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ASP Course Project

Project List [link]

  • Team Jieqiang Tang: [SABR Simulation] Efficient SABR simulation by Leitao et al
  • Team Junjie Zhang: [BSM Implied Volatility] Analytic approximation of BSM implied volatility (Jackel 2016): implement the method, include it to BSM class and write a thorough test code. In python notebook, summarize the method, write a quick help and report strength and weakness.
  • Team Linsheng Zhuang: [Heston Model]: Option pricing by exact Monte-Carlo + Fast Fourier Transform (FFT) method. Contact me for more information.
  • Team Ting Xie:[Heston Model]: Option pricing by exact Monte-Carlo + Fast Fourier Transform (FFT) method. Contact me for more information.
  • Team Raphael Thomas: Heston model simulation
  • ...

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
    • BSM (lognormal) vs Bachelier (normal) model
    • Spread/Basket/Asian option pricing
    • SABR model and other stochastic volatility models

Repository:

File requirements

  • Core implementation (.py): python class and functions
    • Make sure to comment in detail.
    • Integrate into the pyfe folder. Do not mix with testing/manual notebook files.
  • Documentation/Manual (.ipynb): one Jupyter notebook file briefly describing the method (base theory, equations, SDE, strength/weakness, etc), the function prototype and arguments (manual style) and the usage examples
    • The best examples are from numpy documentation: example
  • Validation/Test (.py): one python file briefly test the code/model.
    • Think creatively how to avoid possible errors. For example,
    • BSM/Normal model: make sure to include the analytic-vs-numerical risk test.
    • SV (SABR/Heston): make sure that the price converge to BSM/Normal if alpha(vov parameter) goes to 0
    • Spread/Basket: make sure that the price is same as single asset BSM if the weigit is 1 for only one asset and zero otherwise.

Other guidelines

  • The contribution will be individually graded. Make sure to show the contribution via github desktop commits (not online upload).
  • The presentation next week doesn't have to be complete. Show your plan and understanding so far, e.g. function prototypes & arguments, etc and the tests to put on.

Suggested Papers

  • [BSM Implied Volatility] Analytic approximation of BSM implied volatility (Jackel 2016): implement the method, include it to BSM class and write a thorough test code. In python notebook, summarize the method, write a quick help and report strength and weakness.

  • [Heston Model]: Option pricing by exact Monte-Carlo + Fast Fourier Transform (FFT) method. Contact me for more information.

  • [SABR approximations] Various improvement to Hagan's original paper: Paulot, Obloj, Balland , etc. Contact me for more information.

  • [SABR Simulation] Efficient SABR simulation by Leitao et al

  • [SABR Simulation/Interpolation] SABR simulation by stochastic sollocation Monte Carlo method ( paper 1, paper 2 )

  • [Vanna-Volga method] a smile interpolation method (Wiki, BSM, normal )

Completed Papers

  • [Normal Implied Volatility] Analytic approximation of normal implied volatility (Choi et al 2007): (Contact me if you want to take this project) implement the method, include it to Normal class and write a thorough test code. In python notebook, summarize the method, write a quick help and report strength and weakness.
  • [Normal Implied Volatility] Analytic approximation of normal implied volatility (Le Floc'h 2016, some discussion): implement the method, include it to Normal class and write a thorough test code. In python notebook, summarize the method, write a quick help and report strength and weakness.
  • [Spread option] Very accurate analytic approximation for spread options by Li et al, 2006. Also implement Kirk's approximation covered in class and (Bjersund, Stensland 2014). Implement each method in a new class. In python notebook, summarize the method, write a quick help and report strength and weakness. Compare the three methods.
  • [Basket+Asian option] Pick one method in the following 3 methods in survey of basket option pricing (Krekel at al, 2004, Wilmott magazine, July, 82-89): Implement the method in a new class. In python notebook, summarize the method, write a quick help and report strength and weakness.
    • a) Beisser's conditional expectation
    • c) Levy's log-normal moment matching
    • d) Ju's Taylor expansion
  • [Basket/Spread/Asian Option] A unified numerical method for both spread and basket options: Choi (2017): Contact me
  • [CEV Model] Option pricing under Constant Elasticity of Variance (CEV) model (formula available many on-line sources): implement the method, include it to Normal class and write a thorough test code. In python notebook, summarize the method, write a quick help and report strength and weakness.
  • [SABR Option Pricing] Arbitrage-free pricing method by Kennedy et al, 2011 (Download): simpler approach introduced in class is enough. Implement the method, create a new class ModelKennedy in sabr.py, and write a thorough test code. In python notebook, summarize the method, write a quick help and report strength and weakness.
  • [SABR Calibration] Efficient first guess for SABR calibrations to 3 option prices by Le Floc’h and Kennedy, 2014 (see also here): Implement the method, add to sabr.py, and write a code comparing the efficient against the dumb initial guess. In python notebook, summarize the method, write a quick help and report strength and weakness.