A CONSISTENT STOCHASTIC MODEL OF THE ...

A CONSISTENT STOCHASTIC MODEL OF THE TERM STRUCTURE OF INTEREST RATES FOR MULTIPLE TENORS Joint work with Martino Grasselli and Erik Schlӧgl

Mesias Alfeus November 14, 2017 UTS CRICOS PROVIDER CODE: 00099F

business.uts.edu.au

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.

business.uts.edu.au

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.

business.uts.edu.au

3-MONTH LIBOR–OIS

 “LIBOR—OIS remains a barometer of fears of bank insolvency”- Alan Greenspan.

business.uts.edu.au

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.

 What is then a difference between the two borrowing strategies?

business.uts.edu.au

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

business.uts.edu.au

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.

business.uts.edu.au

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.

business.uts.edu.au

QUALITY OF FIT ON 01/01/2013

(a) 1-factor model - OIS

(b) 3-factor model - OIS

(d) 3-factor model - Basis (c) 1-factor model - Basis business.uts.edu.au

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.

business.uts.edu.au