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ASP Course Project

Repository

List of Projects

Presentation and Deadline

  • Presentation: 10.27 (Thurs) 20 minutes by each group.
  • Pull request deadline: 11.01 (Tues)

File requirements

  • PyFENG repository:
    • Core implementation (.py): python class and functions
    • Make sure to add docstring in detail.
      • Example: bsm.py
      • Specify equation/formula number or page in the original paper
      • The best examples of docstring are from numpy documentation: example
    • Integrate into the PyFENG repository by making pull-requests (pr).
    • Do not place any .ipynb file.
  • Your repository (PHBS_ASP_2021 or any name is OK)
    • Test (.ipynb): one Jupyter notebook file briefly describing the method (base theory, equations, SDE, strength/weakness, etc).
    • Include some test examples (e.g., the same parameter sets from the paper)
  • See past years' proejct:

Project Topics

Topics

  • Among the topics and HWs covered in the class, choose an in-depth research on one topic. You are also welcome to do the project on your own original idea. Otherwise, pick one from my suggestions which are basically understanding and implementing literatures. Topics includes
    • Spread/Basket/Asian option pricing
    • SV models (SABR, Heston, etc)
    • Rough volatility
    • Copula

* Rough Volatility

* Spread/Basket/Asian Option

  • [Partially implemented] 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. https://doi.org/10.1002/fut.21909
  • [Most methods implemented] Krekel M, de Kock J, Korn R, Man T-K (2004) An analysis of pricing methods for basket options. Wilmott Magazine 2004:82–89

Option pricing with Fourier Transform

* GARCH-diffusion model

  • [Implemented] Barone-Adesi G, Rasmussen H, Ravanelli C (2005) An option pricing formula for the GARCH diffusion model. Computational Statistics & Data Analysis 49:287–310. https://doi.org/10.1016/j.csda.2004.05.014
  • Tubikanec I, Tamborrino M, Lansky P, Buckwar E (2021) Qualitative properties of numerical methods for the inhomogeneous geometric Brownian motion. arXiv:200310193 [cs, math] http://arxiv.org/abs/2003.10193
  • [Implemented] Euler/Milstein/Log scheme (in class)
  • [????] Capriotti L, Jiang Y, Shaimerdenova G (2018) Approximation methods for inhomogeneous geometric brownian motion. Int J Theor Appl Finan 22:1850055. https://doi.org/10.1142/S0219024918500553
  • IGBM: Zhao B (2009) Inhomogeneous Geometric Brownian Motion. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.1429449
  • [Consider] PhD Thesis of Ravanelli, C., University of Lugano, Switzerland, https://doc.rero.ch/record/4229/files/1_2003ECO001.pdf
  • [No method] Papadopoulos, Y.A., Lewis, A.L., 2018. A First Option Calibration of the GARCH Diffusion Model by a PDE Method. arXiv:1801.06141 [q-fin].

* SABR model

  • [Implemented but not verified] Cai N, Song Y, Chen N (2017) Exact Simulation of the SABR Model. Oper Res 65:931–951. https://doi.org/10.1287/opre.2017.1617
  • [Implemented but not verified] Leitao Á, Grzelak LA, Oosterlee CW (2017) On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options. Applied Mathematics and Computation 293:461–479. https://doi.org/10.1016/j.amc.2016.08.030

* Heston Model (SV)

  • [No need] Broadie M, Kaya Ö (2006) Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes. Operations Research 54:217–231. https://doi.org/10.1287/opre.1050.0247
  • [Implemented] Glasserman P, Kim K-K (2011) Gamma expansion of the Heston stochastic volatility model. Finance Stoch 15:267–296. https://doi.org/10.1007/s00780-009-0115-y
  • [Implemented] Andersen, L., 2008. Simple and efficient simulation of the Heston stochastic volatility model. The Journal of Computational Finance 11, 1–42. https://doi.org/10.21314/JCF.2008.189
  • [Implemented / 2022 Thesis] Almost exact simulation

* OUSV Model

  • [Implemented] Euler/Milstein
  • [Implemented] Li C, Wu L (2019) Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model. European Journal of Operational Research 275:768–779. https://doi.org/10.1016/j.ejor.2018.11.057
  • [2021 Thesis] Almost exact simulation

* 3/2 SV model

  • [Implemented but not verified] Baldeaux, J., 2012. Exact simulation of the 3/2 model. Int. J. Theor. Appl. Finan. 15, 1250032. https://doi.org/10.1142/S021902491250032X
  • [Implemented but not verified] Almost exact simulation

* Other Simulation-related Papers

  • [Implemented but not verified] General SDE: Beskos, A., Roberts, G.O., 2005. Exact simulation of diffusions. Ann. Appl. Probab. 15, 2422–2444. https://doi.org/10.1214/105051605000000485
  • [Implemented] Computing Moments from Laplace Transform: Choudhury, G.L., Lucantoni, D.M., 1996. Numerical Computation of the Moments of a Probability Distribution from its Transform. Operations Research 44, 368–381. https://doi.org/10.1287/opre.44.2.368

Exotic Derivatives

  • Timer Option
  • SABR Model Simulation
    • Chen B, Oosterlee CW, Van Der Weide H (2012) A low-bias simulation scheme for the SABR stochastic volatility model. Int J Theor Appl Finan 15:1250016. https://doi.org/10.1142/S0219024912500161
    • [Implemented but not verified] Leitao Á, Grzelak LA, Oosterlee CW (2017) On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options. Applied Mathematics and Computation 293:461–479. https://doi.org/10.1016/j.amc.2016.08.030
  • Stochastic volatility inspired (SVI) model (1-person project)
  • Snowball
    • Recently very popular in China. Link

Old Topics