The Use of Numeraires in Multi-Dimensional Black-Scholes Partial Differential Equations

Stochastic differential equations and the Black - Scholes PDE

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

Spectral Approximation of Infinite-Dimensional Black-Scholes Equations with Memory

This paper considers the pricing of a European option using a B, S -market in which the stock price and the asset in the riskless bank account both have hereditary price structures described by the authors of this paper 1999 . Under the smoothness assumption of the payoff function, it is shown that the infinite dimensional Black-Scholes equation possesses a unique classical solution. A spectral...

The use of iterative methods for solving Black-Scholes equation

On Nonlinear Black-Scholes Equations

This paper revisits some solution methods for Black-Scholes equation and some of its nonlinear versions arising in option pricing theory.

Finite integration method for solving multi-dimensional partial differential equations

Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial B...