The Chirality operators for Heisenberg Spin Systems

The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a two-fold Kramers degeneracy. A non-zero chirality implies that the spins are not coplanar, and is a measure of handedness. The chirality operator, which can be treated as a spin-1/2 operator, is explicitly constructed in terms of the spin operators, and is given as commutator of Permutation operators.Comment: 7 pages, report IC/94/23. E-mail: [email protected]

“Does the tail wag the dog? The effect of credit default swaps on credit risk”

Credit default swaps (CDS) are derivative contracts that are widely used as tools for credit risk management. However, in recent years, concerns have been raised about whether CDS trading itself affects the credit risk of the reference entities. We use a unique, comprehensive sample covering CDS trading of 901 North American corporate issuers, between June 1997 and April 2009, to address this question. We find that the probability of both a credit rating downgrade and bankruptcy increase, with large economic magnitudes, after the inception of CDS trading. This finding is robust to controlling for the endogeneity of CDS trading. Beyond the CDS introduction effect, we show that firms with relatively larger amounts of CDS contracts outstanding, and those with relatively more “no restructuring” contracts than other types of CDS contracts covering restructuring, are more adversely affected by CDS trading. Moreover, the number of creditors increases after CDS trading begins, exacerbating creditor coordination failure for the resolution of financial distress

An Examination of the Static and Dynamic Performance of Interest Rate Option Pricing Models In the Dollar Cap-Floor Markets

This paper examines the static and dynamic accuracy of interest rate option pricing models in the U.S. dollar interest rate cap and floor markets. We evaluate alternative one-factor and two-factor term structure models of the spot and the forward interest rates on the basis of their out-of-sample predictive ability in terms of pricing and hedging performance. The one-factor models analyzed consist of two spot-rate specifications (Hull and White (1990) and Black-Karasinski (1991), five forward rate specifications (within the general Heath, Jarrow and Morton (1990b) class), and one LIBOR market model (Brace, Gatarek and Musiela (1997) [BGM]). For two-factor models, two alternative forward rate specifications are implemented within the HJM framework. We conduct tests on daily data from March-December 1998, consisting of actual cap and floor prices across both strike rates and maturities. Results show that fitting the skew of the underlying interest rate distribution provides accurate pricing results within a one-factor framework. However, for hedging performance, introducing a second stochastic factor is more important than fitting the skew of the underlying distribution. Overall, the one-factor lognormal model for short term interest rates outperforms other competing models in pricing tests, while two-factor models perform significantly better than one-factor models in hedging tests. Modeling the second factor allows a better representation of the dynamic evolution of the term structure by incorporating expected twists in the yield curve. Thus, the interest rate dynamics embedded in two-factor models appears to be closer to the one driving the actual economic environment, leading to more accurate hedges. This constitutes evidence against claims in the literature that correctly specified and calibrated one-factor models could replace multi-factor models for consistent pricing and hedging of interest rate contingent claims

The Term Structure of Interest-Rate Future Prices

We derive general properties of two-factor models of the term structure of interest rates and, in particular, the process for futures prices and rates. Then, as a special case, we derive a no-arbitrage model of the term structure in which any two futures rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional autoregressive process for the short-term rate, which exhibits both mean reversion and a lagged persistence parameter. We show that the correlation of the futures rates is restricted by the no-arbitrage conditions of the model. In addition, we investigate the determinants of the volatility of the futures rates of various maturities. These are shown to be related to the volatilities of the short rate, the volatility of the second factor, the degree of mean reversion and the persistence of the second factor shock. We obtain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London Inter-Bank Offer Rate (Libor)] follows a two-dimensional process. Our results lead to empirical hypotheses that are testable using data from the liquid market for Eurocurrency interest rate futures contracts

GROUP AFFILIATION AND THE PERFORMANCE OF INITIAL PUBLIC OFFERINGS IN THE INDIAN STOCK MARKET

We document the effects of group affiliation on the initial performance of 2,713 Initial Public Offerings (IPOs) in India under three regulatory regimes during the period 1990-2004. We distinguish between two competing hypotheses regarding group affiliation: the “certification” and the “tunneling” hypotheses. We lend support to the latter by showing that the underpricing of group companies is higher than that of stand-alone companies. We ascribe the higher initial returns of group IPOs to investor overreaction. Ex post, we find that group-affiliated companies have a higher probability of survival over the long term: groups support their affiliates to maintain their reputation

Incremental Risk Vulnerability

We present a necessary and sufficient condition on an agent’s utility function for a simple mean preserving spread in an independent background risk to increase the agent’s risk aversion (incremental risk vulnerability). Gollier and Pratt (1996) have shown that declining and convex risk aversion as well as standard risk aversion are sufficient for risk vulnerability. We show that these conditions are also sufficient for incremental risk vulnerability. In addition, we present sufficient conditions for a restricted set of stochastic increases in an independent background risk to increase risk aversion.

Intermediation and Value Creation in an Incomplete Market: Implications for Securitization

This paper studies the impact of financial innovations on real investment decisions. We model an incomplete market economy comprised of firms, investors and an intermediary. The firms face unique investment opportunities that are not spanned by the traded securities in the financial market, and thus, cannot be priced uniquely using the no-arbitrage principle. The specific innovation we consider is securitization; the intermediary buys claims from the firms that are fully backed by cash flows from the new projects, pools these claims together, and then issues tranches of secondary securities to the investors. We first derive necessary and sufficient conditions under which pooling provides value enhancement and the prices paid to the firms are acceptable to them compared to the no-investment option or the option of forming alternative pools. We find that there is a unique pool that is sustainable, and may or may not consist of all projects in the intermediary’s consideration set. We then determine the optimal design of tranches, fully backed by the asset pool, to be sold to different investor classes. We determine the general structure of the tranches. The new securities created by the intermediary could have up to three components, one that is a marketable claim, one that represents the arbitrage opportunities available in the market due to special ability to design and sell securities to a subset of investors, and a third component that is the rest of the asset pool which is sold at a price which does not exceed arbitrage based bounds to investors. The presence of these three components in the tranching solution has direct bearing upon the size of the asset pool, and therefore value creation due to financing additional projects

Why do Interest Rate Options Smile?

We address three questions relating to the interest rate options market: What is the shape of the smile? What are the economic determinants of the shape of the smile? Do these determinants have predictive power for the futures shape of the smile and vice versa? We investigate these issues using daily bid and ask prices of euro (€) interest rate caps/floors. We find a clear smile pattern in interest rate options. The shape of the smile varies over time and is affected in a dynamic manner by yield curve variables and the future uncertainty in the interest rate markets; it also has information about future aggregate default risk. Our findings are useful for the pricing, hedging and risk management of these derivatives

The Valuation of American-style Swaptions in a Two-factor Spot-Futures Model1

We build a no-arbitrage model of the term structure of interest rates using two stochastic factors, the short-term interest rate and the premium of the futures rate over the short-term interest rate. The model provides and extension of the lognormal interest rate model of Black and Karasinski (1991) to two factors, both of which can exhibit mean-reversion. The method is computationally efficient for several reasons. First, the model is based on Libor futures prices, enabling us to satisfy the no-arbitrage condition without resorting to iterative methods. Second, we modify and implement the binomial approximation methodology of Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) to compute a multiperiod tree of rates with the no-arbitrage property. The method uses a recombining two-dimensional binomial lattice of interest rates that minimizes the number of states and term structures over time. In addition to these computational advantages, a key feature of the model is that it is consistent with the observed term structure of futures rates as well as the term structure of volatilities implied by the prices of interest rate caps and floors. These prices are shown to be highly sensitive to the existence of the second factor and its volatility characteristics

Credit Risk and the Yen Interest Rate Swap Market

In this paper, we investigate the pricing of Japanese yen interest rate swaps during the period 1990-96. We obtain measures of the spreads of the swap rates over comparable Japanese Government Bonds (JGBs) for different maturities and analyze the relationship between the swap spreads and credit risk variables. Our empirical results in the yen swap market indicate that: 1) the commonly-used assumption of lognormal default-free interest rates and swap spreads is strongly rejected by the data, 2) the term structure of swap spreads displays a humped-shape, and 3) the shocks in the yen swap spread are negatively correlated with the shocks in the comparable default-free spot rates, especially for longer maturities. Our analysis also indicates that yen swap spreads behaved very differently from the credit spreads on Japanese corporate bonds in the early nineties. In contrast to Japanese corporate bonds, we find that the yen swap spread is also significantly related to proxies for the long-term credit risk factor. Furthermore, the swap spread is negatively related to the level and slope of the term structure and positively related to the curvature, indicating that the credit "optionality" is priced in the swap rate. Thus, overall, the yen swap market was sensitive to credit risk during the period of our study