interface does not support overriding the dividend yield on equity index derivatives.

The Nearest Thing to a Solution

P&L attribution is very important to users, and unexplained P&L that is easily understood to be the result of a change in dividend yield should not be a difficult mountain to climb. We have a solution that allows users to see the P&L attributed to a change in dividends.

To explain the daily P&L that arose as a result of changes overnight to dividend yields, it is necessary to price all of the prior day’s deals using the prior day’s market inputs (including prices, rates, volatilities, correlations and dividends). Findur only supports having one version for all users of dividends, so today’s dividends must be saved, most easily using our automated solution. The equity index derivatives must be revalued using the prior day’s market inputs (including prices, rates, volatilities, and correlations) and prior day’s date to abstract from the cost of carry, or theta effects. The change in the MTM is the impact of dividend yields.

This process may be automated because no user should be permitted to suffer the operation manually. In the absence of any enhancements from Openlink, the approach allows a user to reduce residual unexplained P&L, and see the impact of changes in dividend yields.

Roadmap Ideas

We would prefer Openlink improve dividend handling. We can help make the case to the product management team. There are several ways that this would make it considerably easier for users that have a portfolio of equity index derivatives. Saving continuously compounding dividend yields in a market index directly, instead of in the Dividend Manager window, would open opportunities. We understand this would not necessarily be a trivial change for them to make. But storing dividends as market data inputs would allow us to create a user-defined simulation result or a result calculator component. We could then more easily close the deficiencies with missing sensitivities, ‘impact of’ result, and unexplained P&L.

Of course, ideally Openlink would close these gaps in P&L attribution.