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The volatility models covered Normal Inverse Gaussian and Variance Gamma (modeling exponential Levy processes) and the Heston model (stochastic volatility). The 3 models have in common that Vanilla options can be valued by characteristic functions / Fourier techniques / Cosine methods. Market data used for calibration on the underlyings: FTSE 100, Dax, Allianz, Renault with volatility matrices for different strikes / expiries. Various optimization techniques (for synthetic and market data) were applied across the different models and and the quality of the fit was shown
To jump to the conclusion:
- A clever combination of fast solvers for the forward problem (fourier cosine), domain specific minimization algorithms (hybrid 4D/5D minimization) and powerful and computing muscles (NVIDIA Tesla GPU) reduces computing time drastically
- The parameters obtained exhibited good time stability and robustness
- Different volatility models calibrated to the same market data sets may lead to significantly different prices for exotics. Consequently ultra-fast calibration and valuation is a tool to get insight into model risk
At our booth we presented the results in live examples on a concrete Tesla machine from our partner transtec. An amazing machine with 12 CPU cores and 1800 GPU cores that can be easily placed under a desk.
Pictures: Andreas presenting, and one slide of the talk - performance results (to enlarge click on the picture).