Unlimited Liabilities, Reserve Capital Requirements and the Taxpayer Put Option

When firms access unbounded liability exposures and are granted limited liability, then an all equity firm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve capital at stake in the firm. We contribute by (i) valuing this taxpayer put, and (ii) determining the level for reserve capital. Reserve capital levels are designed to mitigate the adverse incentives for unnecessary risk introduced by the taxpayer put at the firm level. In our approach, the level of reserve capital is set to make the aggregate risk of the firm externally acceptable, where the specific form of acceptability employed is positive expectation under a concave distortion of the cash flow distribution. It is observed that in the presence of the taxpayer put, debt holders may not be relied upon to monitor risk as their interests are partially aligned with equity holders by participating in the taxpayer put. Further, it leads to an equity pricing model associated with a market discipline that punishes perceived cash shortfalls.

[1]  E. Eberlein,et al.  The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures , 2002 .

[2]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[3]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[4]  B. Roorda,et al.  COHERENT ACCEPTABILITY MEASURES IN MULTIPERIOD MODELS , 2005 .

[5]  M. Yor,et al.  The Fine Structure of Asset Retums : An Empirical Investigation ' , 2006 .

[6]  Thomas W. Bates,et al.  Why Do U.S. Firms Hold so Much More Cash than They Used to? , 2006 .

[7]  L. J. Savage,et al.  The Utility Analysis of Choices Involving Risk , 1948, Journal of Political Economy.

[8]  Dilip B. Madan,et al.  MARKETS AS A COUNTERPARTY: AN INTRODUCTION TO CONIC FINANCE , 2010 .

[9]  Dilip B. Madan,et al.  New Measures for Performance Evaluation , 2007 .

[10]  E. Seneta,et al.  The Variance Gamma (V.G.) Model for Share Market Returns , 1990 .

[11]  F. Delbaen,et al.  Coherent and convex monetary risk measures for bounded càdlàg processes , 2004 .

[12]  F. Delbaen,et al.  Coherent and convex risk measures for bounded cadlag processes , 2003 .

[13]  Armen Hovakimian,et al.  Effectiveness of Capital Regulation at U.S. Commercial Banks, 1985 to 1994 , 2000 .

[14]  Olivier Ledoit,et al.  Gain, Loss, and Asset Pricing , 2000, Journal of Political Economy.

[15]  D. Scharfstein,et al.  Bank Lending During the Financial Crisis of 2008 , 2009 .

[16]  R. C. Merton,et al.  On the Pricing of Corporate Debt: The Risk Structure of Interest Rates , 1974, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[17]  Chris I. Telmer Asset-Pricing Puzzles and Incomplete Markets , 1993 .

[18]  R. C. Merton,et al.  An analytic derivation of the cost of deposit insurance and loan guarantees An application of modern option pricing theory , 1977 .

[19]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[20]  Hélyette Geman,et al.  Pricing and hedging in incomplete markets , 2001 .

[21]  D. Madan Capital requirements, acceptable risks and profits , 2009 .

[22]  Uwe Küchler,et al.  Coherent risk measures and good-deal bounds , 2001, Finance Stochastics.

[23]  A. S. Cherny,et al.  Weighted V@R and its Properties , 2006, Finance Stochastics.

[24]  E. Eberlein,et al.  Hyperbolic distributions in finance , 1995 .

[25]  Marc Yor,et al.  SELF‐DECOMPOSABILITY AND OPTION PRICING , 2007 .

[26]  Wim Schoutens,et al.  Conic Coconuts: The Pricing of Contingent Capital Notes Using Conic Finance , 2010 .

[27]  W. Sharpe CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[28]  M. Yor,et al.  Stochastic Volatility for Lévy Processes , 2003 .

[29]  Darrell Duffie,et al.  Asset Pricing with Heterogeneous Consumers , 1996, Journal of Political Economy.

[30]  P. Carr,et al.  The Variance Gamma Process and Option Pricing , 1998 .

[31]  Chi-Fu Huang,et al.  Foundations for financial economics , 1988 .

[32]  Luigi Zingales,et al.  Paulson&Apos;S Gift , 2009 .

[33]  Ole E. Barndorff-Nielsen,et al.  Processes of normal inverse Gaussian type , 1997, Finance Stochastics.

[34]  Frank Riedel,et al.  Dynamic Coherent Risk Measures , 2003 .

[35]  D. Madan,et al.  Non Gaussian Models of Dependence in Returns , 2009 .

[36]  Charles E. Hegji,et al.  The S & L insurance mess : how did it happen? , 1989 .

[37]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[38]  Thomas R. Hurd,et al.  A Fourier Transform Method for Spread Option Pricing , 2009, SIAM J. Financial Math..

[39]  E. Oja,et al.  Independent Component Analysis , 2013 .

[40]  N. Arshadi,et al.  The S&L Insurance Mess: How Did It Happen? , 1989 .