pde_setup: Setting up PDE problem

In shill1729/FeynmanKacSolver: Feynman-Kac PDE solver for Ito diffusions and processes

Description

Sets up grid and function evaluations over grid to create tridiagonal system coefficients for the solver to take.

Usage

pde_setup(f, contract_specs, numeric_specs)

Arguments

f	the list of coefficient functions (f.mu, f.vo, f.rate)
contract_specs	list of variables defining contract specifications, see details
numeric_specs	list of variables defining numerical specifications, see details

Details

A basic discretization scheme is used, functions are evaluated via loops then coefficients are returned in a list. For risk neutral pricing the drift and rate functions should match. The list contract_specs must contain

• spot numeric, the spot price

• div numeric, the dividend yield rate

• maturity numeric, the time until expiration in trading years (DTE/252)

• payoff the payoff name: "put", "call", "strangle", "straddle", "iron_condor", "put_debit", "call_debit", "indicator" and "cdf"

• payoff_param list of parameters for the payoff function

, while the list numeric_specs should contain

• N time-resolution (integer)

• M space-resolution (integer)

• B boundary for the log-price space, which can be optional

Value

list containing

• grid.x, a discretized interval of the spatial/price variable

• grid.t, a discretized interval of the time variable

• alpha, the lower diagonal in the tridiagonal matrix in the linear system resulting from the discretized PDE

• beta, the diagonal in the tridiagonal matrix in the linear system resulting from the discretized PDE

• delta, the upper diagonal in the tridiagonal matrix in the linear system resulting from the discretized PDE

• spot, the given spot price, needed to be passed to pde_solve

• div, the dividend rate, also needed to be passed to pde_solve

• m, the drift rate at the current time and price level

• v, the volatility at the current time and price level

• r, the risk-free rate, at the current time and price level

shill1729/FeynmanKacSolver documentation built on May 19, 2020, 8:23 p.m.