PyfengForPapers

A collection of Jupyter notebooks (.ipynb) using the PyFENG package to reproduce results from financial engineering papers. PyFENG is pre-installed on Google Colab — click any badge to run. See PyFENG Installation for local setup.

List of Implemented Papers

• notebook
  • Choi J (2025) Exact simulation scheme for the Ornstein–Uhlenbeck driven stochastic volatility model with the Karhunen–Loève expansions. Operations Research Letters, 60:107280 [DOI | arXiv | SSRN]
• notebook
  • Choi J, Huh J & Su N (2024). Tighter ‘uniform bounds for Black–Scholes implied volatility’ and the applications to root-finding. Operations Research Letters, 57, 107189 [DOI | arXiv | SSRN]
• notebook
  • Choi J & Seo BK (2024). Option pricing under the normal SABR model with Gaussian quadratures. Journal of Computational Finance, 28(2), 1-20 [DOI | arXiv | SSRN]
• notebook
  • Choi J (2023). Equivalent CEV Volatility. Bloomberg Quant Seminar.
• notebook
  • Choi J & Chen R (2022). Improved iterative methods for solving risk parity portfolio. Journal of Derivatives and Quantitative Studies, 30(2), 114-124 [DOI | arXiv | SSRN]
• notebook
  • Choi J et al. (2022). A Black-Scholes user’s guide to the Bachelier model. Journal of Futures Markets, 42(5), 959-980 [DOI | arXiv | SSRN]
• notebook
  • Choi J & Wu L (2021). A note on the option price and ‘Mass at zero in the uncorrelated SABR model and implied volatility asymptotics.’ Quantitative Finance, 21, 1083 [DOI | arXiv | SSRN]
• notebook
  • Choi J & Wu L (2021). The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model. Journal of Economic Dynamics and Control, 128, 104143 [DOI | arXiv | SSRN]
• notebook
  • Choi J, Liu C, & Seo BK (2019). Hyperbolic normal stochastic volatility model. Journal of Futures Markets, 39(2), 186–204 [DOI | arXiv | SSRN]
• notebook
  • Bernard C, Cui Z (2014). Prices and Asymptotics for Discrete Variance Swaps. Applied Mathematical Finance, 21(2), 140-173 [DOI | arXiv]
• notebook
  • Several SABR Model papers by Antonov and co-authors.
  • Antonov A, & Spector M (2012). Advanced analytics for the SABR model [SSRN]
  • Antonov A, Konikov M, & Spector M (2013). SABR spreads its wings. Risk, 2013(Aug), 58–63
  • Antonov A, Konikov M, & Spector M (2019). Modern SABR Analytics. Springer International Publishing [DOI]
• notebook
  • Baldeaux J (2012). Exact simulation of the 3/2 model. International Journal of Theoretical and Applied Finance, 15:1250032 [DOI | arXiv]
• notebook
  • Wu X-Y, Ma C-Q, Wang S-Y (2012). Warrant pricing under GARCH diffusion model. Economic Modelling, 29:2237-2244 [DOI]
• notebook
  • Krekel M, de Kock J, Korn R, & Man TK (2004). An analysis of pricing methods for basket options. Wilmott Magazine, 2004(7), 82–89
• notebook
  • Barone-Adesi G, Rasmussen H, Ravanelli C (2005). An option pricing formula for the GARCH diffusion model. Computational Statistics & Data Analysis 49:287–310 [DOI]
• notebook
  • Ball CA, Roma A (1994). Stochastic Volatility Option Pricing. Journal of Financial and Quantitative Analysis 29:589–607 [DOI]
• notebook
  • Schöbel R, Zhu J (1999). Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension. Review of Finance 3:23–46 [DOI]
• notebook
  • Choudhury GL, Lucantoni DM (1996). Numerical Computation of the Moments of a Probability Distribution from its Transform. Operations Research, 44:368-381 [DOI]
• (notebook coming soon)
  • Choi J (2018). Sum of all Black-Scholes-Merton models: An efficient pricing method for spread, basket, and Asian options. Journal of Futures Markets, 38:627–644 [DOI | arXiv | SSRN]

PyFENG Installation

• For the first-time installation,

  pip install pyfeng

• For an upgrade,

  pip install --upgrade pyfeng

• If running on your modified implementation,
  • Make a local copy of PyFENG repository by forking or download
  • Make necessary modifications
  • Uncomment the following lines in the beginning of notebook file. Then, the local PyFENG will be used

    %load_ext autoreload
    %autoreload 2

    import sys
    sys.path.insert(sys.path.index('')+1, 'PATH_TO_LOCAL_PYFENG')