Robust financial market benchmarks

Darrell Duffie , Piotr Dworczak 01 November 2014



Over-the-counter markets depend on benchmarks – trillions of dollars in loans and swaps are negotiated by reference to benchmark interbank offered rates, such as LIBOR, EURIBOR, and TIBOR.[1] The WM/Reuters fixings are the dominant benchmarks in the over-the-counter foreign exchange market, which covers over $5 trillion per day in transactions.[2] Benchmarks also provide price transparency to markets for commodities such as silver, gold, oil, and natural gas, as well as manufactured products such as pharmaceuticals. [3],[4]

Recent scandals involving the manipulation of LIBOR, EURIBOR, and the WM/Reuters foreign exchange fixings have shaken confidence in financial benchmarks. Global banks are also now more reluctant to support these benchmarks in the face of potential regulatory penalties and private litigation. For example, of the 44 banks contributing to EURIBOR before the initial reports of manipulation, 18 have already dropped out of the participating panel (Brundsen 2013).

Regulators have responded not only with sanctions, but also by taking action to support more robust benchmarks. The Financial Stability Board has set up several international working groups charged with recommending reforms to interest-rate and foreign-exchange benchmarks, with the objective of maintaining their usefulness by reducing their susceptibility to manipulation. These groups – the Official Sector Steering Group (2014), Market Participants Group (2014), and Foreign Exchange Benchmark Group (2014) – have issued reports detailing recommendations for how to meet new international standards for benchmarks established by IOSCO, the International Organisation of Securities Commissions (2013). The UK is preparing a comprehensive regulatory framework for benchmarks (Bank of England 2014).

New research on setting robust benchmarks

Under the IOSCO standards, benchmarks should be anchored in actual transactions, and not rely merely on judgemental reports by bank officials. But there has not been much research regarding how benchmarks should weigh transactions data in light of potential manipulation. In recent work, we characterise how a benchmark administrator would optimally weigh transaction prices to produce a fixing, assuming that the administrator cannot directly assess penalties or rewards.[5]

Our model features a benchmark administrator who observes the prices and quantities of transactions generated by the anonymous traders. Whether or not they are manipulated, the transaction prices are noisy signals of the fundamental value of the underlying asset. Noise can arise, for example, from market imperfections and timing differences. For example, the main WMR benchmarks for currency exchange rates on a given day are currently based on transactions that take place within 30 seconds of 4:00pm London time, and are based on trades that occur at bids or asks, including some uncertain price impacts.

Our modelled benchmark administrator is restricted to a benchmark fixing that is linear with respect to transaction prices, with weighing coefficients that can depend on the size of the transaction. A common fixing method used in equity and bond markets is the ‘volume weighted average price’ (VWAP), for which the weight on a given transaction price is proportional to the size of the transaction. Such a benchmark is approximated with a large number of transactions within the family of fixing designs that our modelled benchmark administrator can consider.

Traders have private information concerning how much their profit is increased by a given distortion of the benchmark, and observe private signals regarding the fundamental value of the benchmark asset. Traders can manipulate by making a transaction at an artificially inflated or reduced price in order to gain from the associated distortion of the benchmark. Manipulation involves a cost to the trader that depends on the distortion in the transaction price. For example, in order to cause an upward distortion in the benchmark, a trader would need to buy the underlying asset at a price above its fair market value. In order to manipulate the price downward, the agent would need to sell the asset at a price below its true value. Either way, by trading at a distorted price, the agent suffers a loss. But the trader may have other positions, such as swaps, which market prices or settlement payments are linked to the benchmark fixing, and may be able to generate a net manipulative profit, provided that the cost of the distortionary transactions is exceeded by the added profit on the pre-existing contract positions.

Our mechanism designer chooses fixing weights that minimise the mean squared error of the benchmark, given the incentives of manipulators in response to the chosen weights.

Our main findings are as follows.

  • First, it is typically impossible to implement a complete absence of manipulation.

This result can arise as a consequence of the disproportionately small size of the market determining the fixing (for example, with LIBOR, unsecured bank borrowing) relative to the market for other instruments that are dependent on the fixing (such as interest rate swaps). Surprisingly, even if no manipulation is implementable, it is not optimal from the viewpoint of maximising fixing accuracy. A benchmark that completely eliminates incentives to manipulate will necessarily use the non-manipulated data in a statistically inefficient way. Thus, to minimise the overall fixing distortion, there is a nonzero probability of manipulation.

  • Second, we show that weights assigned to the observed prices should be increasing in the size of corresponding transactions, even if the precision of signals is constant in transaction size.

In particular, almost zero weight must be put on small transactions. This is intuitive, and stems from the fact that it is cheap for agents to make small manipulated transactions. For instance, Scheck and Gross (2013) describe a strategy said to be used by oil traders to manipulate the daily oil price benchmark published by Platt's: “Offer to sell a small amount at a loss to drive down published prices, then snap up shiploads at the lower price”. Moreover, the weighing function should flatten out (or even be constant) for large transactions. This is in order to avoid overweighing manipulated transactions made by agents with particularly strong incentives to manipulate (for example, by a bank with a large long position in swaps based on LIBOR). We characterise the exact shape of the optimal weighing function. An example optimal weighing is shown in Figure 1 below.

Figure 1. An example of an optimal weight

Concluding remarks

We do not analyse estimators that assign different weights to transactions based on the transactions prices themselves (that is, nonlinear estimators). This extension is an obvious next step. For example, some benchmarks such as LIBOR dampen or eliminate the influence of outlier prices.

Another approach to making benchmarks more robust to manipulation is to enlarge the set of transactions used to determine benchmark fixings, so that manipulated trades or reports have less influence on the fixing. The benchmark administrator can widen the time window over which prices are averaged to determine the benchmark, and by broadening the set of instruments or types of trades that are used. Specific recommendations have been made for both interbank offered rates and for WMR foreign exchange benchmarks. [6],[7] (Table 1 provides sample information for transactions data collected by the Market Participants Group for the purpose of a proto-type transactions-based fixing for LIBOR). A further benefit arises from reducing the heavy reliance of derivatives markets on benchmarks such as LIBOR that are fixed on the basis of a small set of transactions. This is desirable whenever there is an alternative suitable benchmark that is more robust to manipulation, as explained by Duffie and Stein (2014).

Table 1. Transactions data on unsecured bank borrowing

Source: Market Participants Group on Reference Rate Report, Final Report, March 2014.

The statistics shown are daily average, maxima, and minima for the number of trades, number of issuers, and dollar volume of unsecured bank borrowing transactions in the commercial paper (CP) and certificate-of-deposit (CD) markets. These statistics are based on a sample from a unit of J.P. Morgan over the period 2011 through January 2014. Maturity buckets are defined as follows: O/N=1 day to 4 days, 1W=6 days to 8 days, 1M=28 days to 32 days, 3M=85 days to 95 days, 6M=175 days to 185 days. 


[1] The Market Participants Group on Reference Rate Reform (chaired by one of the authors of this note) reports that over $3 trillion  in syndicated loans and over $1 trillion in variable-rate bonds reference US dollar LIBOR. The MPG report lists many other fixed-income products that are negotiated at a spread to IBORs. As of the end of 2013, the Bank for International Settlements report a total notional outstanding of interest rate derivatives of $583 trillion US, the vast majority of which reference LIBOR or EURIBOR. Extremely popular benchmarks for overnight interest rates include SONIA (Sterling OverNight Index Average) and EONIA (Euro OverNight Index Average).

[2] The Financial Stability Board reports that 160 currencies are covered by the WM/Reuters benchmarks. These benchmarks are fixed at least daily, and by currency pair within the 21 major ‘trade’ currencies.

[3]The London Bullion Market Association provides benchmarks for gold and silver. Platts provides benchmarks for oil, refined fuels, and iron ore (IODEX). Another major oil price benchmark is ICE Brent.

ICIS Heren provides a widely used price benchmark for natural gas.

[4] Gencarelli discusses concerns regarding the integrity of the Average Wholesale Price (AWP) drug-price benchmarks.

[5] Coulter and Shapiro (2013) and Duffie et al. (2014) consider the design of mechanisms that directly penalise reports. Two rather different incentives for manipulation have been identified. The first, dramatically exacerbated by the recent financial crisis, was to improve market perceptions of a submitting bank's creditworthiness, by understating the rate at which the bank could borrow. (The reports of each individually named bank are revealed to the market.) The second incentive was to profit from LIBOR-linked positions held by the bank. For example, in a typical e-mail uncovered by investigators, a trader at a reporting bank wrote to the LIBOR rate submitter: “For Monday we are very long 3m cash here in NY and would like setting to be as low as possible...thanks.” This second form of manipulation, revealed by investigators to have been active over many years, is the main subject of our recent research on fixing design.

[6] See Market Participants Group on Reference Rate Reform (2014), and Official Sector Steering Group (2014). On widening the time window for LIBOR fixing, see Duffie et al. (2013).

[7] See Foreign Exchange Benchmark Group (2014).


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Bank for International Settlements (2013), “Triennial Central Bank Survey OTC Interest Rate Derivatives Turnover in April 2013: Preliminary Global Results”, Monetary and Economic Department, Bank for International Settlements, September. 

Brundsen, J (2014), “ECB Sees Rules to Stem Bank Exodus from Benchmark Panels”, Bloomberg, 19 June 

Coulter, B and J Shapiro (2014), “A Mechanism for LIBOR,” Working Paper, University of Oxford. 

Duffie, D, and P Dworczak (2014), “Robust Benchmark Design”, Working Paper, Graduate School of Business, Stanford University, June. 

Duffie, D, P Dworczak, and H Zhu (2014), “Benchmarks in Search Markets”, Working Paper, Graduate School of Business, Stanford University, October.  

Duffie, D, D Skeie, and J Vickery (2013), “A Sampling-Window Approach to Transactions-Based LIBOR Fixing”, Federal Reserve Bank of New York Staff Report Number 596, February.

Duffie, D, and J Stein (2014), “Reforming LIBOR and Other Financial-Market Benchmarks,” Working Paper, Graduate School of Business, Stanford University. 

Foreign Exchange Benchmark Group (2014), “Foreign Exchange Benchmarks Consultative Document”, Financial Stability Board, 15 July.  

Gencarli, D (2002), “Average Wholesale Price for Prescription Drugs: Is There a More Appropriate Pricing Mechanism,” NHPF Issue Brief, Volume 775 (June), pp. 1-19.

Hou, D, and D Skeie (2013), “LIBOR: Origins, Economics, Crisis, Scandal and Reform”,  The New Palgrave Dictionary of Economics, Online Edition, 2013, edited by Steven N. Durlauf and Lawrence E. Blume.

International Organization of Securities Commissions (2013), “Principles for Financial Benchmarks, Final Report”, FR0/17, July. 

Market Participants Group on Reference Rate Reform (2014), “Final Report”, Financial Stability Board, 17 March. 

Official Sector Steering Group (2014), “Reforming Major Interest Rate Benchmarks”, Financial Stability Board, 22 July. 

Scheck, J and J Gross (2013), “Traders Try to Game Platts Oil-Price,” Wall Street Journal, 19 June. 

Snider, C, and T Youle (2012), “The Fix is In: Detecting Portfolio Driven Manipulation of the LIBOR”, Working Paper, UCLA, December. 

United Kingdom Financial Conduct Authority (2012), “The Wheatley Review of LIBOR: Final Report”, September. 

Vaughn, L (2014), “Gold Fix Study Shows Signs of Decade of Bank Manipulation”, Bloomberg, 28 February. 




Topics:  Financial markets

Tags:  financial benchmarks, Libor scandal, optimal weights

 Dean Witter Distinguished Professor of Finance at Stanford University's Graduate School of Business. 

Ph.D. student at Graduate School of Buisness, Stanford University. 

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