[Quantlib-users] calculating option price with PDE solver

[Yevgeniy G. <yev...@la...>]

Hi,

we're trying to use QuantLib PDE solver to calculate option prices (calls and puts).  Our final code will include vol adjustment based on time, but for the first version we're trying to implement a call option price with a constant vol.

The results I'm getting don't match the expected: the red line shows intrinsic value of the option (y) depending on percent strike (x).  The blue line is calculated by PDE.

[cid:image001.png@01D82358.969B6450]

Can you help finding the error?

Here's the code:

from typing import List
import QuantLib as ql
import numpy as np
import pylab as pl

class DiffusionOperator:
    def __init__(self, t_max: float, x_values: List[float], cur_vals_t: List[float]):
        self.__mesher = ql.FdmMesherComposite( ql.Predefined1dMesher(x_values))
        self.__t_max = t_max
        self.__n = len(x_values)
        self.__x_values = ql.Array(x_values)
        self.__cur_vals_t = ql.Array(cur_vals_t)
        self.__dx = ql.FirstDerivativeOp(0, self.__mesher)
        self.__ddx = ql.SecondDerivativeOp(0, self.__mesher)
        self.__map = ql.TripleBandLinearOp(0, self.__mesher)

    def size(self) -> int:
        return 1

    def setTime(self, t1: float, t2: float):
        self.__map.axpyb( ql.Array(1, 1.0), self.__dx, self.__ddx.mult(self.__cur_vals_t), ql.Array())

    def apply(self, r: ql.Array) -> ql.Array:
        return self.__map.apply(r)

    def solve_splitting(self, direction: int, r: ql.Array, dt: float) -> ql.Array:
        return self.__map.solve_splitting(r, dt, 1.0)

if __name__ == "__main__":
    n_points = 500; n_time_steps = 800; x_min = 0.1; x_max = 4; t_max = 0.2; bs_vol = 0.1;
    x_values = np.arange(x_min, x_max + 1e-8, (x_max - x_min) / (n_points - 1))
    cur_values_t = 0.5 * bs_vol**2 * x_values*x_values
    y0 = np.maximum(0, 1 - x_values)
    y_values = ql.Array( list(y0.copy()) )
    op = DiffusionOperator(t_max, list(x_values), list(cur_values_t))
    mesher = ql.FdmMesherComposite(ql.Predefined1dMesher(x_values))
    solver = ql.FdmBackwardSolver(
        ql.FdmLinearOpCompositeProxy(op),
        ql.FdmBoundaryConditionSet(
            [ql.FdmDirichletBoundary(mesher, 1, 0, ql.FdmBoundaryCondition.Lower),
            ql.FdmDirichletBoundary(mesher, 0, 0, ql.FdmBoundaryCondition.Upper)]  ),
        ql.FdmStepConditionComposite(ql.DoubleVector(), ql.FdmStepConditionVector()),
        ql.FdmSchemeDesc.CrankNicolson()
    )
    solver.rollback(y_values, t_max, 0.0, n_time_steps, 0)
    pl.plot(x_values, y_values, '.')
    pl.plot(x_values, y0, 'r-')
    pl.show()





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