Implementation - 2023.2 English

Vitis Libraries

Release Date
2023.2 English

In the Theory Section, the pricing process is described. However, this process can only be executed in the condition of Equation (3) is given. This means that the coefficients in Equation (3) must be calculated first. This calculation process is called Calibration and executes prior to the Pricing process. Therefore, in the implementation, the American Monte Carlo Engine contains two processes: Calibration and Pricing, as illustrated in Figure 60.

The McAmericanEngine structure
th: 50%


Why two processes are required in MCAmericanEngine and only one process, pricing, is enough for European Option Monte Carlo engine?

For European Option, the exercise price of the stork at the last time step \(T\) needs to be and only need to be calculated. However, for American Option, the exercise price of the stock at all time steps \(t, 0 \leq t \leq T\) are required to be computed. Therefore, the mathematical model of American Option Monte Carlo employs several basis functions, refer to Equation (3).
In the aspect of basis functions, the European Option employed only one basis function: \(S_T\), where \(T\) is the maturity date. By introducing multiple basis functions, the coefficients are also introduced. Thus, the calibration process is deployed to compute these coefficients.