Ultra-short tenor yield curve for intraday trading and settlement

Abstract

Due to the increasing prevalence of high-frequency algorithmic trading and fintech developments like blockchain, there is a shift towards very short trading horizons and immediate settlement. This creates a demand for an ultra-short tenor interest rate curve that is updated in real-time. Our paper develops a practical market model for the equilibrium intraday interest rates which provides market makers adequate incentives to attenuate flash crashes. Our model suggests that the intraday CHF interest rates should have been highly negative during the flash crash of EURCHF on 15 January 2015, which could potentially stop the long CHF short EUR strategy and reduce the severity of the crash.

Keywords:

• Intraday yield curve
• flash crash
• duration and time deformation

JEL Classifications:

• G01
• G12
• G14
• G23
• C01
• C15
• C41
• C58

Acknowledgements

We would also like to thank the participants of the SNB-CIF conference 2019, Shanghai FinTech Conference 2017, AMBS seminar, Matthias Jüttner, Eduardo Salazar, Michael Brennan and two anonymous referees for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ser-Huang Poon http://orcid.org/0000-0002-7297-9401

Notes

1 See Peters and Panayi (2016) for a detailed description of how the technology works. Currently the blockchain needs about 10 minutes to update all the ledgers, but the technology is currently being developed such that settlement would be achieved in milliseconds (see for example McKinsey & Company 2015).

2 The difference between the rate charged on an overnight loan delivered at 9 a.m. and a loan with the same maturity delivered at 10 a.m. implicitly defines the price [difference] of an hourly loan.

3 Here, we see that the interest rate reference period is ex ante and not ex post.

4 Over longer horizons, the differentials of inflation should be subtracted from the UIP, and the relationship is known as real exchange rate-real interest rate (RERI) (see for example Hoffmann and MacDonald 2009). Since our focus is on high-frequency intervals (daily or intraday), we do not consider the effects of inflation.

5 Risk premium tends to vary slowly over time. Here, we assume a time-varying π estimated using a rolling window of 500 days.

6 Chaboud and Wright (2005) use bilateral Japanese yen, German mark/euro, Swiss franc and pound sterling 5-min average bid and ask spot exchange rates viz-a-viz the US dollar provided by Olsen and Associates over the 15-year period 1988-2002 and discarding weekends from 23:00 GMT on Friday to 22:55 GMT on Sunday.

7 While the assumption that the foreign intraday interest rate is known or remains constant may sound contradictory, our focus here is to demonstrate that our methodology can be used to adjust short tenor interest rates for the local rate in real-time and in response to flash crashes. If all intraday interest rates are unknown, a more complex setting involving multiple currencies is needed to simultaneously estimate all parity relationships. This is beyond the scope of this paper and will be left for future research.

8 More recently, Feng, Song, and Wirjanto (2015) also estimated a time-deformed model for IBM stock returns with stochastic volatility using the method of simulated moments(MSM). Their choice of MSM is motivated by the analytically intractable likelihood function. We decided against this estimation method after having difficulty with optimising globally over all parameters when the sample consists of an extremely large amount of data. We also find the model to be very sensitive to the starting values used.

9 Easley and O'Hara (1992) argue that news arrival generates very frequent transactions with very short durations. In contrast, large duration should have lower volatility. Manganelli (2005) finds empirically that, for heavily traded stocks, volatility has a significant and negative impact on duration; low durations follow large volatilities. However, in an order-driven (instead of pricing-driven) market, a higher volatility should lead to a higher duration as traders are discouraged to trade immediately due to higher cost of liquidity consumption and higher benefit of liquidity provision.

10 The choice of using 1000 in-sample observations for estimations is arbitrary and constitutes for our dataset of the last 2-3 hours observations. Shortly after the crash on 15 Jan at 10a.m., the last 1000 observations consists of the last 1.5 hours of observations. One could also use for example all observations in the last hour, etc. Further fine-tuning for optimal in- and out-of-sample sizes could be made but is out-of-scope of this paper.

11 http://www.olsendata.com/

12 Feng, Song, and Wirjanto (2015) also use this method to deal with multiple observations within a second. Another method is to use volume weighted averages within the same second (see for example, Engle and Russell 1998).

13 We also omit data from 15th and 16th of January when estimating the diurnal factor due to the flash event on 15th January 2015.

14 We tried adding an indicator variable $I_k$ to Equation (8(8) $r_k/\sqrt{d_k}={\rho }_2{r}_{k-1}/\sqrt{d_{k-1}}+e_k+{\varphi }_2{e}_{k-1}+{\kappa }_2{d}_k.$(8) ) or (10(10) ${\sigma }_k^2={\omega }_2+{\alpha }_2{e}_{k-1}^2+{\beta }_2{\sigma }_{k-1}^2+{\gamma }_2{d}_k^{-1}$(10) ) during the flash crash that takes a value of 1 for a structural break during or after a flash event and zero otherwise. This however did not alleviate the problem of explosive GARCH estimates.

15 Overnight rates used are obtained from Bloomberg.

16 Effects of the crash are removed from the risk premium estimates because this effect should be captured in the interest rates. In our framework here, interest rates of different tenors are the tools for combating the swings in exchange rate.

17 We thank a referee for this suggestion.

Additional information

Funding

The funding from Manchester University FinTech Initiative 2017 is gratefully acknowledged.