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After graduating in 1979, Peter was a Senior Simulation Scientist at the Computer Modelling Group (CMG) in Calgary, where he developed petroleum reservoir simulation software. After leaving CMG, Peter was the founding President of Dynamic Reservoir Systems (DRS), also in Calgary. DRS produced reservoir simulation software for PC's, using the then enormous amount of memory available (640K). DRS had three employees: a president and two vice-presidents. After selling out his shares in DRS (now owned by Duke ) in 1987, Peter joined the University of Waterloo, where he is now a Professor in the Cheriton School of Computer Science. Peter's current research focuses on Computational Finance. He is a member of the Editorial Board of Applied Mathematical Finance and is the Editor-in-chief of the Journal of Computational Finance.
In recent years, Peter has also carried out research related consulting for such organizations as: SunLife of Canada, NOVA, the Electric Power Research Institute, Smithville Bedrock Remediation Corporation, Los Alamos National Laboratory, Oak Ridge National Laboratory, and HydroGeoLogic.
While at Waterloo, Peter has held such administrative positions as: Associate Chair Graduate Studies (1991-1993), Director of the Institute for Computer Research (1995-1998), Associate (Vice) Director of the Cheriton School of Computer Science (2002-2005), and Scientific Director of the Institute for Quantitative Finance and Insurance (2006-2008).
Peter left CMG (the Computer Modelling Group) in 1985. About ten years ago, shares of CMG were trading at about $0.25. Look at the CMG share price. Peter thinks about this everyday.
Want to know why the banks and insurance companies are having problems? What's wrong with the models used by banks? CS774 will discuss the numerical algorithms used by financial institutions to price and hedge risk. We will be looking at some interesting issues which arise when taking into account realistic market effects (liquidity, price impact, jump processes). No background in finance is assumed. Overview slides
Institute studies algorithms for insurance An interview for the KW Record.
Hedging your bets. An interview for the Mathematics Faculty Annual Report.
For a brief overview, click here.
If that's got you interested, here is a 16 page pdf file with more information that you can download. An introduction to Option Pricing.
For even more information, you can read the 80 page pdf file An introduction to Computational Finance without Agonizing Pain.
A short description of the Computational Finance Project.
Banks, Bonuses and Busts (pdf poster) A jaundiced view of the financial sector.
Hedging Your Bets (pdf poster).
Optimal Investment in a Pension Plan (pdf poster).
Optimal strategy: Guaranteed Minimum Withdrawal Benefit (GMWB) This pdf figure shows the optimal strategy for the holder of a GMWB guarantee. This is an example solution of an optimal stochastic control problem.
"The moral swamp that is retail brokerage corrodes the rest of the financial industry, and much of corporate America with it." William Bernstein, "Corporate Finance and Original Sin," Financial Analysts Journal, Volume 62:3 (2006) pages 20-23.
"Even if top management wants to maximize long-term bank value, it may find it difficult to create incentives and control systems that steer subordinates in this direction. Given the competition for talent, traders have to be paid generously based on performance. But, many of the compensation schemes paid for short term risk-adjusted performance. This gave traders an incentive to take risks that were not recognized by the system, so they could generate income that appeared to stem from their superior abilities, even though it was in fact only a market-risk premium. The classic case of such behavior is to write insurance on infrequent events such as defaults, taking on what is termed tail risk. If a trader is allowed to boost her bonus by treating the entire insurance premium as income, instead of setting aside a significant fraction as a reserve for an eventual payout, she will have an excessive incentive to engage in this sort of trade." The credit crisis: conjectures about causes and remedies, D. Diamond, R. Rajan, Chicago School of Business
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Variable Annuities : A great way to book short term profits (and get paid large bonuses) and let your shareholders take the losses.
A quote from The Economist, "Inside the Banks", January 24, 2009. An imaginary conversation between the risk officer and senior management.
A quote from The Financial Analysts Journal, "A Simple Theory of the Financial Crisis; or Why Fischer Black Still Matters", Vol 65(3) (2009) 17-20. A comment on the compensation system.
Don't blame the quants: Steve Shreve
The Credit Crunch of 2007: What Went Wrong? Why? What Lessons Can Be Learned: John Hull
More thoughts on the credit crisis: Chicago Graduate School of Business
Comments on Geithner's plan and alternatives Luigi Zingales, Chicago
Optimal trade execution: a mean-quadratic-variation approach
November 1, 2009)Continuous time mean variance asset allocation: a time consistent strategy.
(October 23, 2009)Analysis of a Penalty Method for Pricing a Guaranteed Minimum Withdrawal Benefit (GMWB)
(May 9, 2009)Numerical Solution of the Hamilton-Jacobi-Bellman Formulation for Continuous Time Mean Variance Asset Allocation
(to appear, Journal on Economic Dynamics and Control)A Hamilton Jacobi Bellman Approach to Optimal Trade Execution
(Revised, June 24, 2009)Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals
(Accepted in Applied Mathematical Finance)Pricing Hydroelectric Power Plants with/without Operational Restrictions: a Stochastic Control Approach
(Book Chapter: Nonlinear Models in Mathematical Finance, Edited by M. Ehrhardt, Nova Science Publishers, 2008, pages 253-281)The effect of modelling parameters on the value of GMWB guarantees
(Journal Version: Insurance: Mathematics and Economics 43 (2008) 165-173.)Implications of a regime switching model on natural gas storage valuation and optimal operation.
(Accepted in Quantitative Finance)A numerical scheme for the impulse control formulation for pricing variable annuities with a Guaranteed Minimum Withdrawal Benefit (GMWB)
(Journal Version: Numerische Mathematik 109 (2008) 535-569.)Maximal use of central differencing for Hamilton-Jacobi-Bellman PDEs in Finance
(Journal version: SIAM Journal on Numerical Analysis 46 (2008) 1580-1601)A semi-Lagrangian approach for natural gas storage valuation and optimal operation
(Journal version: SIAM J. Scientific Computing 30 (2007) 339-368.)Robust numerical valuation of European and American options under the CGMY process
(Journal Version: Journal of Computational Finance 10:4 (Summer:2007) 31-69.)Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance
(Journal Version: Journal of Computational Finance 11:2 (2007/2008: Winter) 1-44.)Infinite reload options: pricing and analysis
(Journal Version: J. Computational Applied Mathematics 222 (2008) 54-81.)Dynamic hedging under jump diffusion with transaction costs
(Journal Version: Operations Research 57 (2009) 541-559.)Valuing guarantees on spending funded by endowments
(March 15, 2006)Numerical solution of two asset jump diffusion models for option valuation
(Journal Version: Applied Numerical Mathematics 58 (2008) 743-782)Hedging with a correlated asset: solution of a nonlinear pricing PDE
(Journal Version: Journal of Computational and Applied Mathematics 200 (2007) 86-115)Calibration and hedging under jump diffusion
(Journal Version: Review of Derivatives Research 9 (2006) 1-35)A semi-Lagrangian approach for American Asian options under jump diffusion
(Journal Version: SIAM J. Sci. Comp. 27 (2005) 315-345)Numerical methods and volatility models for cliquet options
(Journal Version: Applied Mathematical Finance 13 (2006) 353-386)Pricing methods and hedging strategies for volatility derivatives
(Journal Version: Journal of Banking and Finance 30 (2006) 409-431)Convertible bonds with call notice periods
(IASTED conference on Financial Engineering and Applications, Banff, 2003)A penalty method for American options with jump diffusion processes
(Journal Version: Numerische Mathematik, 97:2 (2004) 321-352.)Robust numerical methods for contingent claims under jump diffusion processes
(Journal Version: IMA J. Num. Anal., 25 (2005) 87-112.)Wireless network capacity investment
(Journal version: European Journal of Operational Research 176 (2007) 584-609)Analysis of the stability of the linear boundary condition for the Black-Scholes equation
(Journal Version: J. Comp. Fin., 8:1 (Fall, 2004) 65-92)The valuation of convertible bonds with credit risk
(Journal Version: J. Derivatives, 11 (Fall, 2003) 9-29.)Hedging Segregated Fund Guarantees
(Book Chapter Version: in The Pension Challenge: Risk Transfers and Retirement Income Security, Edited by Olivia Mitchell and Kent Smetters, Oxford University Press (2003), pages 214-237.)Numerical convergence properties of option pricing PDEs with uncertain volatility
(Journal Version: IMA J. Num. Anal., 23 (2003) 241-267.)Understanding the behaviour and hedging of segregated funds offering the reset feature
(Journal Version: North Amer. Act. J., 6 (2002) 107-125.)Managing telecommunication networks under uncertainty
(Journal Version: IEEE Trans. Networks, 10 (2002) 579-588.)Stochastic Simulations For Problems in Finance with Optimal Decisions PDF version ( 2Meg ) PS version ( 700k)
(Book Chapter Version: Computational Methods in Decision-making, Economics and Finance, Edited by E. Kontoghiorches, B. Rustem, S. Siokos, Kluwer Series in Applied Optimization, Kluwer, Amsterdam (2002) pages 269-294.)Negative coefficients in two factor option pricing models
(Journal Version: J. Comp. Fin., 7:1 (Fall, 2003) 37-73 )Remedies for non-smooth payoffs in option pricing
(Journal Version: J. Comp. Fin., 6:4 (Summer, 2003) 25-40.)Quadratic convergence of a penalty method for valuing American options
(Journal Version: SIAM J. Sci. Comp., 23 (2002) 2095-2122.)A numerical PDE approach for pricing callable bonds
(Journal Version: Appl. Math. Fin., 8 (2001) 49-77.)Valuation of segregated funds: shout options with maturity extensions
(Journal Version: Insurance: Mathematics and Economics, 29 (2001) 1-21.)An object oriented framework for valuing shout options on high performance computer architectures.
(Journal Version: J. Econ. Dyn. Control, 27 (2003) 1133-1161.)Shout options: a framework for pricing contracts which can be modified by the investor
(Journal Version: J. Comp. Appl. Math., 134 (2001) 213-241.)A finite volume approach for contingent claims valuation
(Journal Version: IMA J. Num. Anal. 21 (2001) 703-731.)Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers.
(Journal Version: Appl. Num. Math. 36 (2001) 427-445.)Convergence of lattice and PDE methods for valuing path dependent options using interpolation.
(Journal Version: Review of Derivatives Research, 5 (2002) 273-314.)Discrete Asian barrier options
(Journal Version: J. Comp. Finance 3 (Fall, 1999) 41-68.)Discrete Parisian and delayed barrier options: A general numerical approach
(Journal Version: Adv. Futures Options Research 10 (1999) 1-16.)A finite element approach to the pricing of discrete lookbacks with stochastic volatility
(Journal Version: Appl. Math. Finance 6 (1999) 87-106.)
Undergraduate courses: introduction to scientific computing, numerical linear algebra, numeric computation for dynamical simulation, software system design and implementation. Graduate courses: numerical solution of partial differential equations, preconditioners for sparse matrices, numerical solution of nonlinear hyperbolic partial differential equations, computational finance.
I have a C++ version of the Watsit sparse matrix solver package (scaler only for now). The solver is based on a PCG-like method which uses an incomplete LU factorization preconditioner. Level or drop tolerance preconditioning can be specified. This package has been successfully tested on problems in CFD, 3-D linear elasticity, option pricing, semi-conductor device simulation, and multi-phase subsurface flow. You can download the pdf user manual.
I also have an older f77 version of the sparse solver, both block and scaler versions. This code has been licensed to many organizations, such as Lawrence Berkeley Laboratory, TRW, Westinghouse, AECL, Sandia National Laboratory, Philips Petroleum, and Los Alamos National Laboratory. You can download the postscript user manual.
You can download a pdf version of my full curriculum vitae.