The notional principal of global interest rate swap markets annually exceeds US$300 trillion, and their value exceeds US$10 trillion. Since 2008, in this market we observe the phenomenon of significant "basis spreads" added to one side of single-currency floating-for-floating swaps, as well as spreads between the term structures of interest rates implied by standard interest rate swaps, overnight index swaps and basis swaps. Under classical textbook theory, these spreads should not exist, and the debate on how to explain these spreads in a consistent manner continues among academics and practitioners alike. We take the view that the persistence of these spreads indicates that the market is pricing a risk that is not captured by existing standard models. These risks driving the spreads are closely related to the risks affecting the funding of banks participating in benchmark interest rate panels (such as LIBOR or BBSW), specifically “roll-over” risk. This is the risk incurred when borrowing at a shorter frequency and lending at a longer frequency, thus relying on being able to more frequently refinance one's borrowing. Our approach is to model this roll-over risk in such a way that it comprises of funding liquidity and credit risk components. The significance of this modeling approach is that we are able to extract current market information about roll-over risk from liquidly traded financial products, by calibrating the model (simultaneously and in a consistent manner) to market data for standard interest rate swaps, overnight index swaps, basis swaps and interest rate cap contracts. (based on joint work with Martino Grasselli and Erik Schlogl).

1. UTS CRICOS PROVIDER CODE:00099F
A CONSISTENT STOCHASTIC MODEL OF THE TERM
STRUCTURE
OF INTEREST RATES FOR MULTIPLE TENORS
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Joint work with Martino Grasselli and Erik Schlӧgl
Mesias Alfeus
November 14, 2017

2. AFTERMATH OF THE GFC
 The 2007 Global Financial Crisis (GFC) has highlighted new market
risks and these are now priced in the market.
 In particular, funding liquidity and credit downgrade risk has led to
spread between discount curves for different payment frequencies.
 This contradicts the classic textbook theory.
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3. MONEY MARKET INSTRUMENTS
 LIBOR or the London Interbank Offered rate is a rate at which AA rated
banks can obtain unsecured fund from each other; a measure of funding
costs at every point in time.
 A total of about $150 trillion of financial products are indexed to the LIBOR.
 OIS is an interest rate swap in which the floating leg is linked to an index of
daily overnight rates.
 A tenor swap exchanges two floating rate payments of the same currency
based on different tenor indices.
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4. 3-MONTH LIBOR–OIS
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 “LIBOR—OIS remains a barometer of fears of bank insolvency”- Alan Greenspan.

5. ROLL—OVER RISK
Example
Suppose a LIBOR panel bank want to borrow in the interbank market for 1
month. Then it has two options. On the one hand it can borrow for one month
at prevailing 1-month LIBOR rate. On the other hand, it can borrow overnight
at the Federal funds rate and keep rolling it over daily for the next 30 days.
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 What is then a difference between the two borrowing strategies?

6. OUR APPROACH
 The objective of the research paper is to construct an explicit model for
roll-over risk.
 We take the view that basis spread is due to a new perception by the
market of risks involved in the execution of textbook arbitrage strategies.
 We decompose roll-over risk into downgrade risk and funding liquidity risk
components as the main driver of basis spreads.
 This gives a better analysis of the forward-looking information content
about roll-over risks in prices of liquidly traded financial instruments
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7. APPLICATION
 The model could be useful to policymakers e.g. introduction of lending
facilities such as TAF and can guide the monetary easing that the Federal
Reserve has implemented exactly 10 years ago.
 The model is consistent with the interest rate swap market practice for
pricing, hedging and risk management since the onset of the GFC.
 Our modelling approach provides an important insight on risk-neutral
expectation about roll-over risk from liquidly traded market data.
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8. DATA
 The set-up and implementation of the model is currency independent.
 We collect USD data only. However, the discussion applies to other
currencies.
 We collect USD OIS rates, IRS, and BS available from Bloomberg for
maturities up to 10 years.
 The sample period starts from 01/01/2013-12/06/2017.
 We use the standard bootstrap with interpolation method to construct the
USD OIS discount factors.
 The model parameters are calibrated to quoted market data.
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9. QUALITY OF FIT ON 01/01/2013
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(a) 1-factor model - OIS (b) 3-factor model - OIS
(c) 1-factor model - Basis (d) 3-factor model - Basis

10. CONCLUSION
 We focused on a high-dimensional modelling problem existing in the
single-currency tenor swap market.
 Calibrated the model using adaptive simulated annealing.
 Could use the model for pricing relative to market of bespoke tenor.
 Could extract risk–neutral expectations of roll–over risk from liquid market
prices.
 Further empirical study of roll–over risk dynamics is underway.

11. business.uts.edu.au