Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market

We study the numerical solutions for an integro-differential parabolic problem modeling a process with jumps and stochastic volatility in financial mathematics. We present two general algorithms to calculate numerical solutions. The algorithms are implemented in PDE2D, a general-purpose, partial differential equation solver.     

Optimizing a portfolio of mean-reverting assets with transaction costs via a feedforward neural network

Optimizing a portfolio of mean-reverting assets under transaction costs and a finite horizon is severely constrained by the curse of high dimensionality. To overcome the exponential barrier, we develop an efficient, scalable algorithm by employing a feedforward neural network. A novel concept is to apply HJB equations as an advanced start for the neural network. Empirical tests with several practical examples, including a portfolio of 48 correlated pair trades over 50 time steps, show the advantages of the approach in a high-dimensional setting. We conjecture that other financial optimization problems are amenable to similar approaches.     

The subprime asset-backed securities market and the equity prices of large complex financial institutions

In this paper, we investigate the relationship between the subprime asset-backed collateralized debt obligations (CDO) market and Large Complex Financial Institutions (LCFIs). We attempt to account for the dynamics between the ABX index returns and the banks’ equity returns through conditioning our analysis on the historical correlation between the variables. Three key results emerge from the analysis. First, we find a positive correlation between movements of the ABX index and the equity returns for all the LCFIs. Second, the volatility of ABX index returns tend to be transmitted to the volatilities of the equity returns of the financial institutions. Third, ABX prices changes lead equity returns changes of the European-based LCFIs. For the US LCFIs a two-way linkage emerges.     

The determinants of recovery from the Black Saturday bushfire: demographic factors,behavioural characteristics and financial literacy

We investigate the contribution of demographic factors, behavioural characteristics and financial literacy to recovery from the financial losses inflicted by the Black Saturday bushfire. Behavioural characteristics (such as overconfidence, self-serving and loss aversion biases) in conjunction with bushfire survivors’ knowledge of financial indicators are used to determine recovery time. Data are collected through in-depth interviews with bushfire survivors, academics and experts in natural disasters. The results show that demographic, behavioural and financial literacy factors have the potential to enhance the recovery process.     

The geometry of crashes. A measure of the dynamics of stock market crises

This paper investigates the dynamics of stocks in the S&P 500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose that is a robust index of the dynamics of the market structure and provides information on the intensity and the sectoral impact of crises. With this measure, we analyse the effects of extreme phenomena on the geometry of the market. Nine crashes between 1987 and 2001 are compared by looking at the way they modify the shape of the manifold that describes the S&P 500 market space.     

Momentum effects in China: A review of the literature and an empirical explanation of prevailing controversies

The contribution of this paper is to enable solid conclusions to be drawn about the existence of momentum effects in China as the current evidence is unsatisfactory. We review and analyse the existing empirical studies on momentum and contrarian strategies in China and show that many of the findings in these studies appear inconsistent, if not actually contradictory. To clarify this confused situation we initially identify common findings in the diverse and seemingly contradictory body of existing empirical evidence. Subsequently, we systematically assess how the design of empirical studies affects the results of investigations in this area. We do this by conducting an empirical analysis of monthly data on Chinese A shares, varying one factor in the research design at a time (sample period, equally or value-weighed portfolios, skipping a period between portfolio formation and holding periods, and exclusion of post-IPO observations). This allows us to pinpoint directly how each of these factors affects momentum profits and thus when these profits are likely to be observed. It also indicates why studies using different designs might have arrived at seemingly inconsistent conclusions. Overall, we draw a number of conclusions: there appear to exist medium- and longer-term reversals in the pre-2001 period and short-term reversals and longer-term momentum effects thereafter; there is substantial time-variation in the profits to momentum strategies; small stocks exhibit stronger reversals than their larger counterparts; a large fraction of portfolio returns occur in the first month after formation; there is evidence of post-IPO price drifts. In summary, this study reconciles and explains the inconsistent evidence on the existence of momentum and contrarian effects in China allowing clear conclusions to be drawn.     

A multivariate analysis of REIT performance by financial and real asset portfolio characteristics

This paper examines the risk-adjusted performance of real estate investment trusts (REITs) from 1986 through 1990 in relation to financial and property characteristics of their portfolios. The Sharpe measure of risk-adjusted rate of return was regressed against financial ratios and property investment ratios for a sample of equity and mortgage REITs. The results show that, in general, financial ratios (gross cash flow, leverage, asset size), regional location of properties, and types of real estate investments determine the risk-adjusted performance. More specifically, location of properties in the western United States, ownership of health care properties, and investment in securitized mortgages positively affect the risk-adjusted return. The individual financial variables were not found to be statistically significant in influencing REIT returns.     

Change analysis of a dynamic copula for measuring dependence in multivariate financial data

This paper proposes a new approach to measure dependencies in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes within the dependence structure. Recently, two methods have been proposed using copulas to analyse such changes. The first approach investigates changes within the parameters of the copula. The second determines the sequence of copulas using moving windows. In this paper we take into account the non-stationarity of the data and analyse the impact of (1) time-varying parameters for a copula family, and (2) the sequence of copulas, on the computations of the VaR and ES measures. We propose tests based on conditional copulas and the goodness-of-fit to decide the type of change, and further give the corresponding change analysis. We illustrate our approach using the Standard & Poor 500 and Nasdaq indices in order to compute risk measures using the two previous methods.     

Quantile regression estimates and the analysis of structural breaks

The paper considers a test for structural breaks based on quantile regressions instead of OLS estimates. Besides granting robustness, this allows us to verify the impact of a break in more than one point of the conditional distribution. The quantile regression test is then repeatedly implemented as a diagnostic tool to uncover partial or spurious breaks. The test is also implemented to measure the contribution of each explanatory variable to the instability of the regression coefficients, thus finding which one of the different possible sources of breaks linked to the nature of the explanatory variables is the most effective. A real data example of exchange rates shows the presence of a time-driven break, but only at the lower quartile, while the analysis of the explanatory variable excludes its involvement in the break. Since the asymptotic distribution of the OLS test for structural change depends on i.i.d. normal errors and on the exogeneity of the explanatory variables, a Monte Carlo study analyses the behavior of OLS and quantile regression tests for structural changes with lagged endogenous variables, non-normal errors, spurious or partial breaks, and misspecification.     

Posterior analysis of mergers and acquisitions in the international financial market: A re-appraisal

Do mergers and acquisitions (M&A) improve the wealth status of investors, and if so, amidst persistence of volatility shocks? This paper tests these propositions by employing in the first step, a modified event study approach, and estimating a long-memory conditional volatility model, in the second step. The financial and policy implications of M&A are varied and contestable, yet, from an investor’s perspective, the long-term adjusted gain from M&A depends not only on the immediate growth of wealth, but also the fact that such a growth would accompany reduced rate of volatility persistence. Although in the beginning, a high persistence of volatility cannot be ruled out, its presence in the longer-run implies that the wealth gains from M&A are unstable, leading perhaps to a further collapse of both the merged/merger and acquired/acquiring firms. We estimate a long-memory Generalized Conditional Heteroscedasticity (GARCH) model with a Markovian transition for a number of international firms, specifically in Asia, to show in the first place, whether volatility shocks display differential memory in the pre- and post-M&A periods and whether the asymmetric high persistence is in the aftermath of M&A. Our results point at a significant ‘non-zero’ and positive gain for investors following M&A, but this is combined with greater volatility persistence.     

Systematic mistakes in the mortgage market and lack of financial sophistication

Institutions often offer a menu of contracts to consumers in an attempt to create a separating equilibrium that reveals borrower types and provides better pricing. We test the effectiveness of a specific set of contracts in the mortgage market: mortgage points. Points allow borrowers to exchange an upfront amount for a decrease in the mortgage rate. We document that, on average, points takers lose about $700. Also, points takers are less financially savvy (less educated, older), and they make mistakes on other dimensions (e.g., inefficiently refinancing their mortgages). Overall, our results show that borrowers overestimate how long they will stay with the mortgage.     

The capital market implications of the frequency of interim financial reporting: an international analysis

This study examines empirically the extent to which the frequency of interim financial reporting affects stock price volatility over the course of the fiscal year in four countries with different interim reporting regimes: the United States and Canada with quarterly reporting, and Great Britain and Australia with semi-annual interim reporting. It is hypothesized that, in the tradeoff between timeliness and predictive value of the interim reports, semi-annual interim reporting will lead to lesser price volatility after accounting for other potential influences. These expectations are supported in the results found. Moreover, additional tests conducted on American ADRs of British and Australian companies show that those firms have higher volatility than comparable purely domestic firms on their home stock exchanges.

Requiem for a market: an analysis of the rise and fall of a financial futures contract

Futures contracts often include a variety of delivery optionsthat allow participants flexibility in satisfying the contract.These options have the potential to broaden the appeal of thecontact. However, if these options are valuable, they may reducethe hedging effectiveness of the contract. This article analyzesthe GNMA CDR futures contract that appears to have failed becauseof flaws in the contract's design. For the first 6 years followingits introduction, the contract attracted significant and increasingvolume, but, subsequently, the volume declined to almost zero.Over the years during which the volume experienced its mostdramatic decline, the Treasury-bond futures contract provideda better hedge for current coupon GNMA securities than did theGNMA CDR futures contract. And, over this same period, the valueof the quality option embedded in the contract often exceeded5 percent of the futures price and reached a level of 19 percentat one point. We interpret the evidence to indicate that thecontract failed because the delivery options reduced the hedgingeffectiveness of the contract for current coupon mortgage securities.     

International linkage of the Russian market and the Russian financial crisis: A multivariate GARCH analysis

This study considers the linkage of the Russian equity market to the world market, examining the international transmission of the Russia's 1998 financial crisis utilizing the GARCH–BEKK model proposed by Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Economet. Theor. 11, 122–150]. We find evidence of direct linkage between the Russian equity market with regards to returns and volatility, while the weakness of the linkage suggests that the Russian equity market was only partially integrated into the world market. At the time of the crisis, evidence of contagion is clear.     

On an efficient multiple time step Monte Carlo simulation of the SABR model

In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options.     

Analysing liquidity and absorption limits of electronic markets with volume durations

This paper focuses on the liquidity of electronic stock markets applying a sequential estimation approach of models for volume duration with increasing threshold values. A modified ACD model with a Box–Tukey transformation and a flexible generalized beta distribution is proposed to capture the changing cluster structure of duration processes. The estimation results with German XETRA data reveal the market's absorption limit for high volumes of shares, expanding the time costs of illiquidity when trading these quantities.     

Expected earnings growth and the cost of capital: an analysis of accounting regime change in the European financial market

This study focuses on the relation between the cost of equity capital and earnings expectations when the properties of accounting that determine earnings vary across different regulatory regimes. More particularly, it addresses the European setting where different types of GAAP regime have continued to function in the presence of the gradual harmonization of the underlying legal framework, and where the adoption of internationally recognized accounting standards by certain firms has anticipated the requirement for International Financial Reporting Standards. On the basis of estimates of the cost of equity that are implied by analysts' earnings forecasts, the article provides evidence that financial market integration may have already contributed to mitigating the economic consequences of accounting diversity, and that switching to IFRS could have a short lived impact on capital markets. Moreover, based on firm level transparency and disclosure rankings provided by Standard and Poor's, it is shown how the quality of financial reporting conditions the implied cost of equity under different GAAP.     

Sample Size and the Strength of Evidence: A Bayesian Interpretation of Binomial Tests of the Information Content of Qualified Audit Reports

Lindley (1957) demonstrated that, from a Bayesian standpoint, a given level of statistical significance P carries less evidence against the null hypothesis H _o the larger (more powerful) the test. Moreover, if the sample is sufficiently large, a result significant on H _o at 5% or lower may represent strong evidence in support of H _o, not against it. Contrary to Lindley's argument, a great many applied researchers, trained exclusively in orthodox statistics, feel intuitively that to'reject' the null hypothesis H _o at (say) α= 5% is more convincing evidence, ceteris paribus , against H _o the larger the sample. This is a consistent finding of surveys in empirical psychology. Similarly, in accounting, see the principles for interpreting statistical tests suggested by Burgstahler (1987). In econometrics, 'Lindley's paradox' (as it has become known in statistics) has been explained in well known books by Zellner (1971), Leamer (1978) and Judge, Hill, Griffiths, Lutkepohl and Lee (1982), but is not widely appreciated. The objective of this paper is to reiterate the Bayesian argument in an applied context familiar to empirical researchers in accounting.