We know that decomposition is the base of problem solving, so we break down a contract into smaller parts to both understand and price it better.
Some products can indeed be reduced to characteristics that allow the pricing using a ‘Static Replication’ model, which is the one that generates the best price.
This pricing model is particularly accurate because it computes the price using only market information. Don’t worry about the selection of model parameters, LexiFi Apropos does it automatically for asset classes and volatility interpolation.
The first step of the pricing routine is a decomposition process of the contract in subcontracts. Each subcontract is independent and has its own pricing computation. For each subcontract, in addition to the price, the software creates replication strategies and calculates discount rate, forward, payoff description and Greek parameters. From this it compute the global product price and product Greeks.
As usual LexiFi’s clients have the possibility to further inspect the process and have more information about each subcontract strategy. Inspect the strategy’s final payoff and look at the graph of the density of the underlying at the maturity. The red dots in the middle of the graph correspond to the underlying strategy’s strike prices and the outside dots are the values of the strategy at the boundaries.
All the details of the replication portfolio, such as weights, prices and associated Greeks, are rigorously registered in LexiFi’s groundbreaking Algebra language, so that it is possible to use the contract also outside the static replication pricing model.
Figure 1: Details of a pricing by static replication
Figure 2: Greek parameters are available for each simulation of a pricing by static replication