Target volatility option pricing in the lognormal fractional SABR model

We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decomposition formula in terms of Malliavin derivatives is also provided. Alternatively, we also derive closed form expressions for a small volatility of volatility expansion of the price of a target volatility option. Numerical experiments show the accuracy of the approximations over a reasonably wide range of parameters.     

Hybrid scheme for Brownian semistationary processes

We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to approximate the kernel function by a power function near zero and by a step function elsewhere. The resulting approximation of the process is a combination of Wiener integrals of the power function and a Riemann sum, which is why we call this method a hybrid scheme. Our main theoretical result describes the asymptotics of the mean square error of the hybrid scheme, and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments, where we examine the finite-sample properties of an estimator of the roughness parameter of a Brownian semistationary process and study Monte Carlo option pricing in the rough Bergomi model of Bayer et al. (Quant. Finance 16:887–904, 2016), respectively.     

Pricing CIR Yield Options by Conditional Moment Matching

We propose an approximation scheme for the pricing of yield options in the CIR model using conditional moment matching based on the gamma and lognormal distributions. This method is fast and simple to implement, and it shows a high degree of accuracy without being subject to the numerical instabilities that can be encountered with more sophisticated approaches.     

On the accuracy of phase-type approximations of heavy-tailed risk models

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.     

Endogenous current coupons

We consider the problem of identifying current coupons for agency-backed to-be-announced pools of residential mortgages. Such coupons, or mortgage origination rates, ensure par-valued pools. In a doubly stochastic reduced form model which allows prepayment intensities to depend upon both current and origination mortgage rates, as well as underlying investment factors, we identify the current coupon as a solution to a degenerate elliptic, nonlinear fixed point problem. Using Schaefer’s theorem, we prove existence of a current coupon. We also provide an explicit approximation to the fixed point, valid for compact perturbations off a baseline factor-based intensity model. A numerical example is provided which shows that the approximation performs well in estimating the current coupon.     

A Historical Analysis of the Taylor Curve

Taylor (1979) shows that there is a permanent trade‐off between the volatilities of the output gap and inflation. Although a number of papers argue that the so‐called Taylor curve is a policy menu, we use it as an efficiency locus to gauge the appropriateness of monetary policy. We examine the efficiency of U.S. monetary policy from 1875 onward by measuring the orthogonal distance between the observed volatilities of the output gap and inflation from the Taylor curve. We also identify time periods in which the variability of the U.S. economy changed by observing shifts in this efficiency frontier.     

Optimal equity valuation using multiples: The number of comparable firms

We examine how the accuracy of a multiples-based valuation changes as the number of comparable firms used to estimate the valuation multiple increases. Our research is motivated by a contrast between the approach followed by practitioners, who typically use a small number of closely comparable firms, and the academic literature which often uses all firms in an industry. Using a simple selection rule based on growth rates, we find that using 10 closely comparable firms is as accurate on average as using the entire cross-section of firms in an industry. The loss of accuracy from using five comparable firms rather than 10 firms or the entire industry is not great.     

Maximum likelihood estimation of stochastic volatility models

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a short-dated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.     

Pricing options on discrete realized variance with partially exact and bounded approximations

We derive efficient and accurate analytic approximation formulas for pricing options on discrete realized variance (DRV) under affine stochastic volatility models with jumps using the partially exact and bounded (PEB) approximations. The PEB method is an enhanced extension of the conditioning variable approach commonly used in deriving analytic approximation formulas for pricing discrete Asian style options. By adopting either the conditional normal or gamma distribution approximation based on some asymptotic behaviour of the DRV of the underlying asset price process, we manage to obtain PEB approximation formulas that achieve a high level of numerical accuracy in option values even for short-maturity options on DRV.     

Confined exponential approximations for the valuation of American options

We provide an alternative analytic approximation for the value of an American option using a confined exponential distribution with tight upper bounds. This is an extension of the Geske and Johnson compound option approach and the Ho et al. exponential extrapolation method. Use of a perpetual American put value, and then a European put with high input volatility is suggested in order to provide a tighter upper bound for an American put price than simply the exercise price. Numerical results show that the new method not only overcomes the deficiencies in existing two-point extrapolation methods for long-term options but also further improves pricing accuracy for short-term options, which may substitute adequately for numerical solutions. As an extension, an analytic approximation is presented for a two-factor American call option.     

On the Information in the Interest Rate Term Structure and Option Prices

We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.     

The effect of repeat restructuring charges on analysts’ forecast revisions and accuracy

The primary objective of this study is to examine the effect of prior restructuring charges on analyst forecast revisions and accuracy. We find evidence that analysts respond differently to first-time restructuring firms than to repeat restructuring firms. Analysts revise their forecasts of both one-year-ahead earnings and five-year long-term growth in earnings more negatively for first-time restructuring firms than for firms with prior charges. When we examine forecast errors in the year subsequent to the restructuring, we find that current charges complicate analysts’ earnings forecast task. We further find that the decline in analyst forecast accuracy is mitigated by prior charges within past two years.     

Which form of hedging matters — Operational or financial? Evidence from the US oil and gas sector

We examine the extent and impact of operational and financial hedging on commodity price risk in US oil and gas companies. We find significant exposure to underlying commodity movements. Using a combination of hand collected and publicly available data we examine the impact of hedging strategies. We find no evidence that operational hedging, defined here as multinationality, is effective. In contrast, we find that financial hedging is significant and impactful. Sub-period analysis shows that the effectiveness of financial hedging diminishes when commodity price volatility is high.     

Investor Reaction to Celebrity Analysts: The Case of Earnings Forecast Revisions

We examine the effects of analysts' celebrity on investor reaction to earnings forecast revisions. We measure celebrity as the quantity of media coverage analysts receive in sources included in the Dow Jones Interactive database, and find that media coverage is positively related to investor reaction to forecast revisions. The effect of celebrity on the reaction to forecast revisions remains significant after controlling for forecast performance variables examined in prior studies (ex post forecast accuracy, ex ante accuracy, award status, and other variables shown to be related to forecast accuracy). While these results are consistent with the familiarity of the analyst's name affecting the market reaction, we cannot rule out that our measure of celebrity is correlated with error in the performance measures we examine and/or correlated with other unexamined dimensions of forecast performance. A content analysis of a random subsample of the media coverage of our sample analysts suggests that our findings likely are not due to the increased availability of forecast revisions. Finally, an investigation of the excess returns around the quarterly earnings announcement date suggests that market participants react too strongly to forecast revisions issued by analysts with high levels of media coverage. Taken together, these findings suggest that an analyst's level of media coverage can affect the initial market reaction to his forecast revisions.     

Second order approximations for limit order books

In this paper, we derive a second order approximation for an infinite-dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g. the volume standing at the top of the book). We study the fluctuations of the price and volume process relative to their first order approximation given in ODE–PDE form under two different scaling regimes. In the first case, we suppose that price changes are really rare, yielding a constant first order approximation for the price. This leads to a measure-valued SDE driven by an infinite-dimensional Brownian motion in the second order approximation of the volume process. In the second case, we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process. Our results can be used to derive confidence intervals for models of optimal portfolio liquidation under market impact.     

On the Structure of Analyst Research Portfolios and Forecast Accuracy

This study provides insights into the forces and constraints that shape analyst research coverage along country and sector dimensions and the impact of the structure of an analyst's portfolio on forecast accuracy. We find that analyst specialization by country and sector is sensitive to the extent to which firms  within  a country or sector and firms  across  country-sectors are exposed to common economic forces, the potential for revenue generation, and broker culture. Our tests indicate that existing research on the relation between analyst portfolio structure and forecast accuracy may suffer from an endogeneity bias. We use our analysis of analyst specialization to develop controls for this bias. Once we employ these controls, we find that country diversification is associated with superior forecast accuracy. However, the relation between sector diversification and forecast accuracy is context-specific. Specifically, sector diversification enhances forecast accuracy in an international context, while it detracts from forecast accuracy in a domestic U.S. context.     

A practical approach to semideviation and its time scaling in a jump-diffusion process

One of the most popular risk-adjusted fund return measures in the asset management industry is the Sortino ratio. It is an alternative to the Sharpe ratio that differentiates harmful volatility from general volatility by taking into account the standard deviation of negative asset returns, a quantity called semideviation. Indeed, the semideviation is generally preferred to the standard deviation when the distribution of the returns is skewed. A common method to annualize it is to use the square-root-of-time rule, where an estimated quantile of a return distribution is scaled to a lower frequency by the square root of the time horizon. However, this relation does not generally hold for this risk measure and often gives a terrible estimation of it. The aim of this paper is to provide a practical approach to semideviation by explaining how it should be computed. We propose and justify the use of a new model, which delivers a more accurate estimation of the downside risk. It is a generalization of the Ball-Torous approximation of a jump-diffusion process, which can be applied when the volatility is constant or stochastic. In the latter case, we use Markov Chain Monte Carlo (MCMC) methods to fit our stochastic volatility model. We also derive an exact formula for the semideviation when the volatility is kept constant, explaining how it should be scaled when considering a lower frequency. For the tests, we apply our methodology to a highly skewed set of returns based on the Barclays US High Yield Index, where we compare different time scalings for the semideviation. Our work shows that the square-root-of-time rule provides a poor approximation of the semideviation, and that the simplification brought by Ball and Torous should be replaced by our new methodology, as it gives much better results.     

Is universal banking justified? Evidence from bank underwriting of corporate bonds in Japan

We examine the extent to which universal banking in Japan creates conflicts of interest. We find that as banks enter the securities business, they discount the price of the corporate bonds they underwrite significantly in an effort to attract investors, thereby generating conflicts of interest that are harmful to issuers. Further, we find that close prior lending relationships between banks and their client issuers is the driving force behind such conflicts and that competition from investment houses limits but does not eliminate these conflicts. Our results contrast sharply with the evidence for the US, which largely shows a certification role for banks.     

Nonlinear portfolio selection using approximate parametric Value-at-Risk

As the skewed return distribution is a prominent feature in nonlinear portfolio selection problems which involve derivative assets with nonlinear payoff structures, Value-at-Risk (VaR) is particularly suitable to serve as a risk measure in nonlinear portfolio selection. Unfortunately, the nonlinear portfolio selection formulation using VaR risk measure is in general a computationally intractable optimization problem. We investigate in this paper nonlinear portfolio selection models using approximate parametric Value-at-Risk. More specifically, we use first-order and second-order approximations of VaR for constructing portfolio selection models, and show that the portfolio selection models based on Delta-only, Delta–Gamma-normal and worst-case Delta–Gamma VaR approximations can be reformulated as second-order cone programs, which are polynomially solvable using interior-point methods. Our simulation and empirical results suggest that the model using Delta–Gamma-normal VaR approximation performs the best in terms of a balance between approximation accuracy and computational efficiency.     

An investigation into the measurement of graph distortion in financial reports

The Graph Discrepancy Index (GDI), which originates from the lie factor introduced by Tufte (1983), is the mechanism commonly used in the financial graphics literature to determine whether graphs are distorted and to quantify the extent of such distortion. Although the GDI is critical to the financial graphics literature, little or no attention has been paid to its robustness and accuracy. We critically examine the mathematical characteristics of the GDI and show its limitations as a measure of graph distortion. We review a number of cases to demonstrate these limitations and present an alternative measure of graph distortion—the Relative Graph Discrepancy index (RGD). Numerous simulations suggest that the RGD overcomes the problems associated with the GDI. The RGD is also tested on data presented in earlier research and the results are compared to those obtained using the GDI. In comparison with the GDI, we find that the RGD is more consistent and produces slightly stronger results. We stress, however, that this is not a best or definitive measure but is intended to start a research process that leads to a generally accepted measure.