Abstract

(I) Lenders will often restructure a loan rather than foreclose on a property because it is less value-destroying. A loan modification primarily entails a change in the loan rate, principal balance and/or remaining time to maturity. We analyze optimal loan modification schemes in a stochastic home price and stochastic interest-rate environment. Lenders maximize their loan values by minimizing the value of the borrower's option to default on the loan. We argue that, controlling for the borrower's ability to pay, loan modifications via rate reductions and maturity extensions are suboptimal, leading to dissipation in loan value to the lender, and resulting in a high probability of re-default by homeowners even after modification of their loans. In contrast, loan write-downs (the Principal Principle), not a favored recipe, and sometimes prohibited by covenants, are mostly optimal. A recent innovation, the shared appreciation mortgage, enhances the ability to pay, mitigates adverse selection, and reduces the present value of expected deadweight foreclosure costs.

(II) The supply of foreclosed homes topped 2 million in September 2010. One of the tools in battling the current foreclosure crisis is loan modification. This paper presents a model for the optimal principal reset in a loan modification, thereby maximizing the loan value to the lender bank and minimizing the likelihood of foreclosure by the homeowner. Reducing the loan-to-value (LTV) ratio will reduce the present value of future payments on the loan, but will also reduce the probability of default, thereby saving deadweight foreclosure costs. The optimal trade-off of these two countervailing effects will pinpoint the optimal LTV at which the loan must be reset. We present a reduced-form barrier option decomposition of the loan value that makes the optimization of LTV easy to implement. An extension of the model is shown to account for varying growth rate assumptions about house prices. The model in this paper accounts for the home-owner's ability to pay and willingness to pay, and uses the framework to model shared-appreciation mortgages (SAMs). We show that SAMs are structures that mostly improve the lender's loan value.

About the Speaker

Sanjiv Das is Professor of Finance and Chair of the Finance Department at Santa Clara University's Leavey School of Business. He previously held faculty appointments as Associate Professor at Harvard Business School and UC Berkeley. He holds post-graduate degrees in Finance (M.Phil and Ph.D. from New York University), Computer Science (M.S. from UC Berkeley), an MBA from the Indian Institute of Management, Ahmedabad, B.Com in Accounting and Economics (University of Bombay, Sydenham College), and is also a qualified Cost and Works Accountant. He is a senior editor of The Journal of Investment Management, co-editor of The Journal of Derivatives, and Associate Editor of other academic journals. Prior to being an academic, he worked in the derivatives business in the Asia-Pacific region as a Vice-President at Citibank. His current research interests include: the modeling of default risk, machine learning, social networks, derivatives pricing models, portfolio theory, and venture capital. He has published over seventy articles in academic journals, and has won numerous awards for research and teaching. His recent book "Derivatives: Principles and Practice" was published in May 2010.

Abstract

Credit ratings and accounting-based Altman Z-scores are two important sources of information for assessing the creditworthiness, or likelihood of defaults, of firms. In this paper, we build a fexible, quantitative model based on a double Hidden Markov Model, (DHMM), to extract information about the "true" credit qualities of frms from both the Z-scores evaluated from the accounting ratios of the firms and publicly available credit ratings of the frms produced by rating agencies. The evolution of the "true" credit quality over time is estimated from observed data using filtering methods and the EM algorithm. Recursive updates of optimal estimates are provided via fltering so that the model is "self-tuning", or "self-calibrating". We illustrate the practical implementation of the proposed model using actual accounting ratios data of firms from different regions and their credit ratings data from Standard & Poors.

About the Speaker

Robert Elliott received Bachelors and Masters degrees from Oxford University, and his Ph.D.and D.Sc. from Cambridge University. He has held positions at Newcastle, Yale, Oxford, Warwick, Hull, Alberta, and visiting positions in Toronto, Northwestern, Kentucky, Brown, Paris, Denmark, Hong Kong and Australia. From 2001 to 2009 he was the RBC Financial Group Professor of Finance at the University of Calgary, Canada, where he is also an Adjunct Professor in both the Department of Mathematics and the Department of Electrical Engineering. Currently he is an Australian Professorial Fellow at the University of Adelaide. Professor Elliott has authored nine books and over 400 papers. His book with PE Kopp "Mathematics of Financial Markets" was published by Springer in 1999 and has been reprinted three times. The Hungarian edition was published in 2000 and the second Edition was published in September 2004. An edition in China was published in 2010. Springer Verlag published his book "Binomial Methods in Finance", written with John van der Hoek, in the summer of 2005. He has also worked in signal processing and his book with L Aggoun and J Moore on "Hidden Markov Models: Estimation and Control" was published in 1995 by Springer Verlag and reprinted in 1997. A revised and expanded edition was printed in 2008. His book with L Aggoun "Measure Theory and Filtering" was published by Cambridge University Press in June 2004. His earlier book "Stochastic Calculus and Applications" was published by Springer in 1982 and a Russian translation appeared in 1986.