Peter Carr

Finance and Risk Engineering Department Chair (deceased)

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The entire NYU Tandon community mourns the passing of Peter Carr, the beloved chair of the Department of Finance and Risk Engineering and a highly-regarded researcher.

In Memoriam Remembering Peter Carr

For the last 5 years, Dr. Peter Carr has been the Chair of the Finance and Risk Engineering Department at the NYU Tandon School of Engineering. Prior to that, he headed various quant groups in the financial industry for twenty years. He also presently serves as a director for the Society of Quantitative Analysts (SQA) and a trustee for the National Museum of Mathematics, and WorldQuant University. Prior to joining the financial industry, Dr. Carr was a finance professor for 8 years at Cornell University, after obtaining his Ph.D. from UCLA in 1989. He has over 85 publications in academic and industry-oriented journals and serves as an associate editor for 8 journals related to mathematical finance. He was selected as Quant of the Year by Risk Magazine in 2003 and Financial Engineer of the Year by IAQF/Sungard in 2010. From 2011 to 2014, Dr. Carr was included in Institutional Investor's Tech 50, an annual listing of the 50 most influential people in financial technology.

In the five years, Dr. Carr has been FRE Department Chair, applications for the MS in Financial Engineering program increased from 1,300 per year to 1,979 per year. For the 2019 class, the quant GRE was 169.2/170 and the GPA was 3.85. Additionally, FRE climbed seven positions over the last four years in QuantNet rankings, an online summer course was initiated two summers ago and an on-campus boot camp was initiated in the summer of 2018, and six electives on machine learning in finance were introduced.

Papers for Seminar Presentations

Stoptions: Representations and Applications

Education

University of Toronto 1981
Com, Accounting/Economics

University of Toronto 1983
MBA, Accounting/Finance

University of California, 1989
PhD, Finance

Experience

Banc of America Securities
Principal
From: January 1999 to May 2001

NYU Courant Institute
Director Masters MF Program
From: June 2003 to May 2016

Bloomberg LP
Head of Quantitative Financial Research
From: May 2003 to March 2010

Morgan Stanley
Global Head of Market Modeling
From: April 2010 to April 2016

Publications

Journal publications:

"Robust Replication of Volatility and Hybrid Derivatives on Jump Diffusions" (PDF) (with R. Lee and M. Lorig), Mathematical Finance Volume 31, Issue 4, October 2021
"Semi-Analytical Solutions for Barrier and American Options Written on a Time-Dependent Ornstein–Uhlenbeck Process" (PDF)
(with A. Itkin), The Journal of Derivatives, 2021.
"Probabilistic Interpretation of Black Implied Volatility" (PDF) (with L. Wu and Y. Zhang), to appear in Conference Proceedings for the 45th Anniversary of Black Merton Scholes.
"Decomposing Long Bond Returns: A Decentralized Theory" (PDF) (with L. Wu), Review of Finance, forthcoming.
"Robust Replication of Volatility and Hybrid Derivatives on Jump Diffusions" (PDF) (with R. Lee and M. Lorig), Mathematical Finance, forthcoming.
"Additive logistic processes in option pricing" (PDF) (with L. Torricelli), Finance and Stochastics, 2021.
"Pricing Variance Swaps on Time-Changed Markov Processes" (PDF) (with M. Lorig and R. Lee), SIAM Journal on Financial Mathematics, 2021, volume 12, issue 2.
"Spiking the Volatility Punch" (PDF) (with Gianna Figa' Talamanca), Applied Mathematical Finance, March 2021.
"Option Profit and Loss Attribution and Pricing: A New Framework" (with L. Wu), Journal of Finance, August 2020.
"A Functional Analysis Approach to Static Replication of European Options" (PDF) (with S. Bossu and A. Papanicolaou), Quantitative Finance, November 2020
"Semi-closed form prices of barrier options in the time-dependent CEV and CIR models" (PDF) (with A. Itkin and D. Muravey), The Journal of Derivatives, Fall 2020
"An Expanded Local Variance Gamma model" (PDF) (with A. Itkin), Computational Economics, June 2020
"Using Machine Learning to Predict Realized Variance" (PDF) (with L. Wu and Z. Zhang), Journal Of Investment Management, Vol. 18, No. 2, (2020), pp. 1–16
"Model-free backward and forward PDEs for implied volatility" (PDF) (with A. Itkin), The Journal of Derivatives, Fall 2020
"ADOL - Markovian approximation of rough lognormal model" (PDF) (with A. Itkin), Risk.net, November 2019
Geometric Local Variance Gamma Model" (PDF) (with A. Itkin), The Journal of Derivatives, Winter 2019
Convex Duality and Financial Mathematics, Springer US.
"FX Options in Target Zones (PDF)," (with Z. Kakushadze) Quantitative Finance, vol. 17, issue 10, 2017.
"Why Is VIX a Fear Gauge? (PDF)," Risk and Decision Analysis, vol. 6, no. 2, pp. 179-185, 2017.
“Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions (PDF)” (with L. Wu), Journal of Financial and Quantitative Analysis, 2017.
“Hall of Mirrors (PDF),” Wilmott, May 2017.
"Bounded Brownian Motion (PDF)," Risks, 5(4) 61, 2017.
“Local Variance Gamma and Explicit Calibration to Option Prices (PDF)” (with S. Nadtochiy), Mathematical Finance, vol. 27, no. 1 (2017), pp. 151–93.
“Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer (PDF)” (with G. Rosenberg, A. Haghnegahdar, P. Goddard, K. Wu, and M. De Prado), IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 6 (2016), pp. 1053–60.
“Implied Remaining Variance with Application to Bachelier Model (PDF)” (with J. Sun, Q. Niu, and S. Cao), The Journal of Fixed Income, vol. 26, no. 2 (2016), pp. 78–95.
“Hedging Insurance Books (PDF)” (with D.B. Madan, M. Melamed, and W. Schoutens), Insurance: Mathematics and Economics, vol. 70 (2016), pp. 364–72.
“Adjusting Exponential Lévy Models Toward the Simultaneous Calibration of Market Prices for Crash Cliquets (PDF)” (with A. Khanna and D.B. Madan), Journal of Computational Finance, vol. 20, no. 1 (2016), pp. 89–111.
“Analyzing Volatility Risk and Risk Premium in Option Contracts: A New Theory (PDF)” (with L. Wu), Journal of Financial Economics, vol. 120, no. 1 (2016), pp. 1–20.
"Optimal Rates from Eigenvalues (PDF)” (with P. Worah), Finance Research Letters, Vol. 16 (2016), pp. 230–38.
“Joint Modeling of VIX and SPX Options at a Single and Common Maturity with Risk Management Applications (PDF)” (with D.B. Madan), IIE Transactions, vol. 46, no. 11 (2014), pp. 1125–31.
“On the Hedging of Options on Exploding Exchange Rates (PDF)” (with J. Ruf and T. Fisher), Finance and Stochastics, vol. 18, no. 1, pp. 115–44.
“Static Hedging of Standard Options (PDF)” (with L. Wu), Journal of Financial Econometrics, vol. 12, no. 1 (2014), pp. 3–46.
“First-Order Calculus and Option Pricing (PDF),” Journal of Financial Engineering, vol. 1, no. 1 (2014), pp. 1–19.
“Implied Remaining Variance in Derivative Pricing (PDF)” (with J. Sun), Journal of Fixed Income, vol. 23, no. 4 (2014), pp. 19–32.
"Variation and Share-Weighted Variation Swaps on Time-Changed Lévy Processes (PDF)" (with R. Lee), Finance and Stochastics, vol. 17, no. 4 (2013), pp. 685–716.
"Why Are Quadratic Normal Volatility Models Analytically Tractable? (PDF)" (with T. Fisher and J. Ruf), SIAM Journal on Financial Mathematics, vol. 4, no. 1 (2013), pp. 185–202.
“Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models (PDF)” (with A. Itkin), Computational Economics, 40, 1, Jun., 2012, 63–104.
“Variance Swaps on Time-Changed Lévy Processes (PDF)” (with R. Lee), Finance and Stochastics, Apr. 2012, 335-355.
"Maximum Drawdown Insurance" (PDF) (with H. Zhang and O. Hadjiliadis), International Journal of Theoretical and Applied Finance, 2011.
“Static Hedging under Time-Homogeneous Diffusions (PDF)” (with S. Nadtochiy), SIAM Journal on Financial Mathematics, 2, 1, Dec., 2011, 794–838.
“Explicit Constructions of Martingales Calibrated to Given Implied Volatility Smiles (PDF)” (with L. Cousot), SIAM Journal on Financial Mathematics, 3 1, 2012, 182–214.
“Factor Models for Option Pricing (PDF)” (with D. Madan), Asia-Pacific Financial Markets, Nov. 2011, 1-11.
“Jumps without Tears: A New Splitting Technology for Barrier Options (PDF)” (with A. Itkin), International Journal of Numerical Analysis and Modeling, 8, 4, 2011, 667–704.
“A Simple Robust Link Between American Puts and Credit Protection (PDF)” (with L. Wu), Review of Financial Studies, 24, 2, 2011, 473–505.
“Multi-Asset Stochastic Local Variance Contracts (PDF)” (with P. Laurence), Mathematical Finance, 21,1, Jan. 2011, 2152.
“Pricing Swaps and Options on Quadratic Variation Under Stochastic Time Change Models: Discrete Observations Case (PDF)" (with A. Itkin), Review of Derivatives Research, Springer, 13 2, July, 2010, 141–176.
“Time Changed Markov Processes in Unified Credit-Equity Modeling (PDF)” (with R. Mendoza-Arriaga and V. Linetsky), Mathematical Finance, 20, 2010, 527569.
“A Class of Lévy Process Models with almost exact calibration of both barrier and vanilla FX options (PDF)” (with J. Crosby), Quantitative Finance, May 2010, 1-22.
“Options on Realized Variance and Convex Orders (PDF)” (with H. Geman, D. Madan, and M. Yor), Quantitative Finance, April 2010, 1-10.
“Hedging Variance Options on Continuous Semimartingales (PDF)” (with R. Lee), Finance and Stochastics,14, 2, Feb. 2010, 179–207.
“Local Volatility Enhanced by a Jump to Default (PDF)” (with D. Madan), SIAM Journal on Financial Mathematics, 1, Jan. 2010 2–15.
“Volatility Derivatives (PDF)” (with R. Lee), Annual Review of Financial Economics, Volume 1, Dec. 2009.
“Put-Call Symmetry: Extensions and Applications (PDF)” (with R. Lee), Mathematical Finance, 19, 4, Oct. 2009, 523–560.
“Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation (PDF)” (with L. Wu), Journal of Financial Econometrics, July 2009, 1–41.
“Variance Risk Premia (PDF)” (with L. Wu), Review of Financial Studies, 22, March, 2009.
“On the qualitative effect of volatility and duration on prices of Asian options (PDF)” (with C. Ewald, and Y. Xiao), Finance Research Letters, Sept. 2008.
“Stochastic Risk Premiums: Stochastic Skewness in Currency Options, and Stochastic Discount Factors in International Economics (PDF)” (with L. Wu and G. Bakshi), Journal of Financial Economics, 87, 132–156.
"Realized Volatility and Variance: Options via Swaps" (PDF) (with Roger Lee), RISK, vol 20 issue 5 (2007), 76-83.
“Stochastic Skew for Currency Options (PDF)” (with L. Wu), Journal of Financial Economics, 2007, 86 1, 213–247.
“A New Approach for Option Pricing Under Stochastic Volatility (PDF)” (with J. Sun), Review of Derivatives Research, 10, 2, 87–150.
”On the Numerical Valuation of Option Prices in Jump Diffusion Processes (PDF)" (with A. Mayo), The European Journal of Finance, 2007, 13 4, 353–372.
“Theory and Evidence on the Dynamic Interactions Between Sovereign Credit Default Swaps and Currency Options (PDF)” (with L. Wu), Journal of Banking and Finance, 31, 8, 2007, 2383-2403.
“Self-Decomposability and Option Pricing (PDF)” (with D. Madan, H. G´eman, and M. Yor), Mathematical Finance, 7, 1, 2007, 31–57.
"A Tale of Two Indices" (PDF) (with Liuren Wu), Journal of Derivatives, 2006.
“A Jump to Default Extended CEV Model: An Application of Bessel Processes (PDF)” (with V. Linetsky), Finance and Stochastics, 2006, 10, 303-330.
“Generating Intetrable One Dimensional Driftless Diffusions (PDF)” (with P. Laurence and T. Wang), Comptes Rendus de l’Acad´emie des Sciences, 343, 6, Sept. 2006, 393-398.
“A Note on Sufficient Conditions for No Arbitrage (PDF)” (with D. Madan), Finance Research Letters, 2005, 2, 3.
“Pricing Options on Realized Variance (PDF)” (with D. Madan, H. Géman, and M. Yor), Finance and Stochastics, IX, 4.
“From Local Volatility to Local Lévy Models (PDF)” (with D. Madan, H. Géman, and M. Yor), Quantitative Finance, October 2004, 4, 5, 581–588.
“Time-Changed Lévy Processes And Option Pricing (PDF)” (with L. Wu), Journal of Financial Economics, January 2004, 71, 1, 113–141.
“Bessel Processes, The Integral of Geometric Brownian Motion, and Asian options (PDF)” (with M. Schröder), Theory of Probability and its Applications, 2004, 48, 3, 400–425.
“What Type of Process Underlies Options: A Simple Robust Test (PDF)” (with L. Wu), Journal of Finance, December 2003, 68, 6, 2581–2610.
“Stochastic Volatility for Lévy Processes (PDF)” (with H. Géman, D. Madan, and M. Yor), Mathematical Finance, July 2003, 345–382.
“The Finite Moment Logstable Process And Option Pricing (PDF)” (with L. Wu), Journal of Finance, April 2003, 753–778.
“The Fine Structure of Asset Returns: An Empirical Investigation (PDF)” (with H. Géman, D. Madan, and M. Yor), Journal of Business, 75, 2002, 2, 305–32.
“Pricing and Hedging in Incomplete Markets (PDF)” (with H. Géman and D. Madan), Journal of Financial Economics, 62, 2001, 131–167.
"Covariance contracting for commodities (PDF)" Energy Power and Risk Management, April 2001
“Optimal Positioning in Derivative Securities (PDF)” (with D. Madan), 2001, Quantitative Finance, 1, 1, 19–37.
"Going with the Flow: Alternative Approach for Valuing Continuous Cash Flows" (PDF) (with Alex Lipton and Dilip Madan), Risk Magazine, 2000,13(8), 85–8.
“The Valuation of Executive Stock Options in an Intensity-Based Framework (PDF)” (with V. Linetsky), European Finance Review, 4, 2000, 211-http://engineering.nyu.edu/files/FRLarticle.pdf230.
“Optimal Investment in Derivative Securities (PDF)” (with D. Madan and X. Jin), Finance and Stochastics, 5, 1, 33-60.
"Static hedging of timing risk", P Carr, JF Picron, The Journal of Derivatives, 1999.
"Option Valuation Using the Fast Fourier Transform (PDF)" (with D. Madan), Journal of Computational Finance, Summer 1999, 61-73.
“The Variance Gamma Process and Option Pricing (PDF)” (with D. Madan), European Finance Review, 2, 1998, 79–105.
“Static Hedging of Exotic Options (PDF)” (with K. Ellis and V. Gupta), Journal of Finance,1165-90, June 1998. Reprinted in Quantitative Analysis of Financial Markets, M. Avellaneda, ed., 152–176.
“Randomization and the American Put (PDF),” Review of Financial Studies, 11, 3, 1998, 597–626.
“Alternative Characterizations of American Put Options (PDF)” (with R. Jarrow and R. Myneni), Mathematical Finance, April 1992, 87–105.
“The Stop-Loss Start-Gain Strategy and Option Valuation (PDF)” (with R. Jarrow), Review of Financial Studies, Fall 1990, 469–92.
“The Valuation of Sequential Exchange Opportunities (PDF)” Journal of Finance, Dec. 1988, 1235–56.
“A Note on the Pricing of Commodity-Linked Bonds (PDF)” Journal of Finance, Sept. 1987, 1071–76.

Book publications:

"How I Became a Quant: Insights from 25 of Wall Street's Elite "(PDF), John Wiley & Sons, Inc. 2007
“Forward Evolution Equations for KnockOut Options” (with A. Hirsa), Advances in Mathematical Finance (Festschrift in honor of the 60th birthday of Dilip Madan), Birkhauser Boston, July 2007, M.C. Fu, R.A. Jarrow, J.-Y. Yen, and R.J. Elliott, ed.,
“Real Options and the Timing and Implementation of Emission Limits Under Ecological Uncertainty (PDF)” (with J. Saphores), in Project Flexibility, Agency, and Competition, Oxford University Press, M. J. Brennan and L. Trigeorgis, ed., 1999.
“Learning and Exercising Options to Reduce Capital Project Risk” (with L. Chorn), in Risk Options and Business Strategy, Risk Publications, L. Trigeorgis, ed., 1999, pp. 279–94.
“Determining Volatility Surfaces and Option Values from an Implied Volatility Smile” (with D. Madan), Quantitative Analysis of Financial Markets, vol. II, M. Avellaneda, ed., pp. 163–91.
“Simulating Bermudan Interest Rate Derivatives” (with G. Yang), Quantitative Analysis of Financial Markets, vol. II, M. Avellaneda, ed., pp. 295–316.
“A Discrete Time Synthesis of Derivative Security Valuation Using a Term Structure of Futures Prices” (with R. Jarrow), in the Finance Volume of Handbooks in Operations Research and Management Science, R. Jarrow, V. Maksimovic, & B. Ziemba, ed., pp. 225–49.
“The Valuation of American Exchange Options with Application to Real Options (PDF),” Real Options in Capital Investment: New Contributions, L. Trigeorgis, ed., pp. 109–20,
“Valuing Bonds with Detachable Warrants,” Japanese Financial Market Research, pp. 467–79, W. Bailey, Y. Hamao, & B. Ziemba, eds.
"The Value of Purchasing Information to Reduce Risk in Capital Investment Projects (PDF)" (with Chorn, L.G.), Society of Petroleum Engineers, 1997.