To show achievements, barriers and traps related to the calibration of complex volatility models and the implications and the valuation of exotic options, Andreas discussed in his talk the ability to find an optimization algorithm that delivers model parameter in seconds, the robustness of the parameters and how do the prices of exotic options depend on the chosen model.
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).