Ivan Matić, Radoš Radoičić, Dan Stefanica. A Sharp Pólya-Based Approximation to the Normal Cumulative Distribution Function, Applied Mathematics and Computation, 322, 111-122, 2018. Journal link; SSRN download.
Ivan Matić, Radoš Radoičić, Dan Stefanica. Pólya-based Approximation for the ATM-forward Implied Volatility, International Journal of Financial Engineering, 4, no. 2-3, 2017. Journal link; SSRN download.
Dan Stefanica, Radoš Radoičić. A Sharp Approximation for ATM-Forward Option Prices and Implied Volatilites, International Journal of Financial Engineering, Vol. 3, No. 1 (2016). Journal link; SSRN download.
Domain Decomposition Methods
Dostál, Zdeněk; Horák, David; Stefanica, Dan. A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface. J. Comput. Appl. Math. 231 (2009), no. 2, 577–591
Stefanica, Dan. A balancing algorithm for mortar methods. Domain decomposition methods in science and engineering XVI, 747–754, Lect. Notes Comput. Sci. Eng., 55, Springer, Berlin, 2007
Dostál, Zdeněk; Horák, David; Stefanica, Dan. Quadratic programming and scalable algorithms for variational inequalities. Numerical mathematics and advanced applications, 62–78, Springer, Berlin, 2006
Stefanica, Dan. Lower bounds for additive Schwarz methods with mortars. C. R. Math. Acad. Sci. Paris 339 (2004), no. 10, 739–743
Stefanica, Dan. A numerical study of FETI algorithms for mortar finite element methods. SIAM J. Sci. Comput. 23 (2001), no. 4, 1135–1160
Geophysical Fluid Dynamics
Holland, David; Rosales, Rodolfo; Stefanica, Dan; Tabak, Esteban. Internal hydraulic jumps and mixing in two-layer flows. J. Fluid Mech. 470 (2002), 63–83
Ismailescu, Dan; Stefanica, Dan. Minimizer graphs for a class of extremal problems. J. Graph Theory 39 (2002), no. 4, 230–240
A Linear Algebra Primer for Financial Engineering by Dan Stefanica, 2014.
It is the third book in the Financial Engineering Advanced Background Series, and covers linear algebra concepts for financial engineering applications from a numerical point of view. The book contains many such applications, as well as pseudocodes, numerical examples, and questions often asked in interviews for quantitative positions.
• The Arrow—Debreu one period market model
• One period index options arbitrage
• Covariance and correlation matrix estimation from time series data
• Ordinary least squares for implied volatility computation
• Minimum variance portfolios and maximum return portfolios
• Value at Risk and portfolio VaR
Linear Algebra Topics
• Direct methods for solving linear system. LU and Cholesky decompositions.
• Optimal solvers for tridiagonal symmetric positive matrices
• The Linear Transformation Property
• Multivariate normal random variables
• Efficient cubic spline interpolation
• Ordinary least squares and linear regression
• Gershgorin’s theorem and diagonal dominance
• Sylvester’s criterion
Table of Contents (Download)
- 8.1.1. Implied volatility computation using least squares (Download)
- 8.1. Ordinary least squares (Download)
- 7.4. Necessary and sufficient conditions for covariance and correlation matrices (Download)
- 1.1. Column vectors and row vectors. Covariance matrix computation from time series data. (Download)
- Exercises – Chapter 1 (Download)
150 Most Frequently Asked Questions on Quant Interviews by Dan Stefanica, Rados Radoicic, and Tai-Ho Wang, 2013.
- Mathematics, calculus, differential equations
- Covariance and correlation matrices. Linear algebra
- Financial instruments: options, bonds, swaps, forwards, futures
- C++, algorithms, data structures
- Monte Carlo simulations. Numerical methods
- Probability. Stochastic calculus
A Primer for the Mathematics of Financial Engineering by Dan Stefanica, Second Edition, 2011.
- Table of Contents (Download)
- 3.6.1. Explaining the magic of Greeks computations (Download)
- 5.2.1. The N-dimensional Newton’s Method (Download)
- 6.5. Parallel shifts in the yield curve (Download)
- 6.7. Dollar duration and dollar convexity; bond portfolio immunization (Download)
- 8.6. Integrating the density function of the standard normal variable (Download)
- 9.1. Lagrange multipliers (Download)
- Exercises – Chapter 1 (Download)
- Exercises – Chapter 6 (Download)
Solutions Manual – A Primer for the Mathematics of Financial Engineering by Dan Stefanica, Second Edition, 2011.
Publisher’s discount on Math Primer and Solutions Manual and worldwide shipping from FE Press
Baruch College: Co-Director, Financial Engineering MS Program, 2002 – Present
Baruch College: Associate Professor, Department of Mathematics, 2005 – Present
Baruch College: Assistant Professor, Department of Mathematics, 1999-2005 (on leave 2000-2002)
Massachusetts Institute of Technology: Applied Mathematics Instructor, 2000-2002
Grant Support (selected)
PSC-CUNY 62667-00 40
Contact for Baruch MFE Inquiries
Email: baruch.mfe at baruch.cuny.edu
Email: Dan.Stefanica at baruch.cuny.edu