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Teaching/MH6831

MH6831 · Postgraduate

Quantitative Methods in Finance

MSc in Financial Technology

Trimester 1BBack to module tabs

Course materials and assessment information for registered students are provided through NTULearn. External resource links may require NTU access.

Overview

This course covers basic and essential quantitative methods in finance. Several mathematical and statistical techniques are introduced. This course emphasizes the applications of the quantitative methods in two important areas in finance: asset management and derivative pricing.

Assessment Scheme

  • Continuous Assessment (40%)
  • Final Examination (60%)

Topics

  1. [3hrs] Models for Asset Dynamics I: Discrete-time Approach - Binomial Tree, Additive and Multiplicative Models, Log-Normal Distribution
  2. [3hrs] Models for Asset Dynamics II: Continuous-time Approach - Wiener Process/Brownian Motion, Ito's Lemma, Geometric Brownian Motion
  3. [5hrs] Derivatives Pricing I: Risk-neutral Valuation - Options, Hedging (Discrete- and Continuous-time Models), Greeks
  4. [1hr+1hr-Lab] Derivatives Pricing II: Simulation Techniques - Monte Carlo Approach, Path-Dependent Options
  5. [3hrs] Portfolio Selection I: Modern Portfolio Theory - Markowitz's Mean-Variance Analysis, Intertemporal Portfolio Choice
  6. [2hrs] Portfolio Selection II: Empirical Analysis - Evaluation Methodology, Improvement Schemes (Shrinkage, Factors)

Book References

  1. D. G. Luenberger (2013) Investment Science (2nd Edition). Oxford University Press.
  2. N. H. Chan and H. Y. Wong (2015) Simulation Techniques in Financial Risk Management (2nd Edition). Wiley.
  3. N. H. Chan and H. Y. Wong (2013) Handbook of Financial Risk Management: Simulations and Case Studies. Wiley.
  4. Y.-K. Kwok (2008) Mathematical Models of Financial Derivatives. Springer.
  5. T. Björk (2009) Arbitrage Theory in Continuous (3rd Edition). Oxford University Press.

Paper References for Empirical Portfolio Analysis

  1. [DeMiguel et al. (2009, RFS)] Optimal Versus Naive Diversification - How Inefficient is the 1/N Portfolio Strategy
  2. [Ledoit and Wolf (2004, JPM)] Honey, I Shrunk the Sample Covariance Matrix
  3. [Fan et al. (2008, JoE)] High Dimensional Covariance Matrix Estimation using a Factor Model