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Model Validation: New Approaches in Testing Mathematical and Financial Correctness of Models

The validation of derivative pricing models can be a slow, labor intensive and expensive exercise. In addition, it often provides a limited amount of certainty on the correctness of the pricing models, because methods for validating pricing models are often generic methods that can be applied to any kind of software. However, since pricing models are mathematical models, they satisfy mathematical identities which can provide strong tests that leave very little possibility for error. Furthermore, these tests provide failure conditions that require no human judgment, that can be automated, and that can therefore run over tens of thousands of test scenarios.

Significant advances in computing power such as the cloud and grid computing now make automated testing more accessible to market practitioners, making the testing inexpensive,
rapid, and easy. This results in a faster time-to-market for validating models, and a stronger case can be made to regulators that models are thoroughly tested and correct. In this paper, we will examine model validation as it is typically practiced today and then explore new approaches, including the benefits of testing with mathematical identities.