Calibration of financial models is both science and art—and a really demanding task sometimes. Visixion recently added a number of pre-calibrated objects to DEXISION to allow for a simple and fast valuation of derivatives in a market-consistent manner.
Of course, every specific market-based valuation or pricing task leads in general to specific requirements regarding the calibration of financial models used. However, to have available pre-calibrated base objects in DEXISION simplifies and speeds up the task significantly.
Over night, the DEXISION server re-calibrates the following models for the DAX index:
- Merton (1976) jump diffusion model: a model adding a stochastic jump component to the Black-Scholes model
- Heston (1993) stochastic volatility model: a widely used model to account for stochastic volatility and related market phenomena (e.g. implied volatility surface)
- Bates (1996) stochastic volatility jump diffusion model: a model combining the Merton (1976) and Heston (1993) models
It is well-known that short-term option pricing has to take into account possible jumps of the respective index. It is also well-known that stochastic volatility is generally needed to account for the volatility term structure. Against this background, DEXISION now offers the right model for both short-term options on the DAX and mid-/long-term options on the DAX. In addition, the Bates (1996) model can be used for portfolios comprising options of all kinds of maturities.
Moreover, it is also well-known that the longer the option maturity the more important becomes the modeling of the short rate used for risk-neutral discounting. Therefore, DEXISION now also offers a calibrated Cox, Ingersoll and Ross (1985) short rate model (square-root diffusion). This model takes as input data German Bund yields.
The DAX-calibrated objects currently come with any DEXISION license. Calibrated objects with regard to other indices and markets upon request.