Vadim Linetsky, Ph.D.

Professor
Department of Industrial Engineering and Management Sciences
McCormick School of Engineering and Applied Sciences

Northwestern University
2145 Sheridan Road, Room C251
Evanston, IL 60208-3119
E-mail: linetsky@iems.northwestern.edu
Voice: (847) 491 2084
Fax: (847) 491 8005

My research and teaching interests are in the areas of Financial Engineering, Mathematical and Computational Finance, and Stochastic Modeling.

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Publications in Financial Engineering

EDITED VOLUMES

• John R. Birge and Vadim Linetsky, Editors, Handbook of Financial Engineering, in Handbooks in Operations Research and Management Sciences, Elsevier, Amsterdam, 2007.

Table of Contents

• John R. Birge and Vadim Linetsky, Special Issue of Naval Research Logistics on Applications of Financial Engineering in Operations, Production, Logistics and Management, Volume 53, Issue 7, October 2006, pp. 601-726.

Introduction

OPTIONS PRICING: ANALYTICAL METHODS AND APPLICATIONS

The Path Integral Approach

• V. Linetsky, “The Path Integral Approach to Financial Modeling and Options Pricing,” Computational Economics, 11 (1998) pp. 129-163.

Occupation Times and Barrier and Step Options

• V. Linetsky, “Steps to the Barrier,” RISK, April 1998, pp. 62-65.
• V. Linetsky, “Step Options,” Mathematical Finance, 9 (1999) pp. 55-96.
• D. Davydov and V. Linetsky, “Structuring, Pricing and Hedging Double Barrier Step Options,” Journal of Computational Finance, Volume 5 Issue 2 Winter 2001/2002, pp.55-87.

Valuation and Exercise of Executive Stock Options

• P. Carr and V. Linetsky, “The Valuation of Executive Stock Options in an Intensity-Based Framework,” European Finance Review, 4 (2000) pp.211-230. [Correction]

Analytical Solutions for Barrier and Lookback Options under the Constant Elasticity of Variance (CEV) Model

• D. Davydov and V. Linetsky, “The Valuation and Hedging of Barrier and Lookback Options under the CEV Process,” Management Science, 47 (2001) pp. 949-965.
• D. Davydov and V. Linetsky, “Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach,” Operations Research, 51 (2003) pp.185-209
• V. Linetsky, "Lookback Options and Diffusion Hitting Times: A Spectral Expansion Approach," Finance and Stochastics, 8 (2004) pp.373-398

Note: a generalization of the CEV model to include a jump to default was introduced in “A Jump to Default Extended CEV Model: An Application of Bessel Processes” listed under “Credit Risk Modeling”.

An Analytical Solution for Asian (Average Price) Options

• V. Linetsky, "Spectral Expansions for Asian (Average Price) Options,” Operations Research, 52 (2004) pp.856-867

THE SPECTRAL EXPANSION METHOD IN MATHEMATICAL FINANCE AND APPLIED PROBABILITY

The Method

• V. Linetsky, "Exotic Spectra," RISK, April 2002, pp.85-89.
• V. Linetsky, "The Spectral Decomposition of the Option Value," IJTAF, 7 (2004) pp.337-384

· V. Linetsky, 2007, “Spectral Methods in Derivatives Pricing,” in Handbook of Financial Engineering, Handbooks in Operations Research and Management Sciences, Elsevier, Amsterdam, 2007.

Applications in Mathematical Finance

See papers listed under “Interest Rate Modeling”, “Credit Risk Modeling”, “The Constant Elasticity of Variance (CEV) Model”, and “Mortgage Valuation”.

Applications in Stochastic Modeling and Applied Probability

• V. Linetsky, "The Spectral Representation of Bessel Processes with Drift: Applications in Queueing and Finance," Journal of Applied Probability, 41 (2004) pp.327-344.
• V. Linetsky, "Computing Hitting Time Densities for OU and CIR Processes: Applications to Mean-reverting Models," Journal of Computational Finance, 7 (2004) pp.1-22.
• V. Linetsky, "On the Transition Densities for Reflected Diffusions" Advances in Applied Probability, 37 (2005) 435-460.

THE LAPLACE TRANSFORM APPROACH TO OPTIONS VALUATION

• D. Davydov and V. Linetsky, “Structuring, Pricing and Hedging Double Barrier Step Options,” Journal of Computational Finance, Volume 5 Issue 2 Winter 2001/2002, pp.55-87.
• D. Davydov and V. Linetsky, “The Valuation and Hedging of Barrier and Lookback Options under the CEV Process,” Management Science, 47 (2001) pp. 949-965.

INTEREST RATE MODELING

• V. Gorovoi and V. Linetsky, "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, 14 (2004) pp.49-78.
• V. Gorovoi and V. Linetsky, "Shadow Interest," RISK, December 2003, pp.81-84
• V. Linetsky, "Computing Hitting Time Densities for OU and CIR Processes: Applications to Mean-reverting Models," Journal of Computational Finance, 7 (2004) pp.1-22.

NUMERICAL SOLUTION OF PDE’s IN COMPUTATIONAL FINANCE

· L. Feng, P. Kovalov, V. Linetsky, and M. Marcozzi, 2007, “Variational Methods in Derivatives Pricing,” in Handbook of Financial Engineering, Handbooks in Operations Research and Management Sciences, Elsevier, Amsterdam.

· P. Kovalov, V. Linetsky, M. Marcozzi, 2007, “Pricing Multi-Asset American Options: A Finite Element Method-of-Lines with Smooth Penalty”, 2007, Journal of Scientific Computing, 33(3), 209-237.

· L. Feng and V. Linetsky, 2008, “Pricing Options in Jump-Diffusion Models: An Extrapolation Approach,” Operations Research, 52(2), 304-325. [Appendix can be found here.]

· P. Kovalov and V. Linetsky, 2006, “Pricing Convertible Bonds with Stock Price, Interest Rate and Credit Risks,” under revision.

FAST FOURIER TRANSFORM (FFT)-BASED METHODS FOR LEVY PROCESSES IN COMPUTATIONAL FINANCE

· L. Feng and V. Linetsky, 2006, “Pricing Discretely Monitored Barrier Options and Defaultable Bonds in Levy Process Models: A Hilbert Transform Approach,” Mathematical Finance, to appear.

· L. Feng and V. Linetsky, 2007, “Computing Exponential Moments of the Discrete Maximum of a Levy Process and Lookback Options,” Finance and Stochastics, to appear.

MORTGAGE VALUATION AND PREPAYMENT MODELING

· V. Gorovoi and V. Linetsky, “Intensity-based Valuation of Residential Mortgages: An Analytically Tractable Model,” Mathematical Finance, 17(4), 541-573.

CREDIT RISK MODELING

Unified Credit-Equity Models

• V. Linetsky, “Pricing Equity Derivatives subject to Bankruptcy,” Mathematical Finance, 16(2) (2006) 255-282.

· P. Carr and V. Linetsky, “A Jump to Default Extended CEV Model: An Application of Bessel Processes,” Finance and Stochastics, 10(3), 303-330.

• P. Carr, V. Linetsky, and R. Mendoza, “Time Changed Markov Processes in Credit-Equity Modeling,” submitted for publication.

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Selected Publications in Theoretical and Mathematical Physics Publications

Supergravity and String Theory

• E.S. Fradkin and V. Linetsky, “Superconformal Higher Spin Theory in the Cubic Approximation,” Nuclear Physics B 350 (1991) pp. 274-324.
• E.S. Fradkin and V. Linetsky, “On the Space-Time Interpretation of the Coset Models in D < 26 String Theory,” Physics Letters B 277 (1992) pp. 74-78.

Infinite-dimensional Lie Algebras

• E.S. Fradkin and V. Linetsky, “An Exceptional N = 8 Superconformal Algebra in Two Dimensions Associated with F(4),” Physics Letters B 275 (1992) pp. 345-349.
• E.S. Fradkin and V. Linetsky, “Classification of Superconformal and Quasi-superconformal Algebras in Two Dimensions,” Physics Letters B 291 (1992) pp. 71-76.
• E.S. Fradkin and V. Linetsky, “Infinite-dimensional Generalizations of Finite-dimensional Symmetries,” Journal of Mathematical Physics 32 (1991) pp. 1218-1226.

Geometric Quantization

• E.S. Fradkin and V. Linetsky, “BFV Approach to Geometric Quantization,” Nuclear Physics B 431 (1994) pp. 569-621.
• E.S. Fradkin and V. Linetsky, “BFV Quantization on Hermitian Symmetric Spaces,” Nuclear Physics B 444 (1995) pp. 577-601.