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This essay is a non-technical overview of some subjects related to my field of research, modeling big data using numerics and analytics. You don't have to be a mathematician to read it. If you have any questions or suggestions I'd be glad to hear from you.

This essay is a continuation of Online Marketplace Lending: Applied Mathematical Modelling to discuss this key question:

What are the emergent characteristics or behaviors generated by an established business model process on the long-term financial stability of an online marketplace lending platform?

The financial stability of an online marketplace lending platform is related to the default rate, profitability, survivability (ability to recover the funds) and credit-risk (minimizing the risks), for instance. It comes to this simple situation, if the borrowers may fail to pay, is the platform in a stronger position to recover the funds?
For an example of an established business model to recover the funds or minimize the possibility of the borrower not repaying, see Online Marketplace Lending: Applied Mathematical Modelling.

The purpose of this essay is to discuss the key elements of an online marketplace lending platform that will help to model the platform financial stability ( default rate, profitability , survivability, credit-risk analysis) into dynamic models in way which is analytically tractable, and enables to reproduce few empirical facts in satisfactory manner to handle our question under specific business model process.

The used analytical models in online marketplace lending business applies a data technology-driven approach to profitability, survivability and credit-risk analysis based on datasets. They aggregate datasets with essential features about each borrower to predict default rates without necessary examining together all these features and the observed processes during the platform operation. All these key elements are normally studied separately without considering a time impact analysis. A time impact analysis is important to forecast the default rate process and analyze what is going on and what the outcome will be on the long-term financial stability of an online marketplace lending platform.

The intended purpose is to understand the impact caused by a few sporadic events ( few sporadic loans default ) or series of events (systematic loans default), and how these events will impact the platform survivability during a specific time and also to present a real-time idea of how the key elements of a platform need to be readjusted and reevaluated.

Unlike analytical models, this simulation model provides the changes of system states ( real time dynamic profitability) that can be observed at any point in time based on specific inputs.

Platform Mathematical Modeling

Aim

Our mathematical modeling aims to describe the most important elements in the online marketplace lending platform, their interaction, and their dynamics through mathematical formulations. We consider that each decision related to the financial stability of the platform is the outcome of a complex process that usually involves two complementary processes: one is learning from the past events ( historical loan default rates) and the second is aiming to predict future events ( future loan default rates) that needs to be considered today for adjusting tomorrow platform financial stability.

Borrower and Lender-Investor

We are considering online marketplace lending platform that are operating under installment loan which is type of loan that is re- paid in periodic installments (usually monthly payments) that include principal and interest. The principals are lent mainly by investors. Each period, a number of installment payments are supposed to be transfered from the borrowers to the lenders(investors).

These principals or installment payments would be constrained by the financial resources that investors and borrowers have at their disposal. Both parties may not necessary have large enough resources and are under non-negligible financial constraints. It is reasonable to assume that as the borrower is relatively risk-neutral, the investor is more risk-averse even he is often richer or better diversified than the borrowers. The business models and data-driven algorithms with robust credit scoring models supporting the current marketplace lending platform are supposed to expand access to safe and affordable credit minimizing borrower risks and increase investor confidence in a less favorable credit environment.

Online Marketplace Lending Platform Characteristic.

The online marketplace lending platform’s main priority is to use sound combination of data-driven underwriting, robust credit scoring models, automated and online operations to make installment payments due date more likely possible in order to collect fees.
Our main assumptions:

We assume that not all the borrowers are able to make installment payment every due date, and that the probability that a number of borrowers are able to make installment payments every due date, is determined by a stochastic process. In this case time to make a number of installment payments will be random, and the online marketplace lending platform needs to only form rational expectations about the future to set optimal installment payment process.
The marketplace lending platform is supposed to be constantly proactive, assesses and weigh a number of factors and then makes a prediction for the future installment payments by using strategies, rules and assessing the accuracy of any factor related to the determination of the future installment payments. The marketplace lending platform is combining all these informations to arrive to a function based on the entire future of installment payment process process for a rational profitability or financial performance prediction.

Numerical Results:

The obtained model for online marketplace lending platform profitability dynamics is a system of differential equations. Analytical solutions are derived by using numerical solutions to solve some important scenarios to evaluate the profitability. The model has a number of parameters and functions related to the key elements in our modeling process, i.e. the probability that borrowers are not able to pay the next installment payment and functions representing the analytical behaviors of the expectancy function that the borrowers are skipping the next installment payments and paying the future ones or never.

This expectancy function is certainly affected by the established business model and may be modeled as depending on a number of variables in an exogenously or endogenously fashion. For instance, we assume that more the platform is appreciated more lenders are attracted to platform and more the borrowers are paying the next installment payments. This kind of expectancy function is quantified as a decreasing function, when the platform profitability is rising, the future profitability is expected to rise further or increase adequately.

Quantitative Analysis.

We consider the following scenarios: the borrowers are able to pay the next installment payments on average, 1 month, 2 months, 3 months, 4 months, 5 months.

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Discussion and Conclusion:

In this essay we discussed a time impact model for online marketplace lending platform to evaluate its financial stability. The dynamic models integrate the key elements using realistic assumptions related to the borrowers and the business model of the platform. The mathematical model is able to obtain analytical form solutions throughout using numerical methods. We find that the parameters describing the the borrowers and the expectancy function representing the business model of the platform are central inputs in explaining the capacities of the platform to sustain the long-term financial stability.