.. _sphx_glr_api_gallery_pde_methods_multi_factor:

Multi-factor
------------

Two state variables without a two-dimensional linear solve: the
alternating-direction implicit scheme.


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    <div class="sphx-glr-thumbcontainer" tooltip="With two assets every implicit step couples a whole plane of unknowns. Donald Peaceman and Henry Rachford (1955), modelling oil reservoirs, split each step into two half steps, each implicit in one direction only, so that a step is a set of independent tridiagonal solves. PeacemanRachfordADI prices Margrabe&#x27;s option to exchange one asset for another, whose exact value is Black-Scholes with the second asset as the strike and the volatility of the ratio, \sqrt{\sigma_1^2 + \sigma_2^2 - 2\rho\sigma_1\sigma_2}.">

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  :doc:`/api/gallery/pde_methods/multi_factor/plot_01_peaceman_rachford_adi`

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   /api/gallery/pde_methods/multi_factor/plot_01_peaceman_rachford_adi