Equity swaps in a LIBOR market model

This study extends the BGM (A. Brace, D. Gatarek, & M. Musiela, 1997) interest rate model (the London Interbank Offered Rate [LIBOR] market model) by incorporating the stock price dynamics under the martingale measure. As compared with traditional interest rate models, the extended BGM model is both appropriate for pricing equity swaps and easy to calibrate. The general framework for pricing equity swaps is proposed and applied to the pricing of floating‐for‐equity swaps with either constant or variable notional principals. The calibration procedure and the practical implementation are also discussed. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:893–920, 2007     

Effects of interest rate swaps

In this paper we examine the effect of interest rate swaps on the firm, and identify characteristics of firms that use interest rate swaps, reporting findings consistent with interest rate swaps being used as a risk-reducing instrument. Relative to nonswappers, firms using swaps are more likely to experience decreased cash flow variance in the five-year period subsequent to swap initiation. In addition, firms that engage in swaps are found to be larger and more highly levered than a control sample of nonswappers. Dividing our sample based upon type of swap, we find different characteristics explain different types of swap. In particular we find evidence consistent with swaps from variable to fixed interest rates being engaged in for risk reduction, i.e., hedging purposes.     

Capped equity swaps under the double‐jump stochastic volatility model with stochastic interest rates

This study proposes a double‐jump stochastic volatility model with stochastic interest rates to price capped equity swaps and other multi‐period derivative securities. Closed‐form solutions for capped equity swaps with a fixed or variable notional principle are derived. In addition, numerical examples are employed to analyze comparative statics properties, counterparty risks, and the dynamics of the forward smile. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:340–370, 2011     

Pricing models of equity swaps

This article provides a generalized formula for pricing equity swaps with constant notional principal when the underlying equity markets and settlement currency can be set arbitrarily. To derive swap values using the risk‐neutral valuation method, the swap payment is replicated at each settlement date by constructing a self‐financing portfolio. To obtain the foreign equity index return denominated in the domestic or in a third currency, equity‐linked foreign exchange options are used to hedge the exchange rate risk. It is found that if the swap involves international equity markets, then the swap value contains an extra term which reflects the currency hedging costs. This methodology can easily be applied to price various types of equity swaps simply by modifying the specifications of the model presented here as required. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:751–772, 2003     

A UNIFIED FRAMEWORK FOR PRICING CREDIT AND EQUITY DERIVATIVES

We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid, or over‐the‐counter derivatives. We observe that our model matches the equity option implied volatility surface well since we properly account for the default risk in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque et al., which only accounts for stochastic volatility.     

CREDIT SPREADS, OPTIMAL CAPITAL STRUCTURE, AND IMPLIED VOLATILITY WITH ENDOGENOUS DEFAULT AND JUMP RISK

We propose a two-sided jump model for credit risk by extending the Leland–Toft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) Jumps and endogenous default can produce a variety of non-zero credit spreads, including upward, humped, and downward shapes; interesting enough, the model can even produce, consistent with empirical findings, upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal debt/equity ratio; in fact, with jump risk, highly risky firms tend to have very little debt. (3) The two-sided jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options; although in general credit spreads and implied volatility tend to move in the same direction under exogenous default models, this may not be true in presence of endogenous default and jumps. Pricing formulae of credit default swaps and equity default swaps are also given. In terms of mathematical contribution, we give a proof of a version of the "smooth fitting" principle under the jump model, justifying a conjecture first suggested by Leland and Toft under the Brownian model.     

A term structure model for dividends and interest rates

Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump‐diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method for option pricing. In a calibration exercise we show that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 Index dividend futures and dividend options, and Euro Stoxx 50 Index options.     

Asymmetric information and credit quality: Evidence from synthetic fixed‐rate financing

In this article the usage of synthetic fixed‐rate financing (SFRF) with interest rate swaps (i.e., borrowing short‐term and using swaps to hedge interest rate risk, instead of selecting conventional fixed‐rate financing) by Fortune 500 and S&P 500 nonfinancial firms is examined over the period 1991 through 1995. Credit ratings, debt issuance, and debt maturities of these firms are monitored through 1999. Strong evidence is found supporting the asymmetric information theory of swap usage as described by S. Titman (1992), even after controlling for industry, credit quality, size effects, and the simultaneity of the capital structure and the interest rate swap usage decision. Consistent with theoretical predictions, SFRF firms are more likely to undergo credit quality upgrades. When limiting the sample to firms where asymmetric information costs are potentially the greatest, the results are even stronger. These findings are important because they document that swaps serve a highly valuable service for firms subject to information asymmetries. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:595–626, 2006     

The Term Structure of Simple Forward Rates with Jump Risk

This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on "market models." We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives.     

The interest rate sensitivity of equity prices with respect to systematic risk and leverage

This study extends the previous empirical research into the sensitibity of equity prices to include interest rates. Specifically, the null hypothesis that the interest rate sensitivity of equity prices is independent of the level of systematic risk and financial leverage is tested. The hypothesis is tested using a short-term and long-term interest rate index. The results show that the interest rate sensitivity of equity prices is independent of the amount of financial leverage but not independent of the level of systematic risk.     

Valuation and Hedging of Differential Swaps

This paper derives a general‐form formula for pricing and hedging differential swaps with the principal denominated either in a domestic, foreign, or third‐country currency. We first derive the formula for differential swaps with the principal in a domestic currency and identify an error in the formula of Wei (1994). We then show the pricing duality between differential swaps with the principal in a domestic currency and differential swaps with the principal in a foreign currency. Finally, we complete the pricing and hedging analysis on differential swaps by deriving a formula for differential swaps with the principal denominated in a third‐country currency. Simulation results indicate that constant margin rates are generally smaller than interest rate differentials and decline with the tenor of swaps. Correlation parameters associated with the exchange rate play a more important role than correlation parameters among interest rates in pricing differential swaps. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:73–94, 2002     

Dissecting interbank risk using basis swap spreads

This paper analyses interbank risk using the information content of basis swap (BS) spreads, floating-to-floating interest rate swaps whose payments are associated with euro deposit rates for alternative tenors. To identify the impact of shocks affecting interbank risk, we propose an empirical model that decomposes BS quotes into their expected and unexpected components. These unobservable constituents of BS spreads are estimated by solving a signal extraction problem using a particle filter. We find that expected components covariate with aggregate liquidity and risk aversion while systemic risk arises as the main driver behind unexpected fluctuations. Our empirical findings suggest that macroprudential analysis emerges as a key device to ease asset pricing in a new multi-curve scenario.     

CLOSED FORM PRICING FORMULAS FOR DISCRETELY SAMPLED GENERALIZED VARIANCE SWAPS

Most of the existing pricing models of variance derivative products assume continuous sampling of the realized variance processes, though actual contractual specifications compute the realized variance based on sampling at discrete times. We present a general analytic approach for pricing discretely sampled generalized variance swaps under the stochastic volatility models with simultaneous jumps in the asset price and variance processes. The resulting pricing formula of the gamma swap is in closed form while those of the corridor variance swaps and conditional variance swaps take the form of one‐dimensional Fourier integrals. We also verify through analytic calculations the convergence of the asymptotic limit of the pricing formulas of the discretely sampled generalized variance swaps under vanishing sampling interval to the analytic pricing formulas of the continuously sampled counterparts. The proposed methodology can be applied to any affine model and other higher moments swaps as well. We examine the exposure to convexity (volatility of variance) and skew (correlation between the equity returns and variance process) of these discretely sampled generalized variance swaps. We explore the impact on the fair strike prices of these exotic variance swaps with respect to different sets of parameter values, like varying sampling frequencies, jump intensity, and width of the monitoring corridor.     

Commercial bank stocks, interest rates, and systematic risk

This study examines the effect of interest rate changes on bank equity values. Several versions of the market model were specified and estimated. The results indicate that bank systematic risk differs during periods of changing interest rate levels. In addition, bank portfolio betas appear to increase with time and are positively correlated with interest rates.     

存货质押业务中银行与物流企业Stackelberg博弈行为分析

完全信息下的存货质押融资业务中,物流企业作为先行决策者决定风险承担比例,银行据此决定利率,对实践中双方博弈行为进行分析与求解的数值仿真研究表明:完全信息下由银行和物流企业"双边决定市场"的优势大于由银行单边决定的市场;借款企业高履约水平时,物流企业愿意通过提高自身的风险承担比例来换取银行减让利率;利率敏感度对均衡结果的影响较自有资金敏感度更为显著。     

A GENERAL EQUILIBRIUM MODEL OF A MULTIFIRM MORAL‐HAZARD ECONOMY WITH FINANCIAL MARKETS

We present a general equilibrium model of a moral‐hazard economy with many firms and financial markets, where stocks and bonds are traded. Contrary to the principal‐agent literature, we argue that optimal contracting in an infinite economy is not about a tradeoff between risk sharing and incentives, but it is all about incentives. Even when the economy is finite, optimal contracts do not depend on principals’ risk aversion, but on market prices of risks. We also show that optimal contracting does not require relative performance evaluation, that the second best risk‐free interest rate is lower than that of the first best, and that the second‐best equity premium can be higher or lower than that of the first best. Moral hazard can contribute to the resolution of the risk‐free rate puzzle. Its potential to explain the equity premium puzzle is examined.     

Debt-equity swaps and the heavily indebted countries

In search of solutions to the international debt crisis, attention has recently been focused on a new financing technique, so-called debt-equity swaps. An essential difference between these and the usual swapping of debt into equity is that the former allow a wider range of applications. The following article seeks to elucidate the possible contribution of debt-equity swaps towards easing the debt burden and to estimate the potential for a reduction in external debt and its effect on the balance of payments of the debtor nation.     

Investing in developing nations using debt-equity swaps

A survey of investors in debt equity swaps oflers some advice for those businesses including them in their ficture plans.     

Market Discipline of Canadian Banks' Letters of Credit Activities: An Empirical Examination

While the motivation and riskiness of US off-balance sheet banking activities have been studied both theoretically and empirically, no such study has been found dealing with Canadian off-balance sheet banking activities, although such activities are numerically huge, and growing larger each year. This article provides support for a market discipline hypothesis of Canadian bank letters of credit activities by employing several market measures of risk from one-factor and multi-factor models, and an implied asset volatility from the option-pricing model. Furthermore, it examines both price and quantity response of off-balance sheet activities in the Canadian banking market by employing a tobit analysis to assess the robustness of our conclusions about market discipline. The results indicate that various market measures of risk and letters of credit are negatively related. Moreover, banks with greater portfolio risk measured in terms of equity and asset risk, high leverage and interest rate risk are less likely to issue letters of credit.     

Assessing credit quality from the equity market: can a structural approach forecast credit ratings?

We investigate the empirical performance of default probability prediction based on Merton's (1974) structural credit risk model. More specifically, we study if distance‐to‐default is a sufficient statistic for the equity market information concerning the credit quality of the debt‐issuing firm. We show that a simple reduced form model outperforms the Merton (1974) model for both in‐sample fitting and out‐of‐sample predictability for credit ratings, and that both can be greatly improved by including the firm's equity value as an additional variable. Moreover, the empirical performance of this hybrid model is very similar to that of the simple reduced form model. As a result, we conclude that distant‐to‐default alone does not adequately capture the firm's credit quality information from the equity market. Copyright © 2007 ASAC. Published by John Wiley & Sons, Ltd.