Sep 27, 2010

Pricing and Hedging Overnight Index Swaps: Two Possible Approaches

The following article is based on a webinar presented on September 22, 2010, by Jon Zucker, Ph.D. – VP Client Solutions Group. You can access the replay here.

It might seem strange to think about using advanced techniques for modeling Overnight Index Swaps (OIS), since the risk in a typical short-dated OIS is relatively small compared to a bond or 30-yr interest rate swap (IRS). However, there are specific peculiarities about the OIS market that argue for careful consideration of valuation and risk measurement of these instruments.

We present two approaches to tackling this challenge. If you simply want to quantify risk or trade long-dated OIS, a simplified method based closely on the IRS market is likely good enough. But if you need to price and hedge short-dated instruments, it becomes more important to use more sophisticated (and potentially somewhat subjective) processes that provide a closer reflection of real-world market dynamics to produce results that are accurate for trading purposes.

Before diving deeper into valuation methodologies, it’s important to have an understanding of the OIS market and why it’s different from the IRS market.

What is the OIS Market?

When we talk about OIS, what is really being discussed is the market to trade overnight rates. This is a highly active and liquid market in all major currencies, with the largest market being in the Euro (the Euro Over-Night Index Average, or EONIA). The instruments involved are cash deposits, futures contracts, and the focus of our discussion here – OIS.

An OIS allows one party to receive a fixed payment against a formula which represents the compounded overnight rate for the given period. By entering into an OIS, the party exactly hedges their funding exposure into a fixed rate. It is generally used by institutions that fund overnight to invest in the short-to-medium-term (generally 3mo to 2yrs). It is also traded by speculators on the spread of overnight rates to other rates, as well as dealer desks who structure OIS contracts.

Why the Interest in OIS Now?

Despite the fact that Overnight Index Swaps (OIS) have been around for over a decade, the global credit crisis of 2008 created a perfect storm that increased interest in these derivative products.

Toward the end of 2008, financial services companies found it hard to raise funds at what had been the benchmark funding term: 3 months. In the US, for example, the spread between the 3-mo LIBOR and the Fed Funds rate (the liquid overnight rate) went from a stable range of 5-10 bps to about 400 bps.


Source: Bloomberg

Funders were forced to look to the overnight market, leading to a surge in OIS volume. At the same time, increased spreads and volatility created an opportunity for speculation on overnight rates. This combination of end-user interest and speculative interest led to increased volume in the OIS market, particularly in the U.S.

What’s Unique About OIS?

Firms often look at OIS and standard interest-rate swaps similarly due to their closely related purpose. However, there are fundamental differences to OIS that need to be considered for pricing and hedging.

  • They tend to have tight bid-offer spreads due to the OIS market’s liquidity
  • Notionals tend to be large – often ten-fold that of a standard IRS
  • The dates and maturity are customized for each contract, because the swap is tied to funding. For example, it’s not uncommon to be asked to quote an OIS for an unusual period – say, a 6-mo OIS beginning on October 5.

These three factors combine to introduce some peculiar modeling challenges. How you approach them depends on how you answer two questions:

  1. What types of OIS are you trading?
  2. How willing are you to introduce subjective inputs in order to gain accuracy?

A Simplified Approach

If you only need to measure risk or are trading long-dated contracts, pricing and risk calculations will likely be close enough using a simplified method that closely resembles the IRS market.

In this case, we use market rates from traded OIS and apply common curve-stripping processes to project overnight rates to be used in pricing. The chart below looks at OIS rates in successive months to six months, and then jumps to a 1-year maturity. The steps in the curve are tied to the maturity dates of each swap.


Source: Numerix

The advantage here is that it’s easy to implement and is reasonably accurate for risk measures and P&L for long-dated positions. But there are intuitive problems with this approach that become apparent when pricing and hedging short-dated OIS.

With the simplified approach, the curve does not account for the specific, predictable dates on which overnight rates will likely change. Looking at the US, most adjustments to monetary policy are announced by the Federal Open Market Committee (FOMC) on scheduled meeting dates. In the example above, each step in rates is based on the instrument maturities, not the FOMC meeting dates.

This method also excludes the tendency of overnight financing rates to spike at the end of what is called the “turn”—the end of the month, quarter and year. This is typically explained as an effect of financial reporting pressures: banks want to make their balance sheets smaller when they take their end-of-period snapshot for reporting to shareholders, so they reduce lending, forcing overnight rates up. It actually matters a lot whether you’re quoting an OIS for Dec 28 vs Jan 3, because if there is a turn financing effect over the end of the year, the price will be quite different.

How do we adjust the curve to account for these predictable factors? The answer is to add flexibility to the process to allow the user to enter additional inputs.

An Advanced Approach – More Accurate, and More Subjective

To enhance the curve-stripping process, three changes can be applied:

1. Increase the number of instruments used to build the curve. To improve granularity, the first step is to use as many instruments as possible. We switch to the use of Fed Funds futures, which trade more liquidly in close maturities. For later maturities, we bring in Eurodollar futures, adjusting for the spread between the overnight rate embedded in Fed Funds futures and the 3-month LIBOR rate embedded in Eurodollar futures. This adjustment can be defended through historical analysis or forward-looking estimation processes, and is the source of basis risk, since we can’t be sure that the overnight-to-3-mo spread will stay constant. The up-side is that you get a more granular picture of the OIS curve.

2. Allow arbitrary transition points for changes in rates. In normal curve building, the transition (or “jump”) points of the curve arise from maturities of the instruments. With the advanced approach, we move these transition points for the curve to dates of FOMC meetings or any other predictable event that could impact rates, tying jump points to actual dates when rates are expected to change.

3. Allow temporary jumps (“spikes”) in rates to account for the “turn.” This factor requires that the trader or risk manager make a subjective estimate of the impact of financing issues at the end of a month/quarter/year. This may test your firm’s willingness to allow subjective inputs, but traders would tell you this capability is necessary to get accurate pricing before and after the turn. Explicit specification of the “turn effect” also allows risk management to accurately measure how changes in rates over the turn affect portfolio value.

Implementing these three changes — using a combination of Fed Funds futures and basis-adjusted Eurodollar futures, forcing the transition dates to correspond with FOMC meetings, and estimating jumps at each quarter-end turn — we re-calculate the curve of projected Fed Funds rates. The tricky part is to adjust the curve so that the discount factor at the maturity of each instrument is unchanged: cashflow received at the maturity of an instrument has the same value both before and after introducing the changes.


Source: Numerix

The advantage to this approach is pretty clear: it provides a more accurate representation for pricing and hedging across FOMC dates and temporary jumps in rates. It is up to the individual firm to decide whether the subjective quality of some of these inputs is worth the added accuracy.

Traders are generally more comfortable with the enhanced method. Risk managers and P&L managers tend to be averse to any element of subjectivity. However, some comfort may be gained by additional investigation of historical relationships and pricing in the market to different dates.

The bottom line in this case is that more accuracy requires a bit of judgment. If you are trading long-dated OIS, the extra accuracy won’t create a significant difference in risk measurement, pricing and hedging. But for short-dated OIS — for which the ability to tailor market dates matters, bid-offer spreads matter, and the need to get an exact price at an exact date matters — the enhanced approach may be necessary.

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