Research articles for the 2019-08-14

Accurate Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Using a Regime Switching Model
Chinonso Nwankwo,Weizhong Dai,Ruihua Liu

We consider a system of coupled free boundary problems for pricing American put options with regime switching. To solve this system, we first fix the optimal exercise boundary for each regime resulting in multi-variable fixed domains. We further eliminate the first order derivatives associated with the regime switching model by taking derivatives to obtain a system of coupled partial differential equations which we called the asset-delta-gamma-speed option equations. The fourth-order compact finite difference scheme and Gauss-Seidel iterative method are then employed in each regime for solving the system of the equations. In particular, the third order Hermite interpolation technique is used for estimating the coupled asset and delta options in the set of equations. The numerical method is finally tested with several examples. Our results show that the scheme provides an accurate solution with the convergent rate in space of 2.44 and the rate in time of 1.86, which is accurate and fast in computation as compared with other existing numerical methods.

Are Affine Volatility Restrictions Still Costly when the Pricing Kernel is Quadratic?
Aoun, Patrick
I compare the quadratic kernel used by Christoffersen, Heston and Jacobs (2013) with the commonly used Rubinstein's (1976) power pricing kernel in terms of option valuation performance. I do so in both affine and nonaffine GARCH(1,1) models. I find that, in both cases, the quadratic kernel outperforms its linear counterpart. I find no evidence that the performance gap between the affine and the nonaffine models shrinks with the quadratic kernel.

Can robust optimization offer improved portfolio performance?: An empirical study of Indian market
Shashank Oberoi,Mohammed Bilal Girach,Siddhartha P. Chakrabarty

The emergence of robust optimization has been driven primarily by the necessity to address the demerits of the Markowitz model. There has been a noteworthy debate regarding consideration of robust approaches as superior or at par with the Markowitz model, in terms of portfolio performance. In order to address this skepticism, we perform empirical analysis of three robust optimization models, namely the ones based on box, ellipsoidal and separable uncertainty sets. We conclude that robust approaches can be considered as a viable alternative to the Markowitz model, not only in simulated data but also in a real market setup, involving the Indian indices of S&P BSE 30 and S&P BSE 100. Finally, we offer qualitative and quantitative justification regarding the practical usefulness of robust optimization approaches from the point of view of number of stocks, sample size and types of data.

Computational method for probability distribution on recursive relationships in financial applications
Jong Jun Park,Kyungsub Lee

In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging error, the Asian option, and statistical hypothesis testing. We propose a method to calculate such a distribution, utilizing a recursive method, and examine it using various examples. The results of the numerical experiment show that our proposed method has high accuracy.

Consistent Treatment of Inflation in Discounted Cash Flow Valuation
Cornell, Bradford ,Gerger, Richard
Since the mid-1960s inflation has been a consistent aspect of the U.S. economy. Even at the relatively low rates of approximately 2% that prevail today, inflation can have an important impact on property tax appraisal and must be treated consistently. In this paper, we derive the proper formulas for taking account of inflation in the context of the constant growth models often used when applying the income approach to valuation. We demonstrate how older approaches, still in widespread use in unitary tax appraisals today, fail to properly adjust for inflation.

Dynamic Dependence Modeling in financial time series
Yali Dou,Haiyan Liu,Georgios Aivaliotis

This paper explores the dependence modeling of financial assets in a dynamic way and its critical role in measuring risk. Two new methods, called Accelerated Moving Window method and Bottom-up method are proposed to detect the change of copula. The performance of these two methods together with Binary Segmentation \cite{vostrikova1981detection} and Moving Window method \cite{guegan2009forecasting} is compared based on simulated data. The best-performing method is applied to Standard \& Poor 500 and Nasdaq indices. Value-at-Risk and Expected Shortfall are computed from the dynamic and the static model respectively to illustrate the effectiveness of the best method as well as the importance of dynamic dependence modeling through backtesting.

Dynamic Relations Between CDS and Stock Markets in Eastern European Countries
Asandului, Mircea,Lupu, Dan,Mursa, Gabriel,Musetescu, Radu
This study examines whether there is a price discovery type relationship between CDS and stock market at the level of 5 Eastern European countries for the period 2004-2014. The analysis follows the pattern of the financial time series: testing the structural breaks, the stationarity, cointegration and subsequently the development of VAR models. The study finds out that before and after the crisis, the stock market has played a crucial role in the price discovery phenomenon while during the financial crisis period and of the sovereign debts there has been an inverse relationship and the CDS has influenced the stock market.

Forecasting U.S. Textile Comparative Advantage Using Autoregressive Integrated Moving Average Models and Time Series Outlier Analysis
Zahra Saki,Lori Rothenberg,Marguerite Moor,Ivan Kandilov,A. Blanton Godfrey

To establish an updated understanding of the U.S. textile and apparel (TAP) industrys competitive position within the global textile environment, trade data from UN-COMTRADE (1996-2016) was used to calculate the Normalized Revealed Comparative Advantage (NRCA) index for 169 TAP categories at the four-digit Harmonized Schedule (HS) code level. Univariate time series using Autoregressive Integrated Moving Average (ARIMA) models forecast short-term future performance of Revealed categories with export advantage. Accompanying outlier analysis examined permanent level shifts that might convey important information about policy changes, influential drivers and random events.

Global Fixed Income Portfolios: A Macroeconomic Invariant Solution
Bruno Scalzo Dees

Global fixed income returns span across multiple maturities and economies, that is, they naturally reside on multi-dimensional data structures referred to as tensors. In contrast to standard "flat-view" multivariate models that are agnostic to data structure and only describe linear pairwise relationships, we introduce a tensor-valued approach to model the global risks shared by multiple interest rate curves. In this way, the estimated risk factors can be analytically decomposed into maturity-domain and country-domain constituents, which allows the investor to devise rigorous and tractable global portfolio management and hedging strategies tailored to each risk domain. An empirical analysis confirms the existence of global risk factors shared by eight developed economies, and demonstrates their ability to compactly describe the global macroeconomic environment.

Hostile Takeovers or Friendly Mergers?: A Real Options Analysis
Ebina, Takeshi,Kumakura, Yuya,Nishide, Katsumasa
This paper analyses a real options model of mergers and takeovers between two firms facing different but correlated uncertainty in profits. It is assumed that firms can choose two alternatives; hostile takeover or friendly merger. In a hostile takeover, a bidder firm takes all the extra value but should incur takeover costs, while in a friendly merger both firms do not bear takeover costs and share the extra value through Nash bargaining. We show how demand uncertainty and takeover costs influence which firm to be a bidder and which form of amalgamation to happen. We also find that a smaller firm can be a bidder to a larger firm in a hostile way, which is sometimes observed in actual markets.

Is being `Robust' beneficial?: A perspective from the Indian market
Mohammed Bilal Girach,Shashank Oberoi,Siddhartha P. Chakrabarty

The problem of data uncertainty has motivated the incorporation of robust optimization in various arenas, beyond the Markowitz portfolio optimization. This work presents the extension of the robust optimization framework for the minimization of downside risk measures, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We perform an empirical study of VaR and CVaR frameworks, with respect to their robust counterparts, namely, Worst-Case VaR and Worst-Case CVaR, using the market data as well as the simulated data. After discussing the practical usefulness of the robust optimization approaches from various standpoints, we infer various takeaways. The robust models in the case of VaR and CVaR minimization exhibit superior performance with respect to their base versions in the cases involving higher number of stocks and simulated setup respectively.

Measuring the Ex-Ante Incentive Effects of Bankruptcy Reorganization Rules
Agrawal, Ashwini K.,Gonzalez-Uribe, Juanita,Martinez-Correa, Jimmy
The recent wave of corporate liquidations across Europe has led to bankruptcy reforms that enable debt holders to implement reorganization plans without management consent. Critics of similar policies claim that low usage of these procedures by insolvent firms illustrates their ineffectiveness at mitigating liquidation rates. We argue that this perspective is misleading, because it ignores the “ex-ante” incentive effects of these reforms on solvent firms’ equity holders. Using administrative microdata, we show that similar reforms in Denmark actually led to a steep decline in liquidations. While few insolvent firms enter newly established restructuring procedures, solvent firms show markedly improved debt repayment patterns. We estimate that the ex-ante effects of these procedures are six times larger than their ex-post effects.

Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data
Kyungsub Lee,Byoung Ki Seo

This study examine the theoretical and empirical perspectives of the symmetric Hawkes model of the price tick structure. Combined with the maximum likelihood estimation, the model provides a proper method of volatility estimation specialized in ultra-high-frequency analysis. Empirical studies based on the model using the ultra-high-frequency data of stocks in the S\&P 500 are performed. The performance of the volatility measure, intraday estimation, and the dynamics of the parameters are discussed. A new approach of diffusion analogy to the symmetric Hawkes model is proposed with the distributional properties very close to the Hawkes model. As a diffusion process, the model provides more analytical simplicity when computing the variance formula, incorporating skewness and examining the probabilistic property. An estimation of the diffusion model is performed using the simulated maximum likelihood method and shows similar patterns to the Hawkes model.

Nonparametric modeling cash flows of insurance company
Valery Baskakov,Nikolay Sheparnev,Evgeny Yanenko

The paper proposes an original methodology for constructing quantitative statistical models based on multidimensional distribution functions constructed on the basis of the insurance companies' data on inshurance policies (including policies with deductible) and claims incurred. Real data of some Russian insurance companies on non-life insurance contracts illustrate some opportunities of the proposed approach. The point and interval estimates of net premium, claims frequency, claims reserves including IBNR and OCR, are thus obtained. The resulting estimate of claims reserves falls in the range of reasonable estimates calculated on the basis of traditional reserving methods (the chain-ladder method, the frequency-severity method and the Bornhuetter-Ferguson method).

The proposed methodology is based on additive estimates of a company's financial indicators, in the sense that they are calculated as a sum of estimates built separately for each element of the sample (claim). This allows using the proposed methodology to model insurance companies' financial flows and, in particular, to solve the problems of reserve redistribution between particular segments of insurance portfolio and/or time intervals; to adjust risk as part of financial reporting under IAS 17 Insurance Contracts; and to deal with many other tasks.

The accuracy of insurance companies' financial parameters estimate based on the proposed methods was tested by statistical modeling. IBNR was used as the test parameter. The modeling results showed a satisfactory accuracy of the proposed reserve estimates.

Performance of tail hedged portfolio with third moment variation swap
Kyungsub Lee,Byoung Ki Seo

The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment variation swap under which a predetermined fixed leg and the floating leg of the realized third moment variation are exchanged. The probability density function of the hedged portfolio with the third moment variation swap was examined using a partial differential equation approach. An alternating direction implicit method was used for numerical analysis of the partial differential equation. Under the stochastic volatility and jump diffusion stochastic volatility models, the distributions of the hedged portfolio return are symmetric and have more Gaussian-like thin-tails.

Public Firm Presence, Financial Reporting, and the Decline of U.S. Manufacturing
Glaeser, Stephen,Omartian, James D.
We document evidence of a positive association between public firm presence and import competition. Using cross-sectional differences in the expected costs of the Sarbanes-Oxley Act as an instrument for changes in public firm presence after the Act, we find evidence that public firm presence cause changes in import competition. Subsequent mechanism tests suggest that this effect arises because U.S. securities regulation requires public firms to prepare and make publicly available audited financial reports. Although these reports are purportedly for the benefit of investors, our mechanism tests suggest that foreign competitors also make use of the performance and investment information disclosed in these reports to compete with U.S. firms.

The Central Role of Political Myth in Corporate Law
Macey, Jonathan R.
This Article shows that a variety of fundamental rules of corporate law are based on a set of myths. The Article explains that these myths play an important role in attracting public acceptance and support for what otherwise would be unpopular and controversial regulations. Thus, one can view the role played by myth in corporate law in a particular context as having either positive or negative social effects depending on one’s opinion of the social value of the underlying legal rule that being buttressed and affirmed by the myth. Four political and sociological myths that continue to play important roles in law are examined. These are: (1) the myth that corporations are owned by their shareholders and represent ownership interests in businesses rather than mere financial claims on the cash flows of those businesses, coupled with certain political (voting) rights that protect those claims; (2) the “shareholder value myth,” that corporate officers and directors are legally required to maximize firm value; (3) that subsidiary companies are independent from and not subject to the control of their parent companies and must remain so in order for the parent company to avoid liability for the contract and tort debts of the subsidiary under various alter ego and piercing the corporate veil theories of corporate law; and (4) the legal regulation of insider trading is justified because of the necessity of creating a “level playing field” among participants in financial markets. Reasonable people can disagree about whether the role played by these myths is normatively positive or negative in each of these contexts.

The Modeling of Forecasting the Bankruptcy Risk in Romania
Lupu, Dan,Onofrei, Mihaela
Bankruptcy prediction and the understanding of the causes for economic failure have a financial utility. The purpose of this study is to compare the predictive power, on the Romanian market, of the most popular bankruptcy models considering the firms listed on the BSE during 2007-2011. Using the principal component analysis, the best bankruptcy predictors of the established financial indicators were determined for Romanian companies. Then, by using the multiple discriminant analysis and logit analysis, 12 models were developed in order to determine the best predictive function for bankruptcy.

The implied Sharpe ratio
Ankush Agarwal,Matthew Lorig

In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept -- the implied Sharpe ratio -- which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor's portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's risk-aversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.