Wednesday, August 3, 2011

Valuation of Derivatives: The importance of getting it right


This article appeared in The Edge (Malaysia) on 16 July 2011

The valuation of derivatives has become a common discussion theme since the financial crisis. Complex and structured derivatives like credit debt obligations (CDO) that were believed to be priced at “fair values” barely came close to their realisable values when unwound in the extremely volatile market of 2007 and 2008.
Prior to the crisis, it was not a common practice for the clients of investment banks (e.g. corporations and fund management companies) to question or challenge the valuation of derivatives that were done over the counter (OTC) with the banks. On the other hand, the investment banks were equipped with state of the art models to price these OTC derivatives; however they overlooked some important issues that come with complex models.

This article will zoom into some problematic areas around the valuation of OTC derivatives to illustrate how valuations can go awfully wrong if certain issues are overlooked.

§  Pricing OTC Instruments


With OTC derivatives, unlike exchange-traded instruments, there is no central counterparty to publish the latest and end-of-day market prices. This means that a price must be agreed between the two counterparties at both the beginning of the contract and also on an ongoing basis throughout the duration of the contract. Investors who lack the means of verifying the valuation numbers were happy enough to just receive prices from their counterparty, the investment banks.

It was only during the crisis that the market players realised the huge flaw in this practise as they observed how diverse the derivatives’ values were, compared to the market values. 

§  Valuing counterparty risk

Previously counterparty risk was only a concern of the credit risk management. The simple rule was the lower the credit rating, the higher the collateral demanded from the counterparty. The valuation of derivatives was not connected with this risk which seemed already addressed upfront.

When Lehman collapsed in 2007 and defaulted on its payments on derivatives with its counterparties, collateral (if any) received by its counterparties was barely enough to cover their losses. Now market players are being much more cautious; there is tremendous effort being made in pricing in the counterparty risk in OTC derivatives. 

§  Structured Derivatives

Structured derivatives are bespoke in every sense as they are designed to suit the needs of individual clients. Frequently these structures are priced by the trading desk or controllers, and no one in the financial institution has a second look thereafter. These structures usually have many features that could affect the payoff of the derivative in case of the occurrence of certain events. All of these features need to be priced in the derivative to ensure an appropriate value.

To illustrate with a hypothetical example, an aircraft financing structure could be designed as a securitisation over its ticket receipts. Built into this structure could be an option to the investors to sell back the securities to the investment vehicle (usually a conduit arm of the investment bank arranging the structure) in case the tickets receipts are impaired.

This option needs to be valued and its value is dependent on how the tickets receipts are modelled. Tough questions would arise, for example:
-          How robust is the model in forecasting and simulating the ticker receipts? For example would it breakdown if some parameters were out of range, like in stressful market environments?
-          Does the model encompass all the important parameters like weather, strikes, the general economy, fuel prices, earthquakes, etc in estimating the ticket receipts?

Depending on the path taken by the simulated ticket receipts, there would be scenarios when the option is triggered. Please refer to Chart 1. If the ticket receipts follow the path of 1 or 2, the option is unlikely to have a significant value and will be valued like an “out-of-money” option. But in simulation no. 3, the option crosses the strike (which is the trigger level of ticket receipts that enables the sell back by investors) and would have a significant value.

Chart 1 : Possible simulated paths

Most practitioners before would safely assume from the habitually high ticket receipts that the option has a negligible value and thus would not attach a value to the option. This is not a true picture as the option could have a significant value, depending on the market environment. If there were to be an earthquake which slowed down revenue from the ticket receipts which triggers the sell-back option, the option value will form an integral part of the security. 

§  Model complexity
When valuing derivatives in general, valuation models are used. The more structured the derivative gets, the more complicated the models become. For the simplest kind of derivative, usually exchange-traded futures and options, prices are obtained directly from the closing price of the exchange. For some flow-like OTC derivatives like overnight interest rate swaps, the daily spot curves are pulled from the broker sites into the system to value the positions. 

However, OTC derivatives usually involve non-standard options, illiquid underlying names, or unusual maturities. The parameters then become more judgemental and require frequent reviews. For example, non-standard options commonly derive their implied volatility from the volatility surface provided by a range of standard options with different strikes and maturities. But how sure are we that these volatilities represent the illiquid options? This has a direct impact to the pricing of these options, especially in periods of market stress when volatilities are unusually high. 

Even the choice of models to price the derivative is an important one as the derivative values must relate to market prices.

Calibration of these complex models is important. For example a complex model could have some constants in its model which is derived from calibration with the standard market products. But how sure are we that these constants relate to all market environments? As the market environment changes, the constants will change. This means that these models need frequent recalibrations. In my experience, not all models calibrates well in highly volatile markets.

When it comes to securitised credit products, default probability could become very problematic to estimate. Correlation of defaults is another parameter which should not be taken lightly. Correlation is not constant; it tends to get higher in high default environments. This calls for a stochastic model that throws in various economic states with different correlations of default to price the derivative. 

§  Are we discounting them right?

The accepted norm has been to use the LIBOR curve to discount future cash flows from derivatives. But from my previous article on “Interest rate swaps; post 2008 crisis” on Jan 31, we discovered that in today’s world, LIBOR is not always suitable as it may contain default risk in its spread, disqualifying it to be a truly the risk-free rate. Alternative rates like the funding rates are being used.

Conclusion

We are experiencing a financial world which is unprecedentedly uncertain. Valuation of financial products, primarily derivatives, must be tackled diligently. In the next article, I will discuss some possible approaches and practices that help address this concern.

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