Option Pricing

The repository is a re-factorization (and some extensions) of the code for an FNCE40009 Advanced Derivative Securities assignment.

This repository is mainly designed for those who want to study option pricing. It is built purely on standard NumPy and SciPy packages.

I've tried my best to utilize the speed offered by NumPy array operations rather than using multiple for-loops, without sacrificing the ability to refer the code back to the equations in the textbook.

Debug/Improvements/AddOns will be implemented from time to time.

If you have any questions or want to report a bug, please open an issue. I am open to any corrections/suggestions. If you like it, or if it benefits you in some way, kindly give it a star 😊.

Reference: most of this repository implements algorithms described in the following textbook.

@book{mcdonald2013derivatives,
  title={Derivatives markets (3rd edition)},
  author={McDonald, Robert Lynch},
  year={2013},
  publisher={Pearson Education}
}

Binomial Excel Illustration

Black-Scholes-Merton (BSM)

How to use: example_BSM.py

• Chapter 12.1: European call call_value(), European put put_value()
• Chapter 12.2: (class) GarmanKohlhagenForex
• Chapter 12.5: implied volatility assume BSM model implied_vol()
• Chapter 21.5: Merton jump diffusion merton_jump_diffusion()
• Chapter 22: Exotic options (barrier options) cash_or_nothing_barrier_options()
• Appendix 12.B: delta(), gamma(), theta(), vega(), rho(), psi()

Monte Carlo Simulation

How to use: example_monte_carlo.py

• Chapter 18 & 19.3: stock_price_simulation()
• Chapter 19.8: stock_price_simulation_with_poisson_jump()

The final predicted price is the average of all simulated prices at time T (column T).

Stock price S	h	2h	3h	...	T-h	T
simulation 1						S1,T
simulation 2						S2,T
simulation 3						S3,T
...						...

• vasicek() and cox_ingersoll_ross_model(): stochastic interest rate (work-in-progress).
• heston(): stochastic volatility.

Note: the default case is two tables with constant values. Call these two functions before running stock_price_simulation().

Interest rate r	h	2h	3h	...	T-h	T
simulation 1						r1,T
simulation 2						r2,T
simulation 3						r3,T
...						...

Volatility σ	h	2h	3h	...	T-h	T
simulation 1						σ1,T
simulation 2						σ2,T
simulation 3						σ3,T
...						...

• Chapter 19.4: european_call() & european_put()
• Chapter 14.2 & 19.4: asian_avg_price()
• Chapter 19.6: american_option_longstaff_schwartz(), Longstaff & Schwartz (2001).
• Chapter 14 & 23: exotic options, e.g. barrier_option()
• Chapter 23, exercise 23.12: look_back_european()

More References:

• Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of financial economics, 3(1-2), 125-144.
• Garman, M. B. and Kohlhagen, S. W. (1983). "Foreign Currency Option Values." Journal of International Money and Finance 2, 231-237.
• Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: a simple least-squares approach. The review of financial studies, 14(1), 113-147.

For Fun: