3.8 KiB
3.8 KiB
Bibliography & References
Selected references supporting the mathematics, quantitative-finance models, numerical methods, and software used in the notebook series. Exercise-only and redundant lookup references have been removed so this file reflects the material that remains in the public project.
Brownian motion and stochastic calculus
- Mörters, P. & Peres, Y. Brownian Motion. Cambridge University Press, 2010.
- Karatzas, I. & Shreve, S. E. Brownian Motion and Stochastic Calculus. Springer, 2nd ed., 1991.
- Klebaner, F. C. Introduction to Stochastic Calculus with Applications. Imperial College Press, 3rd ed., 2012.
- Shreve, S. E. Stochastic Calculus for Finance II: Continuous-Time Models. Springer, 2004.
- Øksendal, B. Stochastic Differential Equations. Springer, 6th ed., 2003.
- Protter, P. E. Stochastic Integration and Differential Equations. Springer, 2nd ed., 2005.
- Bachelier, L. “Théorie de la spéculation.” Annales scientifiques de l’École Normale Supérieure 17 (1900). Historical origin of Brownian price modelling.
Quantitative-finance models and barrier problems
- Hull, J. C. Options, Futures, and Other Derivatives. Pearson, 11th ed., 2021.
- Joshi, M. S. The Concepts and Practice of Mathematical Finance. Cambridge University Press, 2nd ed., 2008.
- Glasserman, P. Monte Carlo Methods in Financial Engineering. Springer, 2003.
- Cont, R. & Tankov, P. Financial Modelling with Jump Processes. Chapman & Hall/CRC, 2004.
Gaussian conditioning and numerical linear algebra
- Rasmussen, C. E. & Williams, C. K. I. Gaussian Processes for Machine Learning. MIT Press, 2006. Free full text: https://gaussianprocess.org/gpml/.
- Anderson, T. W. An Introduction to Multivariate Statistical Analysis. Wiley, 3rd ed., 2003.
- Revuz, D. & Yor, M. Continuous Martingales and Brownian Motion. Springer, 3rd ed., 1999.
- Golub, G. H. & Van Loan, C. F. Matrix Computations. Johns Hopkins University Press, 4th ed., 2013.
- Strang, G. Introduction to Linear Algebra. Wellesley-Cambridge Press, 6th ed., 2023. Positive-definite matrices and factorisations. Lectures: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/.
- Trefethen, L. N. & Bau, D. Numerical Linear Algebra. SIAM, 1997.
Concise online references
- Wiener process / Brownian motion: https://en.wikipedia.org/wiki/Wiener_process
- Itô’s lemma: https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma
- Geometric Brownian motion: https://en.wikipedia.org/wiki/Geometric_Brownian_motion
- Reflection principle: https://en.wikipedia.org/wiki/Reflection_principle_(Wiener_process)
- Brownian bridge: https://en.wikipedia.org/wiki/Brownian_bridge
- Jump diffusion: https://en.wikipedia.org/wiki/Jump_diffusion
- Maximum drawdown: https://en.wikipedia.org/wiki/Maximum_drawdown
- Cholesky decomposition: https://en.wikipedia.org/wiki/Cholesky_decomposition
- Monte Carlo method: https://en.wikipedia.org/wiki/Monte_Carlo_method
Software and data
- NumPy: https://numpy.org/doc/stable/ — vectorised simulation, array operations, and Cholesky factorisation.
- SciPy: https://docs.scipy.org/doc/scipy/ — Gaussian distribution functions and numerical utilities.
- Matplotlib: https://matplotlib.org/stable/ — notebook figures.
- pandas: https://pandas.pydata.org/docs/ — market-data frames, time indexes, and resampling.
- SymPy: https://docs.sympy.org/ — symbolic checks in the Itô-calculus notebook.
- Requests: https://requests.readthedocs.io/ — HTTP access to the market-data endpoint.
Conventions
Trading time is measured using 252 trading days × 6.5 hours × 60 minutes = 98,280 trading minutes per year. Annualised volatility is scaled by the square root of elapsed trading time.