Liquidity risk and arbitrage pricing theory

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modelling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. Our approach hypothesizes a stochastic supply curve for a securitys price as a function of trade size. This leads to a new definition of a self-financing trading strategy, additional restrictions on hedging strategies, and some interesting mathematical issues.Received: 1 November 2003, Mathematics Subject Classification: 60G44, 60H05, 90A09JEL Classification: G11, G12, G13Umut Çetin: This work was performed while Dr. Çetin was at the Center for Applied Mathematics, Cornell UniversityPhilip Protter: Supported in part by NSF grant DMS-0202958 and NSA grant MDA-904-03-1-0092 The authors wish to thank M. Warachka and Kiseop Lee for helpful comments, as well as the anonymous referee and Associate Editor for numerous helpful suggestions, which have made this a much improved paper.     

Detection of Financial Time Series Turning Points: A New CUSUM Approach Applied to IPO Cycles

This paper presents a new Cumulative Sum approach for the detection of turning points in financial time series that are subject to cyclical mean level and volatility regime shifts. The new CUSUM approach is applied to the problem of detecting turning points in hot issue markets for Initial Public Offerings (IPOs), thus providing a multi-dimensional characterization of states of the IPO cycle.     

Social Security and personal saving: 1971 and beyond

Feldstein (1996, 1974) reported that Social Security in the U.S.A. reduced personal saving (“saving”) in 1992 (1971) by $416 ($61) billion. I reestimate his life-cycle consumption specification using data from the latest NIPA revision, correct his calculations, and find that the implied reduction in 1992 (1971) saving is now $280 ($22) billion, 48% (16%) of actual net private saving, with a standard error of $114 ($14) billion. If structural breaks around WWII and the 1972 Social Security amendments (which raised real per capita SSW by 22%) are allowed, and the market value of Treasury debt included in the specification, the reduction in 1971 and 1992 saving attributable to Social Security is at most 0.55 times its standard error, and 12% of net private saving. I then reestimate the preferred specification of Coates and Humphreys (1999), allowing for these structural breaks and relaxing other restrictions. The implied effect of Social Security on saving is again statistically zero. First version received: September 2000/Final version received: September 2001 RID="*" ID="*"  I thank Les Oxley for pointing out that correcting for AR(1) residuals is not a categorical imperative but a cultural relative, in which case common factor restrictions are crucial.     

Information reduction via level crossings in a credit risk model

This paper provides an alternative credit risk model based on information reduction where the market only observes the firm’s asset value when it crosses certain levels, interpreted as changes significant enough for the firm’s management to make a public announcement. For a class of diffusion processes we are able to provide explicit expressions for the firm’s default intensity process and its zero-coupon bond prices.