# 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.