Time discretization of diffusion equations: convergence of the functional scheme derived from the binomial tree with local volatility.

Julien Baptiste (1, 2) , Emmanuel Lépinette (2)

1 PSL - Université Paris Sciences et Lettres
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We introduce a seemingly new functional scheme which approximates diffusion equations. Contrarily to classical numerical methods, in particular finite difference methods, the principle is only based on a discretization in time. We establish the uniform convergence in time of the scheme and provide the rate of convergence. We illustrate the convergence by numerical examples .

Mots clés: Liquidation value; Financial market models; Transaction costs; European options

Domaines: Equations aux dérivées partielles [math.AP]

Julien Baptiste, Emmanuel Lépinette. Time discretization of diffusion equations: convergence of the functional scheme derived from the binomial tree with local volatility.. 2017. ⟨hal-01507267v2⟩