Physics:Bachelier model
The Bachelier model is the name given by a model of an asset price under brownian motion presented by Louis Bachelier on his PhD thesis The Theory of Speculation (Théorie de la spéculation, published 1900). It is also called "Normal Model" equivalently (as opposed to "Log-Normal Model" or "Black-Scholes Model"). On the day of 2020-04-08, CME Group posted the note CME Clearing Plan to Address the Potential of a Negative Underlying in Certain Energy Options Contracts,[1] saying that after a threshold on price, it would change energy options model from Geometric Brownian Motion model and Black–Scholes model to Bachelier model. In the day 2020-04-20, oil futures reached for first time in history negative values,[2] where Bachelier model took an important role in option pricing and risk management.
The European analytic formula for this model based on risk neutral argument is derived in Analytic Formula for the European Normal Black Scholes Formula (Kazuhiro Iwasawa, New York University, December 2nd, 2001). [3]
The implied volatility under the Bachelier model can be obtained by an accurate numerical approximation.[4]
References
- ↑ "CME Clearing Plan to Address the Potential of a Negative Underlying in Certain Energy Options Contracts". https://www.cmegroup.com/notices/clearing/2020/04/Chadv20-152.html.
- ↑ "An oil futures contract expiring Tuesday went negative in bizarre move showing a demand collapse". 15 December 2003. https://www.cnbc.com/2020/04/20/oil-markets-us-crude-futures-in-focus-as-coronavirus-dents-demand.html. Retrieved 21 April 2020.
- ↑ "Analytic Formula for the European Normal Black Scholes Formula". 2 December 2001. https://www.scribd.com/document/403818289/normal-swaptions-pdf.
- ↑ Choi, Jaehyuk; Kim, Kwangmoon; Kwak, Minsuk (2009). "Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion". Applied Mathematical Finance 16 (3): 261–268. doi:10.1080/13504860802583436. https://www.tandfonline.com/doi/full/10.1080/13504860802583436.
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