Asymptotic analysis for stochastic volatility: martingale expansion

A general class of stochastic volatility models with jumps is considered and an asymptotic expansion for European option prices around the Black–Scholes prices is validated in the light of Yoshida’s martingale expansion theory. Several known formulas of regular and singular perturbation expansions are obtained as corollaries. An expansion formula for the Black–Scholes implied volatility is given which explains the volatility skew and term structure. The leading term of the expansion is always an affine function of log moneyness, while the term structure of the coefficients depends on the details of the underlying stochastic volatility model. Several specific models which represent various types of term structure are studied.     

A synthesis of pure demand analysis

Abstract

§ 1. Summary and comments. Since Augustin Cournot, the pure theory of economic equilibrium consists in a separate analysis of demand and supply, the chief problem being- to prove the existence of a price constellation for which demand equals supply. In the theory of demand involved, it is a fundamental principle that demand is uniquely determined by income and prices. This principle is the central theme of the present paper.     

Free boundary and optimal stopping problems for American Asian options

We give a complete and self-contained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American path-dependent options. The framework is sufficiently general to include geometric Asian options with nonconstant volatility and recent path-dependent volatility models.      

A growth oriented dual income tax

This paper proposes a growth oriented dual income tax by combining an allowance for corporate equity with a broadly defined flat tax on personal capital income. Revenue losses are compensated by an increase in the value added tax. The paper demonstrates the neutrality properties of the reform with respect to investment, firm financial decisions and organizational choice. Tax rates are chosen to prevent income shifting from labor to capital income. The reform decisively strengthens investment of domestically owned firms as well as home and foreign based multinationals and boosts savings. Simulations with a calibrated growth model for Switzerland indicate that the reform could add between 4 to 5 percent of GNP in the long-run, depending on the specific scenario. Given the slow nature of capital accumulation, it imposes considerable costs in the short-run. We consider a tax smoothing scenario to offset the intergenerationally redistributive effects. JEL Classification: D58, D92, E62, G32, H25     

A general HJM framework for multiple yield curve modelling

We propose a general framework for modelling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor’s length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows unifying and extending several recent approaches to multiple yield curve modelling.     

Multilevel dual approach for pricing American style derivatives

In this article we propose a novel approach to reduce the computational complexity of the dual method for pricing American options. We consider a sequence of martingales that converges to a given target martingale and decompose the original dual representation into a sum of representations that correspond to different levels of approximation to the target martingale. By next replacing in each representation true conditional expectations with their Monte Carlo estimates, we arrive at what one may call a multilevel dual Monte Carlo algorithm. The analysis of this algorithm reveals that the computational complexity of getting the corresponding target upper bound, due to the target martingale, can be significantly reduced. In particular, it turns out that using our new approach, we may construct a multilevel version of the well-known nested Monte Carlo algorithm of Andersen and Broadie (Manag. Sci. 50:1222–1234, 2004) that is, regarding complexity, virtually equivalent to a non-nested algorithm. The performance of this multilevel algorithm is illustrated by a numerical example.     

Risk measures for derivatives with Markov-modulated pure jump processes

We consider a regime-switching HJB approach to evaluate risk measures for derivative securities when the price process of the underlying risky asset is governed by the exponential of a pure jump process with drift and a Markov switching compensator. The pure jump process is flexible enough to incorporate both the infinite, (small), jump activity and the finite, (large), jump activity. The drift and the compensator of the pure jump process switch over time according to the state of a continuous-time hidden Markov chain representing the state of an economy. The market described by our model is incomplete. Hence, there is more than one pricing kernel and there is no perfect hedging strategy for a derivative security. We derive the regime-switching HJB equations for coherent risk measures for the unhedged position of derivative securities, including standard European options and barrier options. For measuring risk inherent in the unhedged option position, we first need to mark the position into the market by valuing the option. We employ a well-known tool in actuarial science, namely, the Esscher transform to select a pricing kernel for valuation of an option and to generate a family of real-world probabilities for risk measurement. We also derive the regime-switching HJB-variational inequalities for coherent risk measures for American-style options.     

A dynamic theory of multiple borrowing

Multiple borrowing—when borrower obtains overlapping loans from multiple lenders—is a common phenomenon in many credit markets. We build a tractable, dynamic model of multiple borrowing and show that, because overlapping creditors can impose default externalities on each other, expanding financial access by introducing more lenders can backfire. Capital allocation is distorted away from the most productive uses. Entrepreneurs choose inefficient endeavors with low returns to scale. These problems are exacerbated when investments become more pledgeable or when borrowers have access to more lenders, explaining why increased access to finance does not always improve outcomes.     

A multiple state model for the working-age disabled population using cross-sectional data

A multiple state model describes the transitions of the disability risk among the states of active, inactive and dead. Ideally, estimations of transition probabilities and transition intensities rely on longitudinal data; however, most of the national surveys of disability are based on cross-sectional data measuring the disabled status of an individual at one point in time. This paper aims to propose a generic method of the estimation of the expected transition probabilities when the model allows recovery from disability using the UK cross-sectional data. The disability prevalence rates are modelled by taking into consideration the effect of age and time. Under some plausible assumptions concerning the death rates among inactive and active people, the estimated prevalence rates of disability are used to decompose survival probabilities in each state.     

A framework for the analysis of interview data from multiple field research sites

In general, papers reporting the results of research studies disclose little detail regarding attributes of study design, analytical processes and methods actually used by researchers. This paper describes in some depth the method choices and analytical protocol used in a field study project. The paper describes initially the link between research question, research design and analytical protocol. The major focus of the paper is the application of a systematic analytical protocol designed to encourage completeness and impartiality in the collection and analysis of qualitative data. These method issues are examined in the context of the author's experiences in the field and through the process of data analysis. The methods used are also examined critically in retrospect.     

A Bayesian interpretation of the Federal Reserve's dual mandate and the Taylor Rule

When the Federal Reserve was established by the US Congress in 1913, its charter mandated that the new central bank “promote an elastic currency” and the institution was given extraordinary powers to serve as a lender of last resort to the banking system. Congress was reacting to the cycle of financial panics that had beset the country since the Civil War and had worsened with the Panic of 1907. Congress sought to find a remedy to prevent runs on banks turning into full-fledged financial crises. The term “elastic” in the opening words of the charter was intended to underscore the need for a robust banking system that could withstand shocks and not collapse upon itself. There was no mention whatsoever of a dual mandate of promoting price stability and encouraging full employment.With prodding from the US Congress, the Federal Reserve became highly involved in the management of the economy of the United States after WWII, focusing on inflation and full employment objectives. In 1993 Professor John Taylor set forth an elegant and simple framework (aka, the Taylor Rule) for analyzing the interest rate policy of the Federal Reserve in terms of its dual mandate.This paper examines Federal Reserve behavior from the mid-1950s to 2011 through the lens of the Taylor Rule. Our contribution is to use a dynamic linear model with Bayesian inference to update the evolution through time of the key parameters surrounding the inflation and full employment mandates, using only the information available to the Federal Reserve at each point in time. Our findings provide a more nuanced quantitative view than is previously available in the literature of how the Federal Reserve shifted its management of its dual mandate over time and in response to different economic challenges. Moreover, our research leads to serious questions of how Federal Reserve decision making may change in the future, following the financial panic of 2008, pointing toward numerous avenues for new research.     

Financial distress and the Malaysian dual baking system: A dynamic slacks approach

This paper presents an efficiency assessment of the Malaysian dual banking system using the Dynamic Slacks Based Model (DSBM) in order to assess the evolution of Malaysian Banks’ potential input–saving/output–increase from 2009 to 2013. More precisely, DSBM is used first in a two-stage approach to assess the relative efficiency of Malaysian Islamic and conventional banks by emulating the CAMEL rating systems. Then, in the second stage, Monte Carlo Markov Chain (MCMC) methods applied to generalized linear mixed models (GLMM) are combined with DSBM results as part of an attempt to produce a model for banking performance assessment with effective predictive ability. Results indicate higher inefficiency levels and slacks in Islamic banks when compared to conventional ones. Furthermore, when the scope of analysis is the group of Malaysian Islamic banks, the efficiency levels of foreign banks are lower compared to their national counterparts, suggesting regulatory and cultural barriers. Policy implications are derived.     

A semi-analytic method for valuing high-dimensional options on the maximum and minimum of multiple assets

Valuing high-dimensional options has many important applications in finance but when the true distributions are unknown or complex, numerical approximations must be used. Approximation methods based on Monte-Carlo simulation show a steep trade-off between estimation accuracy and computational efficiency. This article presents an alternative semi-analytic approximation method for pricing options on the maximum or minimum of multiple assets with unknown distributions. Computational efficiency is shown to improve significantly without sacrificing estimation accuracy. The method is illustrated with applications to options on underlying assets with mean-reverting prices, time-dependent correlations, and stochastic volatility The authors would like to thank the two anonymous referees, the associate editor, and Dr. Jess H. Chua at the University of Calgary for valuable comments and insights on this research. This research was partly supported by NUS grant R-146-000-059-112     

A multiple discriminant analysis of BHC commercial paper ratings

The finance literature contains many examples of attempts to classify bond issuers into agency rating categories and to identify the key variables that contribute to bond rating differences. This study extends the classification literature to include bank holding company (BHC) commercial paper issuers. A multiple discriminant model is developed that effectively classifies paper issuers into their respective Moody's rating groups. An additional discriminant model is derived that classifies these issuers into more detailed ‘market’ rating groups.     

Term structure modelling for multiple curves with stochastic discontinuities

Finance and Stochastics - We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate...     

Pricing securities with multiple risks: A case of exchangeable debt

Building on the work of Das and Sundaram (2007), we develop a widely applicable model to price securities subject to interest rate, equity, and default risks and use it to price exchangeable bonds. The extension features a trivariate recombining lattice instead of the original model’s bivariate recombining lattice. We also show how to estimate some critical non-observable inputs to implement the model by using current market data so that the model’s prices reflect current market information. We test the model on a sample of exchangeable bonds to determine the model’s empirical performance. Besides exchangeable bonds, we can also use the model to price securities such as reverse exchangeable bonds, bonds exchangeable to indexes, and bonds exchangeable to commodities.     

Managerial ownership of voting rights: A study of public corporations with dual classes of common stock

Managers of firms with dual classes of common stock can choose different quantities of votes for a given cash flow interest by choosing different quantities of the two securities. We study managerial stock holdings in 45 dual class firms and find that vote ownership per se is an important motivation for these holdings in that corporate officers and their families hold a median 56.9% of the votes and 24.0% of the common stock cash flows. We also find significant family involvement in many sample firms, and document four case studies in which explicit acquisition premiums were paid for superior voting shares.