Mathematics Careers at ANZ

Transcription

1 Presenaion Overview Mahemaics Careers a ANZ A Career Profile Mahemaics in Risk Mahemaics in he Invesmen Bank The Ideal Graduae Miscellaneous Auhor Dr Jaime Bulbeck, Head Quaniaive Services Marke Risk ANZ Marke Risk Dae May, 006 Educaion B.E. (Aero) (Hons) Universiy of Sydney 987 PhD. (Mech. Eng.) Universiy of Melbourne 998 Thesis An Invesigaion of he Invarians of he Velociy Gradien Tensor in Transiioning and Turbulen Fluid Flow Grad. Dip. Applied Finance and Invesmen, Securiies Insiue of Ausralia 990 Chance and Opions Pricing, Mahemaics of Opions Pricing (3 rd /4 h year undergrad mahs courses, Melbourne, Monash) Mahemaics Skill Se -> Calculus, PDEs/ODEs, compuaional mehods, programming (C/Forran), mahemaical modelling Experience Defence Science and Technology Organisiion Engineer Advanced Engineering Laboraories, Aeronauical Research Laboraories, Salisbury S.A. and Fishermen s Bend, VIC Research Scienis Aeronauical and Mariime Research Laboraories Performing Applied Aerodynamic Analysis and Compuaional Fluid Dynamics in suppor of he Ausralian Defence Force s Air Operaions.

2 M! =.6, "=40 High incidence missile flows M local cross-flow separaion bow shocks leading-edge vorical flow Experience ANZ Marke Risk Quaniaive Analys 00- Performing quaniaive financial analysis in suppor of ANZ s Invesmen ANZ Household Name Top 5 Ausralian Company Asses ~AUD$300bn Worh ~AUD$40bn ANZ H06 $.73bn Insiuional H06 $486m Group Risk Insiuional Risk Banking operaions ~ employees Markes H06 $338m Marke Risk

3 Financial Risk Managemen Marke Risk Credi Risk Operaional Risk Financial Risk Managemen Marke Risk Losses on holdings of marke-valued insrumens due o movemens in marke raes Trading Book Foreign Exchange, Ineres Raes, Commodiies, Credi, Energy, Power ec. Boh fundamenal and derivaive conracs in all markes V( he value of all our fundamenal and derivaive conracs a ime P&L, AUD Millions $8 $6 $4 $ $0 -$4 -$6 Hisorical Simulaion VaR, 500 Hypoheical P&Ls Porfolio of 7 USD, JPY and XAU FX Opions M & # L( ; ) $ ( ) ( ( ) ( ) )! i = ( V j r + r ' $ i r i' ! j= % daily rae change " i =,..,500, M = $ Day index a which rae change was applied Probabiliy Financial Risk Managemen Loss Disribuion Marke Risk analysis of a porfolio of derivaives F( x) = P( L( ; < x) i =,..,500 i Hisorical Simulaion P&L disribuion and -day VaR (97.5 percenile larges loss), AUD$.6m ($8.00) ($6.00) ($4.00) ($.00) $0.00 $.00 $4.00 $6.00 $8.00 Millions Wha s he Value-a- Risk (ail measure)? Limis managemen Capial P&L, AUD$, millions P&L Disribuion VaR

4 Financial Risk Managemen Financial Risk Managemen Marke Risk Losses on holdings of marke-valued insrumens due o movemens in marke raes Trading Book Foreign Exchange, Ineres Raes, Commodiies, Credi, Energy, Power ec. Credi Risk Loss due o defaul of a counerpary o whom money has been len Banking Book Commerical+Reail Banking Home loans, credi cards, loan faciliies, line-of-credi ec Loss Densiy Credi Risk analysis of a porfolio of loans p(loss) % 0% 8% 6% 4% % loss densiy, simple binomial disribuion 00 loans, $m each, LGD=00%, year P d =0% 0% loss, AUD$millions & n# l p( l) = $! p q % l " n = 00 p = 0. q = 0.8 n' l Wha s he expeced loss? Pricing Wha s he unexpeced loss? Capial Derivaives he Sell Side and he Buy Side primarily Sell-side bank will package up producs conaining derivaives for cliens o buy, wheher for risk managemen or invesmen purposes. Asse managemen Buy-side asse managers will make invesmens involving derivaives, aking a view on marke direcion Derivaives Pricing and Risk Managemen No Arbirage Pricing Theory (Black/Scholes/Meron) can consruc a self-financing porfolio o replicae he derivaive using a predicable rading sraegy Valuaion is risk-neural he sell-side is agnosic o marke direcion or risk-neural. The iniial value of he self-financing porfolio is he same regardless of where he marke moves Sell-side will make is money by selling a derivaive for more han he value of he replicaing porfolio goal is RISK-FREE PROFITS Heavy Quan work involved in consrucion of he underlying rae models and derivaive pricing models, consrucion of he replicaing porfolios, measuremen of residual risks difficul and lucraive

5 Derivaives Pricing and Risk Managemen e.g. Black-Scholes underlying SDE (Geomeric Brownian Moion) for X dx = µ X d +! X db Le g(x T ) be he price of a derivaive a mauriy =T. Applicaion of Pricing Theory and use of he Feymac-Kac formula gives he PDE for he value of he derivaive! f ( x, + "! wih f(x,t)=g(x) and r equal o he risk-free ineres rae. If he derivaive is a call opion, g(x)=(x-k)+ and he soluion o his equaion is he classic Black Scholes opion pricing formula ' S $ ln % r T K " + ( +! ) ( rt f ( S,0) = [ SN( d) ( Ke N( d (! T )], d & # =! T! f ( x,! f ( x, + r = rf ( x,! x! x Derivaives Pricing and Risk Managemen Example Gold-Linked Noe Invesmen bank may manufacure a fixed income noe for an invesor linked o he price of Gold: Noe deails: y mauriy, USD$0m, offered Dec04 Coupon & principal paid a expiry Coupon 4% if gold says beween USD /oz during 05 oherwise % Suiable for a wholesale invesor keen o ake a view on he Gold Price during 05. Replicaed using a combinaion of a zero coupon bond and a double-no ouch gold opion, priced using Black/Scholes wih volailiy smile correcions in effec, he invesor has sold he gold opion for less han he invesmen bank can buy he fundamenal componens Proprieary Trading Buy-Side of invesmen banking Uses saisical analysis o idenify rading opporuniies Quan Groups a ANZ Markes ~ 8 Marke Risk ~ 4 Credi Risk ~ 8 Oher Businesses ~ 0 All up approx 30

6 The Ideal Quan The Ideal Quan Educaion PhD in a numerae discipline Mahs, Physics, Engineering, Compuaional Finance Financial Educaion (no essenial) Financial Mahemaics subjecs Chance and Opions Pricing, Mahemaics of Opions Pricing basic for Quans Securiies Insiue basic Maser of Applied Finance Macquarie Universiy advanced Maser of Quaniaive Finance - UTS MBA very advanced Skills Mahs Sochasic Calculus, Maringales, Theory of Opions Pricing, Change of Measure, PDEs, Mone-Carlo simulaion ec, Probabiliy heory, Numerical Mehods Programming Skills C/C++, VBA, Daabases (SQL) preferred Ho Topics BGM ineres rae model (erm srucure), Srucured Credi (synheic CDOs, CDO opions, CDO ), Elecriciy Risk Ho Topics Copulas, Fa-ailed dependency srucures, EVT, mulivariae disribuions, convergence of credi & marke risk, holisic capial allocaion The Ideal Quan Some Resources Trais Abiliy o communicae o echnical and non-echnical personnel Analyical abiliy Fron Office Abiliy o work under pressure Abiliy o hink under pressure Abiliy no o ge oo sressed under pressure Jobs Boards (by no means a complee lis Ausralia Bank sies use keywork Quan hp:// Inernaional hp://

7 Some Resources Some Books (by no means a complee lis Finance Texbooks John Hull, Opions, Fuures and Oher Derivaives Baxer and Rennie, Financial Calculus Brigo and Mercurio, Ineres Rae Models Theory and Pracice Some Resources ANZ Conacs ANZ Careers hp:// Graduae program hp:// Good Reads abou Wall Sree Life Michael Lewis, Liars Poker Frank Parnoy, FIASCO Blood in he Waer on Wall Sree