Model mismatch

The Bank of New York's Tim Murphy and Markit's Richard Earl look long and hard at models as they apply to pricing for OTC

The use of over-the-counter (OTC) derivative trades continues to grow significantly. Surveys, articles and conferences continually testify to growing volume of credit default swaps, OTC equity options and other OTC trades and the increasing complexity of trading through the use of hybrid and exotic forms of these transactions.

As increasing levels of institutional capital have moved into strategies employing OTC trades, as identified in The Bank of New York/Casey Quirk and Acito study, Institutional demand for hedge funds: towards 2010, the need for transparency and independence of pricing has emerged as a key challenge for buy-side service providers, back office professionals and risk managers.

As each month passes, the dominant use of counterparty pricing is diminishing and model-based pricing is now emerging as the standard that provides both independence and the opportunity for data transparency.

Model-based pricing, when controlled by the user in the back office or at the service provider, is independent of the trader and the counterparty and can be interrogated by risk reviews and audits as needed. There is a resultant risk, however, that needs to be considered: model risk. Model risk is the risk that the outcome of the simulation does not match reality. For derivative trades, model risk can occur from areas like the choice of model, the quality of the maintenance of the model, model calibration and its maths on the computer, the occurrence of input errors and the data used. Here, we focus on the effect of data inputs on the outcome of modelled measurements of value. The following example illustrates reliance on publicly available data will not ensure an outcome that reflects the market reality.

Example: Corporate Credit Default Swap Valuation

Entity: Dole Food Company, Inc.

Region: North America

Rating: Sub-investment grade

Tier of debt: Senior unsecured

Industry: Food / soft drinks

The CDS on the above debt is fairly liquid and almost all dealers quote live markets primarily for the five-year maturity. Publicly available sources only provide a five-year spread and therefore mark the whole credit curve flat. However, if the data for daily spreads for the full-term structure are collected, as Markit does for 10-12 dealers, and plotted, a much steeper curve emerges. Graph one, bottom right, shows the comparison between Markit's CDS curve and publicly available data. We then went on to consider a CDS trade on the above entity with the following inputs:

Trade Details

Entity: Dole Food Company Inc.

RED Entity Clip: 27BC65

Tier: SNRFOR

Currency: USD

Start date: 20 March 2004

End date: 20 June 2009

Frequency: 3M

Day count: A/360

Recovery: 36.33%

Traded spread: 1.00%

Notional: 10,000,000.00

We calculate the present value of the trade using the market-standard hazard-rate model introduced by JP Morgan and only vary the following inputs:

1Markit's closing consensus curve (term-structure curve on the graph)

2Publicly quoted flat-term structure at the five-year maturity (flat curve at five-year dealer market on the graph)

The resulting present value from curve one is negative $339,297, whereas the resulting present value from curve two is negative $807,879: a difference of approximately $470,000 in present value on a $10m notional, purely due to the use of two different curves.

One curve, the dealer curve, while the most publicly available, does not accurately reflect the term structure of the market for this credit default swap (CDS). The second curve, while containing data that isn't publicly available, more accurately reflects the current levels of the CDS dealer market. Therefore, the consensus curve CDS data more accurately reflects the reality of the CDS market with the required term-structure inputs which are crucial to the accurate valuation of CDS trades. Another example that illustrates the both the importance of accurate market data inputs and the often limited usefulness of publicly available inputs is the equity option valuation.

When pricing OTC options, it can be dangerous to depend entirely on volatilities implied by publicly available listed option data. This is particularly the case for trades deep out-of-the-money or with longer-dated expiries.

Although there is a fairly liquid market in Korea Composite Stock Price Index (KOSPI) 200 options, especially for strikes close to the money and for short-dated expiries, the implied volatilities can be inconsistent and therefore unreliable. Chart two, below left, compares the volatility skew of the KOSPI 200 as implied by exchange-traded option prices, with the OTC skew data collected by Markit. Consider this OTC trade, constructed using options of the same maturity as displayed above:

Instrument: European Call Spread

Underlying: KOSPI 200 Index

Expiry: 18 May 2007

Strike: 177.5 / 182.5

Contract value: KRW 100,000

Number of contracts: 10,000

Pricing this option with the standard Black model, using the listed option data and the Markit data, gives the results in the table. As can be observed from the table below, Markit's implied volatility for the long call option struck at 177.5 is higher than the exchange's, whereas Markit's implied volatility for the short call option struck at 182.5 is lower.

So, if this trade were priced simply from the exchange's option prices, as is common practice in the valuation of such instruments, the inconsistency observed in the corresponding volatility surface would result in a significantly distorted valuation. This translates to a difference in present value for the trade of approximately KRW430m (or about e335,000).

Since we are applying exactly the same pricing methodology to both sets of data, this demonstrates the importance of high-quality, clean volatility data sourced from the OTC market, reflecting current market levels.

For illiquid positions, long-dated options and deep out-of-the-money options, dealer-contributed data is one of the best sources for compiling accurate implied volatilities. Markit collects such OTC skew data and applies this to client valuations.

In both the above examples, very basic OTC trades carry a significant model risk in valuation due to the data inputs to the model. In order to manage this risk, practitioners will need to ensure that they understand the limitations present in all of the data they choose to use and may often have to look beyond the most readily available data, to a source that captures the day-to-day market realities of the instruments or trades being considered.