AI-Based Valuation of Loans with Termination Rights under § 489 BGB
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From Challenge to Innovative Solution
Thousands of VaR scenarios, one neural network and a convincing approach: Finbridge provided specialist support to NRW.BANK in developing an AI-based valuation method for loan termination rights under § 489 BGB.
The result: a significant acceleration of the valuation with comparable accuracy to the established reference model. The valuation process is fully automated, and the business and technical implementation has been successfully completed. The following case study shows how this was achieved and why the approach is also suitable for other products.
Significantly faster valuations with comparable accuracy to the reference model.
Case Study: AI-Based Valuation of Termination Rights in Loans under § 489 BGB: An Application at NRW.BANK
Loans governed by § 489 BGB include a statutory prepayment option, allowing borrowers to repay a fixed-rate loan generally ten years after full receipt of the loan, subject to six months’ notice [1]. From a financial mathematics perspective, this results in an embedded optional component structurally analogous to an American option. A risk-appropriate valuation therefore requires specialised procedures that closely follow the methodology used to price traditional American options.
NRW.BANK initially developed a modern AI-based approach for the valuation of linearly amortising loans (see Fig. 1) within the Monte Carlo simulation framework of the Value-at-Risk (VaR) market risk calculation. Using an established option-pricing model as a benchmark, a neural network was trained. This provides a useful complement to classical models by ensuring high scalability while maintaining transparent model logic – especially when processing thousands of VaR scenarios. Classical models are still used as benchmarks and also serve as the primary model for areas such as profit-and-loss accounting.
While classical models require considerable computing time for a very large number of Monte Carlo scenarios, the AI approach allows a massive acceleration – with comparable accuracy to the benchmark model. The valuation process developed is fully automated, with weekly updates of real portfolio subsets and benchmark validation using the reference model. This solution represents a major advancement for NRW.BANK in the context of modern, model-driven risk control. After the successful business and technical implementation of the AI valuation system, a formal alignment of the governance framework with relevant audit bodies will take place before the final integration into VaR calculations.
AI-based valuation methods enable the efficient processing of thousands of VaR scenarios and complement classical valuation models.
Background: Why American Options Are Complex to Value
American options give the holder the right, but not the obligation, to exercise the option at any time before expiry. European options, by contrast, can only be exercised at maturity. This difference in exercise timing determines the valuation methodology: European options can be valued analytically, e.g. using the Black-Scholes model. American options can only be valued numerically, for example using the Cox-Ross-Rubinstein binomial method or Monte Carlo methods.
Traditional lattice and PDE methods are precise but slow. For stress tests and VaR calculations with thousands of scenarios, this often leads to compromises: the use of simplified approximation methods, the neglect of non-linear effects or the omission of a full repricing.
This is where Deep Pricing comes in. A neural network learns the relationship between the market parameters and the benchmark prices of a reference model. It then replaces the time-consuming numerical calculation for certain scenarios with immediate predictions.
The benchmark price of the reference model serves as the training label for the neural network.
The following overview positions Deep Pricing among the established valuation methods:
| Method | Idea | Strength | Weakness |
|---|---|---|---|
| Binomial/trinomial tree (e.g. Cox-Ross-Rubinstein) | Discrete time/price lattice, backward induction | Simple, provides hedging deltas | Slow with fine lattices |
| Hull-White interest rate lattice | Models interest rate processes with mean reversion | Suitable for callable bonds and swaptions | Smile only via recalibration |
| Finite differences (PDE) | Discretised valuation equation with early exercise | Very precise | Somewhat more complex set-up |
| Longstaff-Schwartz Monte Carlo | Regression of continuation values on simulation paths | Flexible for many risk factors | Requires many paths |
| Deep Pricing (DNN) | Network learns the mapping from parameters to prices | Significantly reduced valuation times after training | Requires reference prices as labels |
Table 1: Comparison of valuation methods for American options (Source: Finbridge)
Outlook: Promising Results for American Options
The valuation of termination rights is only the beginning. Finbridge has also investigated the Deep Pricing approach for classical American options. The results are promising: the neural network delivers prices that are almost identical to those of the reference model, in a fraction of the computing time. This allows for further applications wherever large numbers of valuations need to be performed quickly.
Initial results for American options show almost identical prices in a fraction of the computing time.
Deep Pricing with Finbridge
We support you at every step: from creating the training data and developing and validating the AI model through to integration into your existing calculation processes.
Would you like to know whether Deep Pricing could add value for your institution? Get in touch with us.
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Finbridge is your partner for ML services in finance & banking. Using Machine Learning (ML), we drive innovation, increase efficiency, and improve the customer experience. Our AI solutions support areas such as customer service, risk management, process automation and data analytics. We offer modular ML solutions from our extensive ML toolbox and adapt them flexibly to your needs, whether through customised consulting projects or efficient software packages. Discover business cases for successful use cases.
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Thousands of VaR scenarios, one neural network: discover how Finbridge supported NRW.BANK in developing an AI-based approach to valuing loan termination rights under § 489 BGB. Deep Pricing accelerates valuation while maintaining comparable accuracy to the reference model.
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