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Webcast: Eurodollar Futures v FRA Convexity Correction

Speaker: Dr David Cox

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A course on this topic is available in New York Time Zone, London Time Zone and Singapore Time Zone

Overview

Futures and FRAs are widely used at the short end of the yield curve for trading and managing risk. In this webcast Dr David Cox explains how the difference in convexity between a short term interest rate futures position, such as the Eurodollar contract, and an FRA position affects the relative value of these instruments. The consequence of this if you wish to offset an FRA or swap position with a position in futures or to derive a forward rate from a futures price is looked at in detail.

Webcast Agenda

  • Hedging a single IMM dated FRA position with futures
  • Calculating the number of Futures contracts by matching DV01
  • What happens to the P/L of the position if rates move by a significant amount
  • The impact of the differences in the way that Futures and FRA DV01s change
  • What causes the convexity mismatch
  • The net volatility position
  • How the relative market prices adjust to take the convexity mismatch into account
     

Learning Outcomes

  • How to hedge an FRA position with futures and calculate the number of contracts needed by matching DV01
  • How large rate moves affects the DV01s of the two positions differently
  • How this gives rise to a long convexity position if you have sold FRAs and sold futures
  • What the market does to the relative prices of the FRA and futures contract as a consequence of the difference in convexity
  • How the gap between 100 less the futures price and the FRA rate is dependent on volatility
  • Similarities between a Futures v FRA position and an option position
     

Q&A

1. Is the convexity correction affected by the clearing of an FRA position?
A. No because the FRA is marked to market by the clearing house. The DV01 is calculated in exactly the same way as for the OTC contract and continues to change with rates.

2. I can see that you are long volatility when you sell an FRA and hedge it with Eurodollar futures, but how is this like an option position, where is the premium?
A. If you put on a position where 100 less the futures price is greater than the forward rate and there is no volatility you will incur a loss. This is essentially like paying the option premium over the life of the option.

3. How do you calculate the exact amount of the Futures v FRA convexity correction?
A. There is a very neat process for this described in the article by Burghardt and Hoskins referenced below. The amount of the correction is essentially the covariance between the forward rate and the rate that underpins the discount factor to the end of the forward period calculated for each period of three months and added up over all of the quarters between the start date and each futures contract IMM date.

References
Burghardt, G and Hoskins, B. 1995, The Convexity Bias in Eurodollar Futures, Dean Witter Institutional Futures research note.

Thank you to those attendees who submitted their questions.

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