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Quant Finance Topics

  • Below is an overview of quant finance topics limited by my knowledge and biased by my research

General Tips

  • Pick practical topic. Beneficial to your job or future career?
  • Pay attention to practitioner journals:
    • Risk Magazine: Link
    • Journal of Computational Finance: Link
    • Wilmott Magazine: Link
    • Journal of Derivatives: Link
    • Journal of Portfolio Management: Link
    • Financial Analysts Journal: Link
    • Journal of Financial Data Science: Link
    • Digital Finance: Link
  • Use online resources (Q&A, forum, code, etc):
    • Quantitative Finance Stack Exchange: Link
    • Wilmott Forum: Link. Technical Forum, Trading Forum, Numerical Methods Forum.
    • Quantopian (The Place For Learning Quant Finance): Link
    • Wikipedia / Baidu / Google
    • Github.com (Cite the source!!)

Sell Side Research

  • Relatively more established as a academic field: easier to find literature, easier to add contribution
  • For sell vs buy side, read

Goals of Research

  • How to model financial time series / stochastic process?
    • New process to better fit real data?
    • Mathematically tractable model?
  • Fast and accurate numerical method
    • Efficient pricing of various derivative products
    • Fast simulation for Monte-Carlo method (Variance reduction?)
    • Calibration of model parameters to market prices
  • How to price new derivative product?
    • Method (analytic or MC) available?
  • New model to correctly capture the price from market or real time series?

Stochastic Processes

  • Geometric Browniam Motion: Black-Scholes model
  • Arithmetic BM: Normal (Bachelier) Model
    • [MA Thesis] Wang, Y. (2020). Barrier Option Pricing under Normal Model [Mathesis]. Peking University HSBC Business School.
  • Ornstein-Uhlenbeck (OU) Process: Wiki
  • Constant-Elasticity-Of-Variance (CEV) Model: Wiki
  • Stochastic Volatility Models: see Wiki for SDE.
    • Heston Model: Heston, S.L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6, 327–343. https://doi.org/10.1093/rfs/6.2.327
    • SABR Model: Hagan, P.S., Kumar, D., Lesniewski, A.S., Woodward, D.E. (2002). Managing smile risk. Wilmott Magazine 2002, 84–108.
    • 3/2 Model: Creator unclear.
    • 4/2 Model: Grasselli, M. (2017). The 4/2 Stochastic Volatility Model: A Unified Approach for the Heston and the 3/2 Model. Mathematical Finance 27, 1013–1034. https://doi.org/10.1111/mafi.12124
    • [MA Thesis] Zhang, S. (2020). Using Gaussian Process Regression to Improve the Analytic Approximation Accuracy of Equivalent Volatility in SABR model [Mathesis]. Peking University HSBC Business School.
    • [MA Thesis] Zhuang, L. (2020). Generalized Hyperbolic Distribution: Approximation and Estimation [Mathesis]. Peking University HSBC Business School.
    • [MA Thesis (Best Thesis Award)] Gong, L. (2021). A Normal and Lognormal Hybrid Model for Pricing Interest Rate Derivatives [Mathesis]. Peking University HSBC Business School.
  • Jump diffusion:
  • Rough Volatility (Fractional Brownian Motion, Wiki)

Derivative Products (Payout)

  • Spread/Basket/Asian Option
    • Krekel, M., de Kock, J., Korn, R., Man, T.-K. (2004). An analysis of pricing methods for basket options. Wilmott Magazine 2004, 82–89.
    • 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
    • Fu, L. (2019). Pricing Basket Options with Equivalent Bachelier Model (MA thesis). Peking University HSBC Business School, Shenzhen, China.
  • Timer Option
  • Barrier Option (Knock-in, Knock-out), Rainbow Option, Lookback Option, Compound Option, Etc
  • Cliquet Option
  • Parisian Option
  • American/Bermudan Option
  • VIX Index (Future, Options on Futures, Etc)
  • Variance Swap

Monte-Carlo Simulation

  • Heston Model:
  • 3/2 Model: Baldeaux, J. (2012). Exact simulation of the 3/2 model. Int. J. Theor. Appl. Finan. 15, 1250032. https://doi.org/10.1142/S021902491250032X
  • SABR Model: Cai, N., Song, Y., Chen, N. (2017). Exact Simulation of the SABR Model. Operations Research 65, 931–951. https://doi.org/10.1287/opre.2017.1617 | Choi, J., Liu, C., Seo, B.K. (2019). Hyperbolic normal stochastic volatility model. Journal of Futures Markets 39, 186–204. https://doi.org/10.1002/fut.21967
  • OU Stochastic Volatility Model: 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
  • Example Thesis:
    • [MA Thesis] Chang, X. (2021). The Faster Almost Exact simulation on OUSV model [Mathesis]. Peking University HSBC Business School.
    • [MA Thesis] Wang, C. (2022). A New Method for Almost Exact Simulation of Heston Stochastic Volatility Model [Mathesis]. Peking University HSBC Business School.

Mix and Match for new contribution (The combinations are unlimited !)

  • Model + Product
  • Model + Method
  • Model + Trading Strategy
  • XXX + China Market Data

Caution

  • Stochastic Process
    • What is the characteristics of stochastic processes?
    • Why are they popular? What are the strength/weakness?
  • Derivatives
    • What is the economic background of the derivative products?
    • Why certain products are popular?

Buy Side Research

  • Asset management, Portfolio allocation, Trading strategy.
  • Sometimes the outcome is not published as academic research.

Portfolio Selection/Optimization

  • Minimum variance portfolio
  • Smart Beta (factor investing)
  • Risk parity portfolio (Wiki; Equal Risk Contribution): very popular in asset management industry.
    • Maillard, S., Roncalli, T., Teïletche, J. (2010). The Properties of Equally Weighted Risk Contribution Portfolios. The Journal of Portfolio Management 36, 60–70. https://doi.org/10.3905/jpm.2010.36.4.060
    • Chaves, D., Hsu, J., Li, F., Shakernia, O. (2012). Efficient Algorithms for Computing Risk Parity Portfolio Weights. The Journal of Investing 21, 150–163. https://doi.org/10.3905/joi.2012.21.3.150
    • [MA Thesis] Chen, R. (2021). Multidimensional Root Finding Method for Solving Risk Parity Model [Mathesis]. Peking University HSBC Business School.

Trading Strategy

  • Alpha signal:
  • Can machine learning predict outperforming strategy given economic situation?
  • Consider uncommon asset class (e.g., not equity): commodity, interest rates, FX, etc.

Caution

  • Just showing good performance of strategy is NOT enough.
  • Either need add academic connection or show effort.

FinTech Topics

Bitcoin Literature Review: Link

Crypto + Quant Finance

  • Bitcoin Option Pricing: which process fits bitcoin option markets better?
  • VIX index in Cyprocurrency: Alexander, C., & Imeraj, A. (2019). The Crypto Investor Fear Gauge and the Bitcoin Variance Risk Premium. SSRN Electronic Journal. https://papers.ssrn.com/abstract=3456853

Financial Machine Learning:

  • Current focus is in asset pricing (return prediction)
  • You may often need massive data + computation power. Check availability before!
  • Often there are room for simple but good idea. Consider Replacing linear regression with ML methods?
  • Software tool is readily available (sklearn, keras/tensorflow, pytorch, etc)
  • Extra new information with Natural Language Processing (NLP).
  • ML method may help you future career!

Books and Journals

Papers

  • Gu, S., Kelly, B., & Xiu, D. (2020). Empirical Asset Pricing via Machine Learning. The Review of Financial Studies, 33(5), 2223–2273. https://doi.org/10.1093/rfs/hhaa009 [SSRN]
    • [MA Thesis] Zhou, J. (2021). Empirical asset pricing via machine learning in the Chinese Stock Market [Mathesis]. Peking University HSBC Business School.
  • Gu, S., Kelly, B., & Xiu, D. (2020). Autoencoder asset pricing models. Journal of Econometrics. https://doi.org/10.1016/j.jeconom.2020.07.009
    • [MA Thesis] Yu, X. (2021). Autoencoder Asset Pricing Models in China Stock Market [Mathesis]. Peking University HSBC Business School.
  • Giglio, S., Liao, Y., & Xiu, D. (2021). Thousands of Alpha Tests. The Review of Financial Studies, 34(7), 3456–3496. https://doi.org/10.1093/rfs/hhaa111
  • Li, K., Mai, F., Shen, R., & Yan, X. (2021). Measuring Corporate Culture Using Machine Learning. The Review of Financial Studies, 34(7), 3265–3315. https://doi.org/10.1093/rfs/hhaa079
  • Moritz, B., Zimmermann, T. (2016). Tree-Based Conditional Portfolio Sorts: The Relation between Past and Future Stock Returns. SSRN Journal. https://doi.org/10.2139/ssrn.2740751
  • Chen, L., Pelger, M., Zhu, J. (2019). Deep Learning in Asset Pricing. SSRN Journal. https://doi.org/10.2139/ssrn.3350138
  • Lopez de Prado, M. (2019). Ten Applications of Financial Machine Learning. SSRN Electronic Journal. https://ssrn.com/abstract=3365271

Other Thesis Examples

  • Long, Shuyi (2019). Smart Beta Investing: A New Method Based on Machine Learning and Black-Litterman Model [Mathesis]. Peking University HSBC Business School.
    • Used the probability outcome of ML as in input of the Black-Litterman (asset management) model
  • Ge, Desheng (2020). How can the yield curve predict an economic recession? [Mathesis]. Peking University HSBC Business School.
    • The negative US Treasury yield spread (e.g., 10y - 3m) is considered as the best recession indicator. This paper verify that the yield curve spread (long - short) is indeed the best recession indicator. But the pair and coefficients can be slightly different.