PnL Prediction under Extreme Scenarios

Julien Pantz

Bank of America Merrill Lynch

April 2, 2013

We study the PnL prediction of an option from its Greeks under extreme shocks. In this situation the classical delta gamma approximation fails and adding higher order Greeks does not improve significantly the situation due to the slow convergence of the Taylor’s expansion (which even diverges in the Black-Scholes case). One obvious situation involves a far out of the money option under a scenario pushing the option in the money. Since the Greeks were almost zero initially, the delta-gamma PnL will be almost zero and off the real PnL. Another drawback of expanding further the Taylor’s expansion is the need of high order derivatives which are costly and not reliable especially at the level of the book of a large investment bank derivatives desk. Consequently we find a simple alternative solution involving only 3 deltas which we found by re-interpreting the PnL prediction as a numerical integration problem. More precisely we suggest using the Simpson’s method which predicts correctly the PnL under extreme stressed scenarios.

Number of Pages in PDF File: 8

Keywords: PnL predict, numerical integration, delta-gamma approximation, Trapezoid’s method, Simpson's method, stress testing, scenario hedging

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Date posted: June 20, 2013  

Suggested Citation

Pantz, Julien, PnL Prediction under Extreme Scenarios (April 2, 2013). Available at SSRN: https://ssrn.com/abstract=2281873 or http://dx.doi.org/10.2139/ssrn.2281873

Contact Information

Julien Pantz (Contact Author)
Bank of America Merrill Lynch ( email )
2 King Edward Street
London, EC1A 1HQ
United Kingdom
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