Turbo warrants under stochastic volatility

Turbo warrants have experienced huge growth since they first appeared in late 2001. In some European countries, buying and selling turbo warrants constitutes 50% of all derivative trading nowadays. In Asia, the Hong Kong Exchange and Clearing Limited (HKEx) introduced the callable bull/bear contracts, which are essentially turbo warrants, to the market in 2006. Turbo warrants are special types of barrier options in which the rebate is calculated as another exotic option. It is commonly believed that turbo warrants are less sensitive to the change in volatility of the underlying asset. Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]) has considered the pricing of turbo warrants under the Black–Scholes model. However, the pricing and characteristics of turbo warrants under stochastic volatility are not known. This paper investigates the valuation of turbo warrants considered by Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]), but extends the analysis to the CEV, the fast mean-reverting stochastic volatility and the two time-scale volatility models. We obtain analytical solutions for turbo warrants under the aforementioned models. This enables us to examine the sensitivity of turbo warrants to the implied volatility surface.     

Estimating default barriers from market information

Brockman and Turtle [J. Finan. Econ., 2003, 67, 511–529] develop a barrier option framework to show that default barriers are significantly positive. Most implied barriers are typically larger than the book value of corporate liabilities. We show theoretically and empirically that this result is biased due to the approximation of the market value of corporate assets by the sum of the market value of equity and the book value of liabilities. This approximation leads to a significant overestimation of the default barrier. To eliminate this bias, we propose a maximum likelihood (ML) estimation approach to estimate the asset values, asset volatilities, and default barriers. The proposed framework is applied to empirically examine the default barriers of a large sample of industrial firms. This paper documents that default barriers are positive, but not very significant. In our sample, most of the estimated barriers are lower than the book values of corporate liabilities. In addition to the problem with the default barriers, we find significant biases on the estimation of the asset value and the asset volatility of Brockman and Turtle.     

Firm size,information acquisition and price efficiency

We present a model in a competitive market where traders choose between a small and a large firm to acquire costly private information, but they also obtain free public information by observing equilibrium share prices. Our major finding is the existence of a noisy rational expectation competitive equilibrium, in which there are more informed traders of the large firm than those of the small firm. As a result, share prices of the large firm are more informative than those of the small firm. Our empirical study supports the analytical results. By using a bivariate vector autoregressive regression, we are able to conduct a variance decomposition of share prices for different size portfolios. We find that prices of large-size portfolios are more informative because non-value-related price shocks are less important in driving price changes of large-size portfolios than in the case of small-size portfolios.     

Historical simulation approach to the estimation of stochastic discount factor models

We propose an approach to the estimation of the parameters of stochastic discount factor (SDF) models which is based on the idea that the next period joint distribution of the variables in a SDF and asset returns can be well approximated by their joint historical distribution. The estimates of the SDF parameters may therefore be found as the values of the parameters at which the mean of the historical distribution of the product of the SDF with an asset return equals one. Each time period, the estimates are updated using the most recent periods of data and hence can change over time. This method can be viewed as an alternative to the approaches that specify a particular functional form relating the SDF parameters to proxies for the state of the world.     

Pricing credit default swaps with bilateral value adjustments

The aim of this work is to examine the influence of mutual fund flows on market timing models, thus providing unbiased timing coefficients. However, as this control is motivated by the existing relationship between mutual fund flows and market returns, we first analyse this relationship, considering previous and concurrent market returns. However, unlike existing studies, we do not consider future returns, since investors do not observe them when making investment decisions. Thus, we feel it is more appropriate to consider expected market returns. We construct the expected market returns by running an AR model and considering the available public information about the macro-economy. The relationship is analysed under different conditions, considering a variety of different mutual fund flow measures, and considering (or not) the sensitivity of mutual fund flows to positive and negative market returns. We also propose different controls for the traditional timing models, and we further analyse the reverse-causality problem. The study demonstrates, for a sample of equity mutual funds registered for sale in the USA, that the poor market timing performance found in this and other prior studies can be completely attributed to the perverse effect of the fund managers’ liquidity service.     

Empirical analysis of the average asset correlation for real estate investment trusts

The credit risk capital requirements within the current Basel II Accord are based on the asymptotic single risk factor (ASRF) approach. The asset correlation parameter, defined as an obligor's sensitivity to the ASRF, is a key driver within this approach, and its average values for different types of obligors are to be set by regulators. Specifically, for commercial real estate (CRE) lending, the average asset correlations are to be determined using formulas for either income-producing real estate or high-volatility commercial real estate. In this paper, the value of this parameter was empirically examined using portfolios of U.S. publicly-traded real estate investment trusts (REITs) as a proxy for CRE lending more generally. CRE lending as a whole was found to have the same calibrated average asset correlation as corporate lending, providing support for the recent U.S. regulatory decision to treat these two lending categories similarly for regulatory capital purposes. However, the calibrated values for CRE categories, such as multi-family residential or office lending, varied in important ways. The comparison of calibrated and regulatory values of the average asset correlations for these categories suggests that the current regulatory formulas generate parameter values that may be too high in most cases.     

Modeling default risk with support vector machines

Predicting default risk is important for firms and banks to operate successfully. There are many reasons to use nonlinear techniques for predicting bankruptcy from financial ratios. Here we propose the so-called Support Vector Machine (SVM) to predict the default risk of German firms. Our analysis is based on the Creditreform database. In all tests performed in this paper the nonlinear model classified by SVM exceeds the benchmark logit model, based on the same predictors, in terms of the performance metric, AR. The empirical evidence is in favor of the SVM for classification, especially in the linear non-separable case. The sensitivity investigation and a corresponding visualization tool reveal that the classifying ability of SVM appears to be superior over a wide range of SVM parameters. In terms of the empirical results obtained by SVM, the eight most important predictors related to bankruptcy for these German firms belong to the ratios of activity, profitability, liquidity, leverage and the percentage of incremental inventories. Some of the financial ratios selected by the SVM model are new because they have a strong nonlinear dependence on the default risk but a weak linear dependence that therefore cannot be captured by the usual linear models such as the DA and logit models.     

Bivariate normal mixture spread option valuation

We discuss the pricing and hedging of European spread options on correlated assets when the marginal distribution of each asset return is assumed to be a mixture of normal distributions. Being a straightforward two-dimensional generalization of a normal mixture diffusion model, the prices and hedge ratios have a firm behavioural and theoretical foundation. In this ‘bivariate normal mixture’ (BNM) model no-arbitrage option values are just weighted sums of different ‘2GBM’ option values that are based on the assumption of two correlated lognormal diffusions, and likewise for their sensitivities. The main advantage of this approach is that BNM option values are consistent with both volatility smiles and with the implied correlation ‘frown’. No other ‘frown consistent’ spread option valuation model has such straightforward implementation. We apply analytic approximations to compare BNM valuations of European spread options with those based on the 2GBM assumption and explain the differences between the two as a weighted sum of six second-order 2GBM sensitivities. We also examine BNM option sensitivities, finding that these, like the option values, can sometimes differ substantially from those obtained under the 2GBM model. Finally, we show how the correlation frown that is implied by the BNM model is affected as we change (a) the correlation structure and (b) the tail probabilities in the joint density of the asset returns.     

The Conditional Relationship Between Beta and Returns: A Reassessment

Abstract:  Several recent empirical tests of the Capital Asset Pricing Model have been based on the conditional relationship between betas and market returns. This paper shows that this method needs reconsideration. An adjusted version of this test is presented. It is then demonstrated that the adjusted technique has similar, or lower, power to the more easily implemented CAPM test of Fama and MacBeth (1973) if returns are normally distributed.     

Multi-scale variation,path risk and long-term portfolio management

Mean–variance analysis is constrained to weight the frequency bands in a return time series equally. A more flexible approach allows the user to assign preference weightings to short or longer run frequencies. Wavelet analysis provides further flexibility, removing the need to assume asset returns are stationary and encompassing alternative return concepts. The resulting portfolio choice methodology establishes a reward–energy efficient frontier that allows the user to trade off expected reward against path risk, reflecting preferences as between long or short run variation. The approach leads to dynamic analogues of mean–variance such as band pass portfolios that are more sensitive to variability at designated scales.     

Asymmetry of information flow between volatilities across time scales

Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data-generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and, consequently, the calculation of risk at different time scales.     

Utility valuation of multi-name credit derivatives and application to CDOs

We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based models of default risk, we analyse resulting yield spreads in multi-name credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyse the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.     

An event study of price movements following realized jumps

Price jumps are mostly related to investor reactions to unexpected extreme news. We perform an event study of price movements after jumps to analyse if investors’ reactions are affected by psychological biases. We employ recent non-parametric methods based on intraday returns to separate large price movements that are related to unexpected news from those merely caused by periods of high volatility. In general, we find evidence for irrational pricing, which can be associated with investors’ optimistic behavior in a bull market and the pessimism prevailing in a bear market. Furthermore, our analysis confirms the conjecture that small firms are more subject to speculative trading than large firms.     

Capital allocation for credit portfolios with kernel estimators

Determining the contributions of sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often, economic capital is measured as the Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.     

Multivariate asset price dynamics with stochastic covariation

A Markov chain with an expanding non-uniform grid matching risk-neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with pre-specified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from option data. For Markov chains, dynamically consistent sequences of bid and ask prices are developed by applying the theory of nonlinear expectations with drivers given by concave distortions applied to the one-step-ahead risk. The procedures are illustrated by generating dynamically consistent bid ask sequences for a variety of structured products, such as locally capped and floored cliquets, rolling calls and puts and hedged and unhedged variance swap contracts. Two-sided nonlinear barrier pricing of straddles is also accomplished. All methods are illustrated on the surface of JPM on October 15, 2009.     

Transaction costs,liquidity risk,and the CCAPM

In this paper, we make a liquidity adjustment to the consumption-based capital asset pricing model (CCAPM) and show that the liquidity-adjusted CCAPM is a generalized model of Acharya and Pedersen (2005). Using different proxies for transaction costs such as the effective trading costs measure of Hasbrouck (2009) and the bid-ask spread estimates of Corwin and Schultz (2012), we find that the liquidity-adjusted CCAPM explains a larger fraction of the cross-sectional return variations.     

Credit ratings and the cross-section of stock returns

Low credit risk firms realize higher returns than high credit risk firms. This is puzzling because investors seem to pay a premium for bearing credit risk. The credit risk effect manifests itself due to the poor performance of low-rated stocks (which account for 4.2% of total market capitalization) during periods of financial distress. Around rating downgrades, low-rated firms experience considerable negative returns amid strong institutional selling, whereas returns do not differ across credit risk groups in stable or improving credit conditions. The evidence for the credit risk effect points towards mispricing generated by retail investors and sustained by illiquidity and short sell constraints.     

VaR and expected shortfall: a non-normal regime switching framework

We have developed a regime switching framework to compute the Value at Risk and Expected Shortfall measures. Although Value at Risk as a risk measure has been criticized by some researchers for lack of subadditivity, it is still a central tool in banking regulations and internal risk management in the finance industry. In contrast, Expected Shortfall is coherent and convex, so it is a better measure of risk than Value at Risk. Expected Shortfall is widely used in the insurance industry and has the potential to replace Value at Risk as a standard risk measure in the near future. We have proposed regime switching models to measure value at risk and expected shortfall for a single financial asset as well as financial portfolios. Our models capture the volatility clustering phenomenon and variance-independent variation in the higher moments by assuming the returns follow Student-t distributions.     

A perfect storm in the financial market

This study provides a model explaining how small changes in asset prices may disrupt an entire financial market. Based on the capital asset pricing model (CAPM), our model implies that during a market crash, asset price changes affect the relative distribution of the CAPM betas of individual assets and force all tradable assets to co-move. Using US stock market data, our empirical results are consistent with the model’s predictions. Overall, the study aids understanding of the price patterns of assets during substantial market downturns, such as financial crises.     

A two-factor model for the electricity forward market

This paper provides a two-factor model for electricity futures that captures the main features of the market and fits the term structure of volatility. The approach extends the one-factor model of Clewlow and Strickland to a two-factor model and modifies it to make it applicable to the electricity market. We will particularly deal with the existence of delivery periods in the underlying futures. Additionally, the model is calibrated to options on electricity futures and its performance for practical application is discussed.