February 21, 2024

Recursive marginal quantization of higher-order schemes

By Joerg Kienitz.

Read the full paper here.


Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large derivative books.

Recursive marginal quantization (RMQ) of the Euler scheme has recently been proposed as an efficient numerical method for evaluating functionals of solutions of stochastic differential equations.

This method involves recursively quantizing the conditional marginals of the discrete-time Euler approximation of the underlying process. By generalizing this approach, we show that it is possible to perform RMQ for two higher-order schemes: the Milstein scheme and a simplified weak order 2.0 scheme.

We further extend the applicability of RMQ by showing how absorption and reflection at the zero boundary may be incorporated, when necessary.

To illustrate the improved accuracy of the higher-order schemes, various computations are performed using geometric Brownian motion and the constant elasticity of variance model.

For both models, we provide evidence of improved weak order convergence and computational efficiency. By pricing European, Bermudan and barrier options, further evidence of improved accuracy of the higher-order schemes is demonstrated.

Read Full Publication

Share this

Other Publications

Effective stochastic volatility: applications to ZABR-type models
February 22, 2024
Read now >
Effective Markovian projection: application to CMS spread options and mid-curve swaptions
February 22, 2024
Read now >
Effective stochastic local volatility models
February 22, 2024
Read now >