Early-warning signal of the recent credit crisis in financial time series

Transcription

1 Early-warning signal of the recent credit crisis in financial time series Drona Kandhai Head of FO Quantitative Analytics - ING Bank University of Amsterdam - Assistant Professor (0.2 fte) Rick Quax and P. M. A. Sloot

2 Interest Rate Derivatives Interest rate derivatives (IRD) Are based on LIBOR rates LIBOR rate is the interest rate at which banks are willing to borrow and lend from and to each other for a certain time window Daily settled by a panel of banks recently disputed a lot! Why are interest derivatives so important? All financial instutions (banks, insurance companies and pension funds) typically enter into interest rate derivates to hedge their interest rate risk LIBOR rates control funding rates for financial institutions

3 Plain Vanilla Interest Rate Derivatives Interest Rate Swaps Consists of a fixed and a floating leg for a certain maturities Fixed leg pays fixed interest rate (K) Floating cash flows are based on 3M or 6M LIBOR Both legs will typically have different coupon frequencies Liquid Market in many currencies In EUR swaps are traded up to even 50 years Markets quotes the fixed rates that makes the swap worth par at inception Products can be priced on a curve No need for a sophisticated model Today s reality a bit more tricky 3

4 Plain Vanilla Interest Rate Derivatives Interest Rate Swaps Market Quotes Largest Derivatives Market MaturityDate Swap Rate 1Y 1,95 2Y 2,41 3Y 2,72 4Y 2,95 5Y 3,14 6Y 3,29 7Y 3,41 8Y 3,52 9Y 3,61 10Y 3,69 11Y 3,76 12Y 3,83 13Y 3,89 14Y 3,94 15Y 3,98 20Y 4,06 30Y 3,92 40Y 3,79 50Y 3,74 4

5 Plain Vanilla Interest Rate Derivatives 5

6 Interest Rate Risk of Financial Institutions lend 200,000 at 5%, fixed for 10 years Risk profile borrow 350,000 at 3%, fixed daily lend 150,000 at 4%, fixed yearly Hedge risk swap

7 Interest rate swap zero risk #1 #2 swap swap contract

8 IRS market propagating failure Banks, pension funds, companies, etc. have swap contracts amongst each other swap Each player has multiple swaps at a given time, with varying Amount of money involved Duration Frequency dynamical weighted network

9 Can we infer instability from swap market? Solution: use public data: daily IRS rates swap USD Swap rates, daily average for maturities 1, 2,, 15, 30 Data s time span: 12 years Both USD and EUR market

10 Can we infer instability from swap market? Postulate I Inferring instability from the data and the more swaps are traded A B long-term C short-term the stronger this cross-maturity correlation short-term long-term

11 Can we infer instability from swap market? Postulate II swap contract X years swap contract + X-1 years swap contract 1 years and so on + forward fee for 1-IRS being X-1 years into future swap contract X-1 years swap contract + X-2 years + swap contract 1 years similar fee

12 Can we infer instability from swap market? Sum of Postulate I and II The rates (%) of the IRS of different maturities form a 1D system: 1-year IRS rate (%) 1-year IRS rate (%) 1-year IRS rate (%) causal relation The more dense is the swap network the stronger the causal relations between the maturities the farther a perturbation can travel through this 1D-system of rates 1-year IRS rate (%) 1-year IRS rate (%) 1-year IRS rate (%)

13 Methods We calculate the distance that fluctuations from the 1-year IRS rates travel through the higher maturities Correlation function: mutual information (Shannon) Becomes information dissipation length (IDL) Benefit: MI also accounts for non-linear relationships Benefit: IDL filters out common external correlations We do this at every time t Higher IDL more stress in risk-trading market (?)

14 Methods: estimating mutual information rate: 1 year t time Info(t, 1 x) MI( 3.34, 4.02 ) rate: x years t time adaptive binning method

15 Results

16 Results: well-known indicators fail consequence, not cause

17 Conclusion 1. Banks trade risks with each other (IRS) 2. This seems to forms a dynamical weighted network of swaps 3. The system is unobservable, but we try to infer this instability from the public data: daily IRS rates 4. Reasoning: denser IRS network higher instability higher IDL 5. IDL indicator forms an early-warning signal More details see: Quax, R., Kandhai, D. & Sloot, P.M.A., Information dissipation as an early-warning signal for the Lehman Brothers collapse in financial time series. Scientific Reports 3, 1898 (2013) Disclaimer: The opinions expressed in this work are solely those of the authors and do not represent in any way those of their current and past employers