Want to explain or better understand the price LexiFi Apropos just returned? LexiFi gives you an in-depth insight into PDE pricing.
Combining access to the contract and to the pricing code, the PDE Inspector provides on demand all relevant information, in an easy to understand form, allowing for a drill down discovery of the pricing process up to the last bit. For products that can be priced using PDE models, users can obtain details of the PDE pricing process and inspect the price matrix on each relevant date instead of the sole price.
Parameters can be selected for a multi-dimensional PDE model pricing, namely the size of spatial discretisation and time steps. The ‘Pricing script’ section of the page details the steps of PDE resolution derived from the contract. It is a fundamental tool to observe the introduction of path-dependent variables.
LexiFi Apropos provides information and graphs on one-dimension PDE models such as the Garman-Kohlhagen model. Several schemes are also available for two-dimension PDE and a two-dimension representation of price matrix is automatically derived for each value of the underlying and for each variance value (for instance in a Heston model). LexiFi uses efficient numerical methods to solve PDE such as change of variables, interpolation and path-dependant inversion for you to benefit from our know-how.
Figures 1, 2, 3 and 4 below illustrate the example of a PDE pricing of an Autocall, maturity 4 years, coupon 4%, barrier 60%, Strike and autocall level 100%.
Figure 1: Price of the Autocall in function of its underlyings
Greeks for free
Moreover, while having to run several Monte Carlo simulations to calculate options sensitivities, one gets the “greeks” for free using PDE methods.
The plot area of the PDE Inspector page LexiFi Apropos allows to draw and inspect the Price as a function of initial factor values. One may also chose to draw specified derivatives of the Price function (Greeks) instead of the Price itself.
Figure 2: Price sensitivity to the Eurostoxx underlying: first partial derivative of the price in function of the EUROSTOXX
Figure 3: Price sensitivity to the S&P500 underlying: first partial derivative of the price in function of the S&P500
Figure 4: Partial derivative of the price in function of the Euro Stoxx 50 and the S&P 500. This figure illustrates the sensitivity of the Autocall’s price to a joint variation of underlyings