Pricing of a structured product on the SX5E when the uncertainty of returns is modeled as a log-stable process

This work presents the participation factor and the valuation of a first-generation structured product with European call options on the Eurostoxx, when the uncertainty of the yields is modeled through log-stable processes. The basic statistics of the index yields are also exposed, the α-stable parameters are estimated, and the valuation of the of the structured models is compared through the log-stable and log-Gaussian models using inputs from the bond markets; concluding that investors obtain higher yields than those of the bond market through both models, and that the differences of the yields depend on the participation factor and on the value of the index at the time of liquidation.     

Can interest rate volatility be extracted from the cross section of bond yields?

Most affine models of the term structure with stochastic volatility predict that the variance of the short rate should play a ‘dual role’ in that it should also equal a linear combination of yields. However, we find that estimation of a standard affine three-factor model results in a variance state variable that, while instrumental in explaining the shape of the yield curve, is essentially unrelated to GARCH estimates of the quadratic variation of the spot rate process or to implied variances from options. We then investigate four-factor affine models. Of the models tested, only the model that exhibits ‘unspanned stochastic volatility’ (USV) generates both realistic short rate volatility estimates and a good cross-sectional fit. Our findings suggest that short rate volatility cannot be extracted from the cross-section of bond prices. In particular, short rate volatility and convexity are only weakly correlated.     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

Gaussian models for Euro high grade government yields

This paper tests affine, quadratic and Black-type Gaussian models on Euro area triple A Government bond yields for maturities up to 30 years. Quadratic Gaussian models beat affine Gaussian models both in-sample and out-of-sample. A Black-type model best fits the shortest maturities and the extremely low yields since 2013, but worst fits the longest maturities. Even for quadratic models we can infer the latent factors from some yields observed without errors, which makes quasi-maximum likelihood (QML) estimation feasible. New specifications of quadratic models fit the longest maturities better than does the ‘classic’ specification of Ahn et al. [2002. ‘Quadratic Term Structure Models: Theory and Evidence.’ The Review of Financial Studies 15 (1): 243–288], but the opposite is true for the shortest maturities. These new specifications are more suitable to QML estimation. Overall quadratic models seem preferable to affine Gaussian models, because of superior empirical performance, and to Black-type models, because of superior tractability. This paper also proposes the vertical method of lines (MOL) to solve numerically partial differential equations (PDEs) for pricing bonds under multiple non-independent stochastic factors. ‘Splitting’ the PDE drastically reduces computations. Vertical MOL can be considerably faster and more accurate than finite difference methods.     

EVIDENCE ON DELTA HEDGING AND IMPLIED VOLATILITIES FOR THE BLACK‐SCHOLES,GAMMA, AND WEIBULL OPTION PRICING MODELS

Modifying the distributional assumptions of the Black‐Scholes model is one way to accommodate the skewness of underlying asset returns. Simple models based on the compensated gamma and Weibull distributions of asset prices are shown to produce some improvements in option pricing. To evaluate these assertions, I construct and compare delta hedges of all S&P 500 options traded on the Chicago Board Options Exchange between September 2001 and October 2003 for the Weibull, Black‐Scholes, and gamma models. I also compare implied volatilities and their smiles (i.e., nonlinearities) among the three models. None of the three models improves over the others as far as delta hedging is concerned. Volatilities implied by all three models exhibit statistically significant smiles.     

Non-linear Gaussian sovereign CDS pricing models

Prior literature indicates that quadratic models and the Black–Karasinski model are very promising for CDS pricing. This paper extends these models and the Black [J. Finance 1995, 50, 1371–1376] model for pricing sovereign CDS’s. For all 10 sovereigns in the sample quadratic models best fit CDS spreads in-sample, and a four factor quadratic model can account for the joint effects on CDS spreads of default risk, default loss risk and liquidity risk with no restriction to factors correlation. Liquidity risk appears to affect sovereign CDS spreads. However, quadratic models tend to over-fit some CDS maturities at the expense of other maturities, while the BK model is particularly immune from this tendency. The Black model seems preferable because its out-of-sample performance in the time series dimension is the best.     

Liquidity,default, taxes,and yields on municipal bonds

We examine the effects of liquidity, default and personal taxes on the relative yields of Treasuries and municipals using a generalized model with liquidity risk. The municipal yield model includes liquidity as a state factor. Using a unique transaction dataset, we estimate the liquidity risk of municipals and its effect on bond yields. Empirical evidence shows that municipal bond yields are strongly affected by all three factors. The effects of default and liquidity risk on municipal yields increase with maturity and credit risk. Liquidity premium accounts for about 9–13% of municipal yields for AAA bonds, 9–15% for AA/A bonds and 8–19% for BBB bonds. A substantial portion of the maturity spread between long- and short-maturity municipal bonds is attributed to the liquidity premium. Ignoring the liquidity risk effect thus results in a severe underestimation of municipal bond yields. Conditional on the effects of default and liquidity risk, we obtain implicit tax rates very close to the statutory tax rates of high-income individuals and institutional investors. Furthermore, these implicit income tax rates are quite stable across bonds of different maturities. Results show that including liquidity risk in the municipal bond pricing model helps explain the muni puzzle.     

Macro-finance VARs and bond risk premia: A caveat

At the turn of the century, US and euro area long-term bond yields experienced a remarkable decline and remained at historically low levels despite rising short-term rates (the so called “conundrum”). Estimating macro-finance VARs and no-arbitrage term structure models, many researchers find that the decline in long-term rates was primarily driven by an unprecedented reduction in risk premia. I show that this result might be an artefact of the class of models employed to study the phenomenon.     

A structural decomposition of the US yield curve

By expanding the macro part of macro-finance models, historical fluctuations in US bond yields turn out to be largely consistent with the rational expectations hypothesis. We estimate a medium-scale macro-finance DSGE model of the term structure to establish this. Our finding contrasts with existing macro-finance models and suggests that their—small-scale or non-structural—perspective on the macroeconomy mutes expectations, thereby underestimating the expectations hypothesis’ potential. Out-of-sample forecasts are competitive with more flexible term structure models. Given the empirical validation, we interpret various episodes through the lens of the model and investigate which structural shocks cause the yield curve to contain information about future growth.     

How much of the corporate bond spread is due to personal taxes?

Existing term structure models of defaultable bonds have often underestimated corporate bond spreads. A potential problem is that investors’ taxes are ignored in these models. We propose a pricing model that accounts for stochastic default probability and differential tax treatments for discount and premium bonds. By estimating parameters directly from bond data, we obtain significantly positive estimates for the income tax rate of a marginal corporate bond investor after 1986. This contrasts sharply with the previous finding that the implied tax rates for Treasury bonds are close to zero. Results show that taxes explain a substantial portion of corporate bond spreads.     

“Hot Hands” in bond funds

We investigate persistence in the relative performance of 3549 bond mutual funds from 1990 to 2003. We show that bond funds that display strong (weak) performance over a past period continue to do so in future periods. The out-of-sample difference in risk-adjusted return between the top and bottom decile of funds ranked on past alpha exceeds 3.5 percent per year. We demonstrate that a strategy based on past fund returns earns an economically and statistically significant abnormal return, suggesting that bond fund investors can exploit the observed persistence. Our results are robust to a wide range of model specifications and bootstrapped test statistics.     

China’s official rates and bond yields

Recent research shows that bond yields are influenced by monetary policy decisions. To learn how this works in a bond market that differs significantly from those in the US and Europe, we model Chinese bond yields using the one-year deposit interest rate as a state variable. We also include the spread between the one-year market interest rate and the one-year deposit interest rate as another factor. The model is developed in an affine framework and closed-form solutions are obtained. We then test the model empirically with a Markov Chain Monte Carlo simulation procedure. The results show that the new model that incorporates the official rate in China characterizes the changing shape of the yield curve well.     

News and the cross-section of expected corporate bond returns

We study the cross-section of expected corporate bond returns using an inter-temporal CAPM (ICAPM) with three-factors: innovations in future excess bond returns, future real interest rates and future expected inflation. Our test assets are a broad range of corporate bond market index portfolios. We find that two factors – innovations about future inflation and innovations about future real interest rates – explain the cross-section of expected corporate bond returns in our sample. Our model provides an alternative to the ad hoc risk factor models used, for example, in evaluating the performance of bond mutual funds.     

The Costs of Issuing Preferred Stock

U.S. firms commonly use preferred stocks to raise external capital. Yet this hybrid security's issuance costs and offer yields have not been previously examined in a systematic manner. We analyze a sample of 3,042 U.S. preferred stocks issued between 1980 and 1999. We find that convertible issues, which are riskier than straight issues, entail higher gross spreads and other direct expenses. Scale, credit rating, and industry effects influence gross spreads and issuance costs. We also compare preferred stocks yields with various bellwether bond yields. Our results support the tax‐based argument that suggests that yields on preferred stocks should be lower than comparable risky bonds.     

Structural models of credit risk are useful: Evidence from hedge ratios on corporate bonds

Structural models of credit risk provide poor predictions of bond prices. We show that, despite this, they provide quite accurate predictions of the sensitivity of corporate bond returns to changes in the value of equity (hedge ratios). This is important since it suggests that the poor performance of structural models may have more to do with the influence of non-credit factors rather than their failure to capture the credit exposure of corporate debt. The main result of this paper is that even the simplest of the structural models [Merton, R., 1974. On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29, 449–470] produces hedge ratios that are not rejected in time-series tests. However, we find that the Merton model (with or without stochastic interest rates) does not capture the interest rate sensitivity of corporate debt, which is substantially lower than would be expected from conventional duration measures. The paper also shows that corporate bond prices are related to a number of market-wide factors such as the Fama-French SMB (small minus big) factor in a way that is not predicted by structural models.     

Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate Derivatives

Most existing dynamic term structure models assume that interest rate derivatives are redundant securities and can be perfectly hedged using solely bonds. We find that the quadratic term structure models have serious difficulties in hedging caps and cap straddles, even though they capture bond yields well. Furthermore, at‐the‐money straddle hedging errors are highly correlated with cap‐implied volatilities and can explain a large fraction of hedging errors of all caps and straddles across moneyness and maturities. Our results strongly suggest the existence of systematic unspanned factors related to stochastic volatility in interest rate derivatives markets.     

Moody's and S&P Ratings: Are They Equivalent? Conservative Ratings and Split Rated Bond Yields

We examine the relative impact of Moody's and S&P ratings on bond yields and find that at issuance, yields on split rated bonds with superior Moody's ratings are about 8 basis points lower than yields on split rated bonds with superior S&P ratings. This suggests that investors differentiate between the two ratings and assign more weight to the ratings from Moody’s, the more conservative rating agency. Moody's becomes more conservative after 1998 and the impact of a superior Moody's rating becomes stronger. Furthermore, the differential impact of the two ratings is more pronounced for the more opaque Rule 144A issues.     

Determinants of bond tender premiums and the percentage tendered

We analyze a large sample of US corporate bond tender offers to understand what affects tender premiums as well as the percentage of bonds tendered. For the average (median) tender offer, the tender price is 5.55% (3.24%) greater than the pre-tender market price while the percentage of bonds tendered is 82.3% (94.6%). Premiums offered by firms are greater when the firm is simultaneously soliciting consents to amend restrictive covenants and when the bond has a greater number of restrictive covenants. Premiums are also greater when long-term risk-free yields are low and the yield curve is flatter – conditions where a firm might want to lock in favorable long-term rates by issuing new debt and retiring old debt. Bondholders respond to higher tender premiums by tendering a greater percentage of their bonds – a 1% increase in tender premium increases the tendering rate by approximately 9%. Bondholders also tender a greater percentage of bonds possessing less desirable characteristics such as a short remaining maturity or bonds that are simultaneously undergoing consent solicitations. Finally, we find that tender offers are easier to complete when bond ownership concentration is greater.     

Structural models of corporate bond pricing with maximum likelihood estimation

This paper empirically examines the proxy, volatility-restriction (VR) and maximum likelihood (ML) approaches to implementing structural corporate bond pricing models, and documents that ML estimation is the best among the three implementation methods. Empirical studies using either the proxy approach or the VR method conclude that barrier-independent models significantly underestimate corporate bond yields. Although barrier-dependent models tend to overestimate the yield on average, they generate a sizable degree of underestimation. The present paper shows that the proxy approach is an upwardly biased estimator of the corporate assets and makes the empirical framework work systematically against structural models of corporate bond pricing. The VR approach may generate inconsistent corporate bond prices or may fail to give a positive corporate bond price for some structural models. When the Merton, LS, BD and LT models are implemented with ML estimation, we find substantial improvement in their performances. Our empirical analysis shows that the LT model is very accurate for predicting short-term bond yields, whereas the LS and BD models are good predictors for medium-term and long-term bonds. The Merton model however significantly overestimates short-term bond yields and underestimates long-term bond yields. Unlike empirical studies in the past, the Merton model implemented with ML estimation does not consistently underestimate corporate bond yields.     

Bond Pricing with a Time‐Varying Price of Risk in an Estimated Medium‐Scale Bayesian DSGE Model

New Keynesian model in which households have Epstein–Zin preferences with time‐varying risk aversion and the central bank has a time‐varying inflation target can match the dynamics of nominal bond prices in the U.S. economy well. The model generates a large steady‐state term spread and its fitting errors for bond yields are comparable to those obtained from a nonstructural three‐factor model, and one‐third smaller than in models with a constant inflation target or risk aversion. Including data on interest rates has large effects on variance decompositions, making investment technology shocks much less important than found in other recent papers.