Quantitative methods in risk management. Introduction part 2

Transcription

1 Quaniaive mehods in risk managemen Inroducion par 2

2 Risk idenificaion LP purchased ŽR bond wih a fixed coupon of 4% and mauriy 5 years. This invesmen has been financed by reail erm deposis wih remaining average mauriy 9 monhs. Idenify he risk facors in his ransacion! Possible risk facors: Increase in long-erm ineres raes (a negaive revaluaion of bond) The increase in shor-erm ineres raes (higher coss o recover deposis) The increase in ŽR credi spread (financial difficulies, repuaional risk) The impac of sysemic risk - he economic crisis would cause a significan drop in he ransporaion secor Loss of repuaion, ŽR credi raing downgrading ignifican early wihdrawal of deposis (funding liquidiy risk) - when he marke is liquid enough, his should no cause any loss excep a possible disrupion in bank's sraegy Illiquid marke (bank needs o sell a bond, bu here is no buyer for i) ŽR will be unable o pay is obligaions once hey are due (credi risk)

3 Risk idenificaion VÚB eners ino a forward conrac wih Commerzbank relaed oa purchase of Facebook shares wih a mauriy of one year [Valuaion funcion: F = e r(t ) ] Possible risk facors: Facebook shares change in prices due o changes in heir financial siuaion or perceived marke Adverse changes in he Facebook share price due o problems in he IT indusry Adverse changes in he Facebook share price due o he urmoil in he sock marke as a whole Changes in ineres raes The increase in credi spread of Commerzbank (if he value of he forward) The growh in a misrus beween banks generally Commerzbank s defaul In case of a fuure (i.e. forward ransacion wih a cenra clearing counerpary): VÚB downgrade could caused an addiional margin call

4 Risk idenificaion Differen conracuial clauses makes a risk managemen significanly more challenging: Possibiliy of an early repaymen Callable bonds he issuer can require an early repaymen Converible bonds Embedded derivaives Example Hammurabi s code, Babylon, abou 1772 BC Covenans Decrease of real esae prices banks can ask for addiional collaeral ubordinariy

5 Inerlinkages beween risks A sory of sorrow (imaginary) Managemen decides o implemen a new (fauly) informaion sysem, inroducing he possibiliy of circumvening dealers limis (operaional risk) Due o an error, a dealer eners ino a significan posiion in Poruguese bonds (operaional risk) A large increase in credi spreads on Poruguese bonds causes significan loss (marke risk - specific ineres rae risk) The bank ries o close he posiion, bu he marke is illiquid (marke liquidiy risk) The name of he bank and he amouns losses leaks o public, causing a repuaional damage (repuaional risk) Deposi wihdrawals rise significanly, he bank has a shorage of liquid asses (liquidiy risk) As a resul of hese significan addiional losses, he bank may become insolven and subsequenly becomes unable o pay is conracual obligaions (credi risk o oher marke paricipans)

6 Risk measuremen ize of posiions / exposures + risk weighs E.g. FX risk posiions in individual currencies ensiiviy analysis Bonds: duraion + convexiy Opions: greeks Gap analysis Ineres rae risk and liquidiy risk P V * 2 ( D P) y ( CP) y 2 cenarion analysis (e.g. liquidiy coverage raio), sress esing aisical models (Value-a-Risk, model of core deposis)

7 Problemaic assumpions The disribuion of risk facors is far from a normal one Fa ails (lepokurosis), assymery (skewness) consequence: volailiy smile Markes are no complee Consequence: corruped hedging sraegies Exisence of a risk-free rae? Counerpary credi risk

8 Risk facors disribuion randard assumpion: Equiy reurns follow normal disribuion One has: ln(1 + x) x, hence Example: &P 500 reurns, sample period: ln 1 ln

9 Risk facors disribuion Equiy reurns have fa ails More appropriae model: -disribuion wih 3 degrees of freedom

10 Counerpary risk Characerisics: mainly associaed wih over-he-couner ransacions consequence: nonlinear pricing funcion in inherenly linear" insrumens example: he equiy forward, wih boh paries having differen defaul probabiliies (forward on Facebook equiies beween Deusche bank (DE) and Piraeus bank (GR)) Presence of a sysemic elemen - single insiuion as a counerpary in a large number of ransacions (problem wih hedging), e.g. Lehman Brohers

11 Counerpary risk - consequences Measure of counerpary risk on inerbank marke: OI spread OI spread = difference beween 3-monh EURIBOR and Overnigh Indexed wap (OI) / EONIA Rae on 3-monhs hp://

12 Counerpary risk - consequences In case of non-exisen counerpary risk, hese ineres rae should be in heory perfecly idenical ource: Michael Nealon, Pricing IR Derivaives Pos-Credi Crunch, FMV Talk

13 Counerpary risk - consequences Hedging agains counerpary risk is difficul ysem componen (concenraion of ransacions in a single counerpary) For example, radiional hedging bonds wih swaps may sill leave large residual risk relaed o changes in spreads uncovered When pricing a paricular insrumen, he mos appropriae yield curve should be seleced in accordance wih is credi risk characerisics OI / secured inerbank deposis / swaps / inerbank deposis / governmen bonds / bonds wih a paricular raing The liquidiy problem becomes more pronounced liquidiy of differen insrumens (bid / ask spread) varies for differen mauriies References: Mercurio, F. (2009): Ineres Raes and The Credi Crunch: New Formulas and Marke Models Amerano, F, M. Bianchei, M. (2009): Boosrapping he illiquidiy: Muliple yield curves consrucion for marke coheren forward raes esimaion (draf: hp://

14 ummary Deep undersanding of all assumpions, model s weaknesses and limiaion is crucial! By definiion, each model is a simplificaion of he realiy Comprehensive mapping posiions on risk facors is challenging The number of risk facors may be sizeable linkages beween risk facors are complex Counerpary risk should no be negleced The problem wih risk hedging Fundamenal equivalence beween yields does no longer apply Applicaion of sophisicaed quaniaive echniques is essenial, bu hey need o be clearly undersood