Financial derivative securities, such as options and futures, can be viewed as a form of insurance. These instruments are routinely used by large corporations to hedge currency fluctuations, uncertain energy costs and commodity price volatility.
Many financial contracts contain embedded options. As a result, individual investors are often unaware that they frequently buy and sell options. Some examples of these embedded options include mortgage prepayment privileges, equity linked GICs, and fixed rate natural gas home heating contracts.
A derivative contract is based on an underlying asset. The standard model for the underlying asset price movement assumes that prices evolve according to a random walk with a drift. It is possible for an option seller to set up a hedging portfolio, which is then dynamically rebalanced in response to changes in the underlying asset price. Then, regardless of the random movement of the asset price, the seller of the option is able to pay out the value of this contract at expiry.
However, there is strong evidence that the normal market behavior assumed by the standard model is punctuated by occasional large jumps or drops in prices (e.g. subprime mortgages). These jump diffusion models present difficult computational challenges for pricing and hedging embedded options. Jump diffusion is an effective way of modelling financial "Black Swans."
Peter's current research is focused on developing algorithms which are used to price and hedge options embedded in pension plan guarantees, convertible bonds, and employee stock options. He has also developed methods for determining optimal hedging strategies for markets which can be modeled by jump diffusion processes.
These sorts of problems all come under the framework of optimal stochastic control. Peter has also developed algorithms for optimal scheduling of trades and and optimal long term asset allocation.
Peter was the Editor-in-Chief of the Journal of Computational Finance during 2008-2013, and continues as a member of the Editorial Board of JCF and Applied Mathematical Finance.
Degrees and awards
BSc, PHD (Western), MSc (Australia National University)
Cheriton Fellow (2010-2013), Blundon Memorial Lecturer (2010); IAM-MITACS-PIMS Distinguished Lecturer (2006); Faculty of Mathematics Fellow, University of Waterloo (2003-2006)
Industrial and sabbatical experience
After graduating in 1979, Peter was a Senior Simulation Scientist with the Computer Modeling Group (Calgary), where he developed software for modeling petroleum reservoirs. After leaving CMG, he was the founding President of Dynamic Reservoir Systems (DRS). DRS was eventually purchased by Duke Engineering, and continues to market the original DRS software.
Since joining the University of Waterloo, Peter has carried out research related consulting for such organizations as TransCanada Pipelines (pipeline simulation), Boeing Corporation (sparse matrix solution methods), the Electric Power Research Institute (high level radioactive waste disposal) and Los Alamos National Laboratory (simulation of pollutant transport).
More recently, Peter has collaborated with Credit Suisse (optimal portfolio allocation), Tata Consulting Services (optimal stochastic control), Morgan Stanley (optimal trade execution), Sun Life Financial (hedging of pension plan guarantees), RBC Financial Group (valuation of demand deposits), TG Information Network (exotic option pricing), ITO33 (convertible bond pricing), and Bell Mobility (optimal timing of capacity upgrades).
P.A. Forsyth and K.R. Vetzal, An optimal stochastic control framework for determining the cost of hedging of variable annuities, Journal of Economic Dynamics and Control, 44 (2014) 29-53.
S.T. Tse, P.A. Forsyth, Y. Li, Preservation of scalarization optimal points in the embedding technique for continuous time mean variance optimization," SIAM Journal on Control and Optimization 52 (2014) 1527-1546.
D.M. Dang, P.A. Forsyth, Continuous time mean-variance optimal portfolio allocation under jump diffusion: a numerical impulse control approach," Numerical Methods for Partial Differential Equations 30 (2014) 664-698.
S.T. Tse, P.A. Forsyth, J.S. Kennedy, H. Windcliff, Comparison between the mean variance optimal and mean quadratic variation optimal trading strategies," Applied Mathematical Finance 20 (2013) 415-449.
Y. Huang, P.A. Forsyth, G. Labahn, Combined fixed point and policy iteration for HJB equations in finance," SIAM Journal on Numerical Analysis 50 (2012) 1849-1860.
Y. Huang, P.A. Forsyth, G. Labahn, Iterative methods for the solution of a singular control formulation of a GMWB pricing problem," Numerische Mathematik 122 (2012) 133-167.