## Biography

**Paul Wilmott** is a mathematician, author and financial consultant, specializing in derivatives, risk management and quantitative finance. He has worked with many leading US and European financial institutions.

Paul studied mathematics at St Catherine’s College, Oxford, where he also received his D.Phil. He founded the Diploma in Mathematical Finance at Oxford University and the journal *Applied Mathematical Finance*. He is the author of *Paul Wilmott Introduces Quantitative Finance* (Wiley 2007), *Paul Wilmott On Quantitative Finance* (Wiley 2006), *Frequently Asked Questions in Quantitative Finance* (Wiley 2009) and other financial textbooks. He has written over 100 research articles on finance and mathematics.

Paul Wilmott was a founding partner of the volatility arbitrage hedge fund Caissa Capital which managed $170million. His responsibilities included forecasting, derivatives pricing, and risk management.

Dr Wilmott is the proprietor of www.wilmott.com, the popular quantitative finance community website, the quant magazine *Wilmott* and is the creator of the Certificate in Quantitative Finance. He is the President of the CQF Institute.

Paul Wilmott was a professional juggler with the Dab Hands troupe, and has been an undercover investigator for Channel 4. Paul is a card-carrying member of the actors’ union Equity. He also has three half blues from Oxford University for Ballroom Dancing. He was the first man in the UK to get an online divorce.

## Blog

Paul’s blog can be found here

## Photo Gallery

A gallery of photos (showing a wide variety of hairstyles) can be found here

## Research interests

- Weaknesses of standard quantitative finance models: discrete hedging, transaction costs, incomplete markets, model error, etc.
- Model robustness: analysing models for sensitivity to assumptions
- Volatility: modelling volatility, testing standard and non-standard models
- Extreme markets: non-probabilistic approaches
- Exotic contracts: pricing and hedging, inherent but obscure risks
- Arbitrage: using classical tools in a non no-arbitrage framework, trading strategy optimization
- Risk management: robustness of risk assessment, minimization of reliance on unreliable data

## Publications

**Books**:

*Option Pricing: Mathematical Models and Computation*. (With J.N.Dewynne and S.D.Howison.) Oxford Financial Press (1993)

*Mathematics of Financial Derivatives: a Student Introduction*. (With J.N.Dewynne and S.D.Howison.) Cambridge University Press (1995)

*Mathematical Models in Finance*. (Ed. with S.D.Howison and F.P.Kelly.) Chapman and Hall (1995)

*Derivatives: the theory and practice of financial engineering*. John Wiley and Sons (1998)

*Paul Wilmott On Quantitative Finance*. John Wiley and Sons (2000)

*Paul Wilmott Introduces Quantitative Finance*. John Wiley and Sons (2001)

*New Directions in Mathematical Finance*. (Ed. with H.Rasmussen.) John Wiley and Sons (2001)

*Best of Wilmott 1*. (Ed.) John Wiley and Sons (2004)

*Exotic Option Pricing and Advanced Lévy Models*. (Ed. with W.Schoutens and A. Kyprianou) John Wiley and Sons (2005)

*Best of Wilmott 2*. (Ed.) John Wiley and Sons (2005)

*Frequently Asked Questions in Quantitative Finance. John Wiley and Sons (2006)*

*Paul Wilmott On Quantitative Finance, second edition*. John Wiley and Sons (2006)

*Paul Wilmott Introduces Quantitative Finance, second edition*. John Wiley and Sons (2007)

*Frequently Asked Questions in Quantitative Finance, second edition*. John Wiley and Sons (2009)

*The Money Formula*. (With David Orrell). John Wiley and Sons (2017)

*Machine Learning: An Applied Mathematics Introduction*. Panda Ohana Publishing (2019)

**Published Papers**:

- A note on the WKB method for difference equations. IMA J. Appl. Math. 34 295—302 (1985).

- On the distribution of impulses in inviscid, incompressible flow: the induced downwash on a rotating wing. Acta Mech. 61 129—137 (1986).

- The induced downwash and lift on a wing of high aspect ratio in unsteady motion. Aero. J. 90 63—72 (1986).

- Matching and singularity distributions in inviscid flow. (With J.R.Ockendon.) IMA J. Appl. Math. 37 199—211 (1986).

- A continuum theory for the mechanics of rock blasting. (With C.P.Please and A.A.Wheeler.) Math. Scientist 11 111—119 (1986).

- A mathematical model of cliff blasting. (With C.P.Please and A.A.Wheeler.) SIAM J. Appl. Math. 47 117—127 (1987).

- On the motion of a small two-dimensional body submerged beneath surface waves. J. Fluid Mech. 176 465—481 (1987).

- The deposition and resuspension of small radioactive particles in a recirculating flow in a reactor. (With C.P.Please.) Math. Engrg. Ind. 1 21—32 (1987).

- A continuum model for two-dimensional dislocation distributions. (With A.K.Head, S.D.Howison, J.R.Ockendon and J.B.Titchener.) Phil. Mag. A 55 617—629 (1987).

- Unsteady lifting line theory by the method of matched asymptotic expansions. J. Fluid Mech. 186 303—319 (1988).

- On the motion of a slender body submerged beneath surface waves. J. Ship Res. 32 208—219 (1988).

- Convective mixing in the mantle: the role of viscosity differences. (With D.A.Spence, J.R.Ockendon, D.L.Turcotte and L.H.Kellogg.) Geophys. J. 95 79—86 (1988).

- Rotation and deformation of a viscous inclusion in Stokes flow. (With D.A.Spence.) Proc. Roy. Soc. A 418 383—403 (1988).

- The stretching of a thin viscous inclusion and the drawing of glass sheets. Phys. Fluids A 1 1098—1103 (1989).

- On a mathematical model for glass fiber tapering. (With J.N.Dewynne and J.R.Ockendon.) SIAM J. Appl. Math. 49 983—990 (1989).

- The stretching of a slender, axisymmetric viscous inclusion. Part I – Asymptotic analysis. SIAM J. Appl. Math. 49 1608—1616 (1989).

- The stretching of a slender, axisymmetric viscous inclusion. Part II – Numerical analysis and results. (With A.D.Fitt.) SIAM J. Appl. Math. 49 1617—1634 (1989).

- The growth kinetics of ledged interphase boundaries: Transient motion; an analytical treatment. (With C.Atkinson.) Proc. Roy. Soc. A 426 377—389 (1989).

- Irregular morphologies in unstable Hele-Shaw free boundary problems. (With A.A.Lacey, S.D.Howison and J.R.Ockendon.) Q. Jl. Mech. Appl. Math. 43 387—405 (1990).

- Modelling separated flows. Proc. 4th Euro. Symp. on Maths. in Industry, 415—421 (1990).

- Models for high Reynolds number flow down a step. (With K.O’Malley, A.D.Fitt, T.V.Jones and J.R.Ockendon.) J. Fluid Mech 222 139—155 (1991).

- Multi-fibre extrusion: a nonlinear integral equation. Proc. 5th Euro. Conf. Math. in Ind. 393—396 (1991).

- Diffusion-controlled kink motion. (With C.Atkinson.) Metall. Trans. A 22 1219—1224 (1991).

- On the optimum hand speed for two-blade razor shaving. (With A.D.Fitt and A.A.Lacey.) Teach. Math. & Appl. 10 122—126 (1991).

- Formation of oscillation marks on continuously cast steel. (With J.R.King, A.A.Lacey and C.P.Please.) Proc. 5th Euro. Conf. Math. in Ind. 267—270 (1991).

- The manufacture of optical fibres. (With J.N.Dewynne and J.R.Ockendon.) Proc. 6th Euro. Conf. Math. in Ind. 309—312 (1992).

- A cellular automaton model for the segregation of a two species granular flow. (With A.D.Fitt.) Phys. Rev. A 45 2383—2388 (1992).

- Multiple ledge and kink interactions. (With C.Atkinson.) Proc. Roy. Soc. A 437 451—460 (1992).

- Inelegant efficiency. (With J.W.Barrett and G.Moore.) Risk 5 82—84 (1992).

- A systematic derivation of the leading-order equations for extensional flow in slender geometries. (With J.N.Dewynne and J.R.Ockendon.) J. Fluid Mech. 244 323—338 (1992).

- A composite cavity model for axisymmetric high Reynolds number separated flow. Part I: Model and analysis. (With A.D.Fitt.) J. Engrg. Math. 26 539—555 (1992).

- Slender axisymmetric fluid jets. (With J.N.Dewynne.) Math. Comp. Model. 18 69—82 (1993).

- Formation of oscillation marks in strand casting. (With J.R.King, A.A.Lacey, C.P.Please and A.Zoryk.) Math. Engrg. Ind. 4 91—106 (1993).

- Partial to the exotic. (With J.N.Dewynne.) Risk 6 (3) 38—46 (1993).

- Properties of moving averages of asset prices. (With C.Atkinson.) IMA J. Math. Bus. Ind. 4 331—341 (1993).

- Counting the costs. (With A.E.Whalley.) Risk 6 (10) 59—66 (1993).

- Some mathematical results in the pricing of American options. (With J.N.Dewynne, S.D.Howison and I.Rupf.) Euro. J. Appl. Math. 4 381—398 (1993).

- Diffusion-controlled kink and ledge motion. (With C.Atkinson.) Int. Conf. Computer-assisted Mat. Design and Process Sim., Tokyo, Sept. 1993, 338—342 (1993).

- A class of one-factor interest rate models. (With R.Klugman.) Proc. 7th Euro. Conf. Math. Ind. 419—426 (1994).

- Exotic financial options. (With J.N.Dewynne.) Proc. 7th Euro. Conf. Math. Ind. 389—397 (1994).

- An integral equation for the value of a stop-loss option. (With A.D.Fitt and J.N.Dewynne.) Proc. 7th Euro. Conf. Math. Ind. 399—405 (1994).

- A comparison of hedging strategies. (With A.E.Whalley.) Proc. 7th Euro. Conf. Math. Ind. 427—434 (1994).

- Discrete charms. Risk, March (1994).

- Slot film cooling: the effect of separation angle. (With A.D.Fitt.) Acta Mech. 103 79—88 (1994).

- Hedging option portfolios in the presence of transaction costs. (With T.Hoggard and A.E.Whalley.) Adv. Fut. Opt. Res. 7 21—35 (1994).

- Interactions of continuous distributions of ledges. (With C.Atkinson.) Proc. Roy. Soc. A 446 277—287 (1994).

- Path-dependent options and transaction costs. (With A.E.Whalley and J.N.Dewynne.) Phil. Trans. Roy. Soc. A. 347 517—529 (1994).

- Slender viscous fibres with inertia and gravity. (With J.N.Dewynne and P.D.Howell.) Q. Jl. Mech. Appl. Math. 47 541—555 (1994).

- Hedge with an edge. (With A.E.Whalley.) Risk, Oct. (1994).

- A cavitating aerofoil with a Prandtl-Batchelor eddy. (With E.Zachariou and A.D.Fitt.) Aero. J. 98 171—176 (1994).

- A note on American options with varying exercise price. (With J.N.Dewynne.) J. Austral. Math. Soc. 37 45—57 (1995).

- A note on average-rate options with discrete sampling. (With J.N.Dewynne.) SIAM J. Appl. Math. 55 267—276 (1995).

- A composite cavity model for axisymmetric high Reynolds number separated flow.Part II: Numerical analysis and results. (With A.D.Fitt.) J. Engrg. Math. 29 63—75 (1995).

- Asian options as linear complementarity problems: analysis and finite-difference solutions. (With J.N.Dewynne.) Adv. Fut. Opt. Res. 8 (1995).

- Hedging in illiquid markets: nonlinear effects. (With P.Schonbucher.) Proc. 8th Euro. Conf. Math. Ind. (1995).

- An asymptotic analysis of a global-time model for option pricing with transaction costs. (With A.E.Whalley.) Proc. 8th Euro. Conf. Math. Ind. (1995).

- Some thoughts on interest rate modelling. (With M.Z.Apabhai, K.Choe and F.Khennach.) Proc. 8th Euro. Conf. Math. Ind. (1995).

- Volatility smiles revisited. Derivatives Week 4 (38) p 8 (1995).

- Mathematical models and partial differential equations in finance. (With A.E.Whalley and J.N.Dewynne.) In ‘Quantitative methods, super computers and AI in finance’ (ed. S.Zenios) 95—124, (1995).

- Portfolio management with transaction costs: an asymptotic analysis. (With C.Atkinson.) Math. Fin. 5 357—367 (1995).

- Spot-on modelling. (With M.Z.Apabhai, K.Choe and F.Khennach.) Risk, Dec. (1995).

- Exotic options: mathematical models and computation. In ‘Frontiers in Derivatives’ (Ed. Konishi and Dattatreya.) (With J.N.Dewynne.) 145—182 (1996).

- Key results in discrete hedging and transaction costs. In ‘Frontiers in Derivatives’ (Ed. Konishi and Dattatreya.) (With A.E.Whalley.) 183—196 (1996).

- An asymptotic analysis of the Davis, Panas and Zariphopoulou model for option pricing with transaction costs. (With A.E.Whalley.) Math. Fin. 7 307—324 (1996)

- Portfolio management with transaction costs. (With C.Atkinson and S.Pliska.) Proc. Roy. Soc. A (1996)

- Crash barriers. (With P.Hua.) Risk, June (1997).

- Expect the worst! (With D.Epstein.) Net Exposure 2 August (1997).

- A model for the value of a business, some optimisation problems in its operating procedures and the valuation of its debt. (With M.Z.Apabhai, N.I.Georgikopoulos, D.Hasnip, R.K.D.Jamie and M.Kim.) IMA J. Appl. Math. 60 1—13 (1998).

- Risk of default in Latin American Brady bonds. (With I.Blauer.) Net Exposure 5 (1998).

- Uncertain parameters, an empirical stochastic volatility model and confidence limits. (With A.Oztukel.) Int. J. Theor. Appl. Fin. 1 175—189 (1998)

- A new model of interest rates. (With D.Epstein.) Int. J. Theor. Appl. Fin. 1 195—226 (1998)

- The valuation of a firm advertising optimally. (With D.Epstein, N.Mayor, P.Schonbucher and A.E.Whalley.) Q. Rev. Econ. & Fin. 38 149—166 (1998)

- Optimal hedging of options with small but arbitrary transaction cost structure. (With A.E.Whalley.) Euro. J. Appl. Math.

- A general framework for hedging and speculating with options. (With R.Korn.) Int. J. Theor. Appl. Fin. 1 507—522 (1998)

- Breaking up is hard to do. (With P.Hua.) Risk magazine, Sept. (1998)

- Pricing and hedging convertible bonds under non-probabilistic interest rates. (With D.Epstein and R.Haber.) J. Fixed Income (1998)

- Exotic passport options. (With H.Ahn and A.Penaud.) Asia-Pacific Financial Markets (1998)

- Value at risk and market crashes. (With P.Hua.) Derivatives Week (1998)

- A comparison of Monte Carlo-type methods for valuing a financial derivative. (With D.Bruno and E.Cortina.) Proc. Euro. Conf. Math. Ind. (1998).

- Exercise class. (With H.Ahn.) Derivatives Week (1998)

- A Foot in Both Camps. Science’s Next Wave (1999)

- A classification of hedging strategies. (With P.Hua) Derivatives Week (1999)

- Extreme scenarios, worst cases, CrashMetrics and Platinum Hedging. (With P.Hua) Risk Professional (1999)

- The way ahead. Optimus 2 16—17 (1999)

- Quantify your risk. Optimus 3 16—17 (1999)

- Parisian options. (With R.Haber and P. Schonbucher.) J. Derivs 6 71—79 (1999)

- A nonlinear non-probabilistic spot interest rate model. (With D.Epstein.) Roy. Soc. Phil. Trans. Special Issue 357 2109—2117 (1999)

- The use, misuse and abuse of mathematics in finance. (2000) Royal Society
*Science into the Next Millennium: Young scientists give their visions of the future*Phil Trans 358 63—73

- From dividend strips to re-convertibles. (With D.Bakstein.) Mongolian Math. Soc. (2000)

- CrashMetrics metodologia: cenários de alta proabilidade de perdas e Platinum Hedging. Tecnologia de Credito (1999)

- The value of market research when a firm is learning: option pricing and optimal filtering. (With D.Epstein, N.Mayor, P.Schonbucher and A.E.Whalley.) In Real Options and Business Strategy (Ed. L.Trigeorgis) Risk Publications (2000)

- The feedback effect of hedging in illiquid markets. (With P.Schonbucher.) SIAM J. Appl. Math. 61 232—272 (2000)

- Uncertainty versus randomness: minimizing model dependence. Int. J. Th. Appl. Fin. 3 493—500 (2000)

- Various passport options and their valuation. (With H.Ahn and A.Penaud) Applied Mathematical Finance 6 275—292 (2000)

- Equity dividend models. (With D.Bakstein) In New Directions in Mathematical Finance. (Eds P.Wilmott and H.Rasmussen.) (2001)

- Pricing bond options in a worst-case scenario. (With D.Epstein.) In New Directions in Mathematical Finance. (Eds P.Wilmott and H.Rasmussen.) (2001)

- CrashMetrics. (With P.Hua.) In New Directions in Mathematical Finance. (Eds P.Wilmott and H.Rasmussen.) (2001)

- Asymptotic analysis of stochastic volatility models. (With H.Rasmussen.) In New Directions in Mathematical Finance. (Eds P.Wilmott and H.Rasmussen.) (2001)

- Optimal portfolios under the threat of a crash. (With R.Korn.) Int. J. Th. Appl. Fin. 5 171—188 (2002)

- The end-of-year bonus: How to optimally reward a trader. (With H.Ahn, J.Dewynne, P.Hua and A.Penaud) Int. J. Th. Appl. Fin. 5 279—306 (2002)

- Non-probabilistic Jump Modelling for Financial Derivatives. (With D.Bakstein.) Proc. ECMI 2000 67—72 (2002)

- GARCH and Volatility Swaps. (With Alireza Javaheri and Espen Haug.) Wilmott (2002)

- Cliquet options and volatility models. Wilmott Dec. 2002 78—83 (2002)

- On exercising American options: the risk of making more money than you expected. (With Hyungsok Ahn.) Wilmott Mar 2003 52—63 (2003)

- Stochastic volatility and mean-variance analysis. (With Hyungsok Ahn.) Wilmott Nov 2003 84—90 (2003)

- GARCH and volatility swaps. (With Alireza Javaheri and Espen Haug.) Quantitative Finance 4 589—595 (2004)

- Which free lunch would you like today, Sir? Delta hedging, volatility arbitrage and optimal portfolios. (With Riaz Ahmad.) Wilmott Nov 2005 64—79 (2005)

- Life settlements and viaticals.
*Wilmott*Mar 2006 56-62 (2006)

- The market price of interest rate risk: Measuring and modelling fear and greed in the fixed-income markets. (With Riaz Ahmad.)
*Wilmott*magazine, January (2007)

- Jump Diffusion, Mean and Variance: How to Dynamically Hedge, Statically Hedge and to Price. (With Hyungsok Ahn.)
*Wilmott*magazine, May 2007 96-109 (2007)

- Dynamic Hedging is Dead! Long Live Static Hedging! (With Hyungsok Ahn.)
*Wilmott*January 2008 80—7 (2008)

- Where Quants Go Wrong: a dozen basic lessons in commonsense for quants and risk managers and the traders who rely on them.
*Wilmott*journal, February 2009 (2009)

- A Note on Hedging: Restricted but Optimal Delta Hedging, Mean, Variance, Jumps, Stochastic Volatility, and Costs. (With Hyungsok Ahn.)
*Wilmott*journal, June 2009 (2009)

- A Note on Hedging Errors in Discretely Hedged Options and Portfolios. (With Yury Rojek.)
*Wilmott*journal Vol 2 Issue 5 261–270 (2010)

- Consistent Yield Curves via Static Hedging. (With Yury Rojek.)
*Wilmott*magazine July 2013

- Modeling Volatility and Valuing Derivatives Under Anchoring. (With Alan L. Lewis and Daniel J. Duffy)
*Wilmott*magazine September 2014

- How I Successfully Forecast the Results of the UK General Election 2015.
*Wilmott*magazine July 2015

- Quantitative Seizing.
*Wilmott*magazine March 2016

- The Pleasure and Pain of Investing: Parallels with exotic options.
*Wilmott*magazine March 2019

- The two best ways to derive the Black–Scholes PDE,
*China Finance Review International*, Vol. 10 No. 2, pp. 168-74 (2019) https://doi.org/10.1108/CFRI-12-2018-0153

- How Good is Black–Scholes–Merton Really? In
*Options – 45 Years Since The Publication Of The Black-Scholes-Merton Model: The Gershon Fintech Center Conference – World Scientific Lecture Notes In Finance*, 2022

## External links

- Magazine in
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