Calibration associated to a given pricing operation involves essentially finding the parameters that best fit available market data given the pricing model to be used.
In the LexiFi Apropos solution, users access a long list of market and proprietary pricing models (the list of supported pricing models can be found here), as well as consistent, high-quality financial market data. Each pricing model has an associated fully documented calibration methodology. LexiFi’s quants provide upon request documentation detailing all model inputs, market data, model choice, calibration assumptions, calendars and more.
Models are automatically pre-calibrated, but always allow for user custom calibration when needed. Users have access to model calibration pages where they can edit both model and calibration parameters as shown in Figure 1 or run calibrations in one click and inspect results in depth.
An automatic cache allows saving and sharing calibration results across multiple pricing jobs as illustrated in Figure 2 with the saved results tab. Calibration results are displayed both in tables and charts, for easy but in-depth analysis.
Dedicated calibration inspectors are available for all models and allow, for instance, to:
Figure 1: An example of the calibration page for the Heston model, where parameters are automatically set, but can also be customized by the user.
Figure 2: Saved Heston model calibration results: shows saved calibration results under the name “Benchmark” using Heston as the model to calibrate EUROSTOXX 50 Index market data.
The local Volatility model calibration example
We have selected the Local Volatility model, as it is widely used by our clients, to show the customization and result discovery possibilities that calibration pages offer to users. We use the EUROSTOXX 50 Index. Figure 3 below shows that users can customize data and parameters as follows:
Figure 3: Calibration user interface for the Local Volatility model
Once the model is calibrated, results are available in both tabular form and as interactive graphical display (same for every models):
Figure 4 :table of Calibration results of the Local Volatility model in a tabular layout. Quoted market data vs. calibration results with the calculated error in basis points and percentage. Monte Carlo pricing results with associated calculated error in basis points and percentages followed by the Regularized implied volatility results calibration.
Figure 5: Volatility surface 3D chart
Figure 6: Implied volatility slice Chart