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Risk-adjusted Lending Conditions: An Option Pricing Approach


In order to operate their lending business profitably, banks must know all the costs involved in granting loans. In particular, all the expenses they incur in covering losses must be included. Provided loan risks can be calculated, it is possible in each case to charge a price that is appropriately adjusted for risk, thus making it possible to make high-risk loans.

In Risk-adjusted Lending Conditions the author presents a model, to measure and calculate loan risks, showing how it functions and how it may be applied. His approach has its origins in the ideas put forward by Black/Scholes in 1973, and thus owes much to option price theory. From this the author has succeeded in developing a solution such that, whatever a company's debt position and however its balance sheet may be structured, any situation can be individually assessed. Building on this, he demonstrates how combinations of loans with the lowest possible interest costs can be tailor-made for any company. The book contains numerous examples, making it easy for practising bankers to see how the model may be applied.

Werner Rosenberger is Managing Director and Head of Methodology at Credit Risk Control of UBS Wealth Management & Business Banking, Zurich.
He was born 1953 in Zurich, Switzerland, where he acquired a diploma in Physics at the Federal Institut of Technology (ETH Zürich). He concluded his studies with a degree in Business Administration of the University of St. Gall, Switzerland. Several years later he completed a doctorate at the University of Zurich.
After his studies he worked first as a marketing manager at Philips (Schweiz) AG, Zurich, for IT-products. After a back packer trip around the world he started a banking career at UBS and Credit Suisse where he worked mainly as company clients relationship manager and as a branch manager before he joined credit risk control.
Preface 1.

Preface 2.

Part I: Outline.


Rating system.

Part II: Mathematical Foundations of the Model.

Probability model: Development of ψj.

Calculation of the shortfall risk hedging rate in the special case of shortfall risks being constant.

Calculation of the shortfall risk hedging rate in the general case of variable shortfall risk.

Shortfall risk on uncovered loans on the basis of statistics.

Part III: Option-Theory Loan Risk Model.

Shortfall risk on uncovered loans to companies on the basis of an option-theory approach.

Loans covered against shortfall risk.

Calculation of the combination of loans with the lowest interest costs.

Part IV: Implementation in practice.

Procedure – according to the model – for assessing the risk in lending to a company.


Final considerations.

Appendix 1: Notation.

Appendix 2: Excel worksheet.

Appendix 3: Property price index.

Appendix 4: Chapter 3 – Derivations.

Appendix 5: Chapter 4 – Derivations.

Appendix 6: Chapter 5 – Derivations.