Quantitative Finance

This paper used complementary panel data models that are fixed effect regression model and panel vector auto regression model. The study was motivated by the hypothesis that both macroeconomic and microeconomic variables have an effect on the loan quality. The first part of the research was to determine the specific macro and microeconomic variables that give rise to the non-performing loans (NPLs) using fixed effect regression model. The empirical findings of this study provide evidence that nonperforming loans depends on macro and micro economic variables, the trend analysis of Zimbabwean commercial banks' shows an upward movement of over the period of study. The study found out that Gross domestic product (GDP), Inflation, loan deposit ratio and bank size had a statistical significant effect on the level of non-performing loans (NPLs). The second part was mainly to model the dynamic relationship of all the variables that were found to affect nonperforming loans (NPLs); this was done through impulse response analysis based on PANEL VAR model. One standard shock to credit growth will be greatly felt in the sixth year, whereas of size of the bank will have a great negative impulse in the seventh year.

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Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models can be set up to determine the optimal index replicating portfolio. In this paper, we propose an alternative based on imposing a constraint on the q-norm, 0 < q < 1, of the replicating portfolios' asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimisation viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance measures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimisation problems. The empirical analysis on real-world financial data allows to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset weights.

The Black Scholes Merton model is a widely used model in the financial world, however the valuation formula is derived on the unrealistic premise of instantaneous delta hedging. This paper thus aims to analyse the impact of delta hedging in discrete-time, assess the impact of using an alternative distribution to model asset returns, as well as to explore optimal hedging strategies. This objective is achieved by simulating hedged portfolios and assessing the nature of the hedging errors that come about as a result of the discrete hedging. The results show that the hedging error that results is driven mainly by the hedging frequency and that the error values are asymmetrically distributed. Additionally, asset returns are shown to be better modeled by a variance gamma distribution and since alternative delta derivations may not make a large difference when compared to the BSM -portfolio diversification is shown to be the only method to reduce this hedging error.

We introduce a novel framework for goals-based wealth management (GBWM), where risk is understood as the probability of investors not attaining their goals, not just the standard deviation of investors' portfolios. Our framework is based on a foundation of developments in behavioral economics and finance and is consistent with modern portfolio theory. Using a simple geometric analysis, we determine a specific portfolio that matches each individual investor's stated goals. Our approach requires information from the investor about their goals, elicited in a clear manner that market research shows is superior to common current practices. This new approach can improve the communication between advisors and clients and produce better advice for enabling clients to attain their goals with high probability through the use of efficient portfolios.

This paper provides a “non-extensive” information theoretic perspective on the relationship between risk and incomplete states uncertainty. Theoretically and empirically, we demonstrate that a substitution effect between the latter two may take place. Theoretically, the “non-extensive” volatility measure is concave with respect to the standard (based on normal distribution) volatility measure. With the degree of concavity depending on an incomplete states uncertainty parameter-the Tsallis-q. Empirically, the latter negatively causes the normal measure of volatility, positively affecting the tails of the distribution of realised log-returns.

Evolutionary game models analyze strategic interaction over time; equilibrium emerges (or fails to emerge) as players/traders adjust their actions in response to the payoffs they earn. This paper sketches some early and some recent evolutionary game models that contain ideas useful in modeling Þnancial markets. It spotlights recent work on adaptive landscapes. In an extended example, the distribution of player/trader behavior obeys a variant of Burgers' partial differential equation, and solutions involve travelling shock waves. It is conjectured that Þnancial market crashes might insightfully be modeled in a similar fashion. * My thanks to the Santa Fe Institute workshop participants for useful comments and to Steve Anderson for reserach assistance.

This study analyzes a neural networks model that forecast Sharpe ratio. The developed neural networks model is successful to predict the position of the investor who will be rewarded with extra risk premium on debt securities for the same level of portfolio risk or a greater risk premium than proportionate growth risk. The main purpose of the study is to predict highest Sharpe ratio in the future. Study grouped the data on yields of debt instruments in periods before, during and after world crisis. Results shows that neural networks is successful in forecasting nonlinear time lag series with accuracy of 82% on test cases for the prediction of Sharpe-ratio dynamics in future and investor's portfolio position.

We analyze the economics of transaction costs in dynamic hedging of contingent claims, making the case for a representative dynamic hedging agent. We argue that the most efficient dynamic hedger incurs no transaction costs when owning options. Furthermore, as options are rarely replicated until maturity, the expected transaction costs of the short options depend mostly on the dynamics of the order flow in the option markets-not on the direct costs of transacting. The conclusion is that transaction costs are a fraction of what has been assumed to be in the literature. For the fficient operators (and those operators only), markets are more dynamically complete than anticipated.

In this paper I combine techniques recently developed by Charles Fefferman with the well-known methods of Joel Lebowitz and Elliott Lieb to resolve some technical problems left unsettled by Lebowitz and Lieb's fundamental 1972 paper "The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei."

In this article, we propose a model that incorporates the preferences of multiple decision makers into a decison-making process using (1) The analytical hierarchy process (AHP); and (2) multiple criteria and multiple constraint levels (MC 2) linear programming in a capital budgeting context. Our model can foster strategic and nonfinaneial factors that are important in the capital budgeting problems of the current business environment. The two-phased solution framework proposed in this article is sufficiently flexible to reach a compromise among decision makers. Our method also facilitates collection of decision makers' preferences to minimize suboptimization of overall company's goals. In addition, application of AHP to derive weights to decision makers' preferences for resource availability decreases the solution complexity. All these characteristics represent a significant improvement compared with previous linear or goal programming approaches to capital budgeting problems.

Given the glut in long-dated callable issuance in late 2014, some commentators see a high risk of upcoming calls, particularly with the rally in USD long ends. But there have now been only four calls out of the ten or so eligible bonds. We do not expect a deluge of calls or new callable issuance for several reasons: the calls themselves were non-economic; Taiwanese insurers are usually unmoved by higher US yields given the separation of TWD and USD investment teams; and TWD depreciation has little effect on investment decisions due to hedging requirements. Moreover, many insurers continue to expect USD hikes, while they are generally full up on exposure to financial issuers, delaying further large USD investment. Finally, rehedging of callables should boost demand for vega, while rehedging suboptimally-called bonds should have much less impact on vega than commonly expected. Consequently, even if there are calls, we believe the impact on vega will be relatively modest. Given the recent tapering in callable issuance, we think now is a good time to go long USD vega. In this paper, we update our earlier note on Forward Volatility (see link) in its many forms, in which we recommended forward vol on the back of our (too) early view that callable issuance would taper. While tapering took several months longer than we expected, vega performed well. We now expect a renewed performance from vega.

This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357-84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.

The aim of this paper is to apply a nonparametric methodology developped by Donoho, Mallat, von Sachs & Samuelides (2003) for estimating an autocovariance sequence to the statistical analysis of the return of securities and discuss the advantages offered by this approach over other existing methods like fixed-window-length segmentation procedures. Theoretical properties of adaptivity of this estimation method have been proved for a specific class of time series, namely the class of locally stationary processes, with an autocovariance structure which varies slowly over time in most cases but might exhibit abrupt changes of regime. This method is based on an algorithm that selects empirically from the data the tiling of the time-frequency plane which exposes best in the least squares sense the underlying second-order time-varying structure of the time series, and so may properly describe the time-inhomogeneous variations of speculative prices. The applications we consider here mainly concern the analysis of structural changes occuring in stock market returns, VaR estimation and the comparison between the variation structure of stock indexes returns in developed markets and in developing markets

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for getting the execution order priority, which is a crucial issue in high frequency trading. By trading with limit orders, the agent faces an execution risk since her orders are executed only when they meet counterpart market orders, which are modelled by Cox processes with intensities depending on the spread and on her limit prices. By holding non-zero positions on the risky asset, the agent is also subject to the inventory risk related to price volatility. Then the agent can also choose to trade with market orders, and therefore get immediate execution, but at a least favorable price because she has to cross the bid-ask spread.

This thesis presents a tool for backtesting algorithmic trading strategies for cryptocurrencies. The tool, called quantbacktest, provides a convenient way to automatically run comparisons of multi-dimensional parameter spaces for algorithmic trading strategies. The tool supports any algorithmic strategy to be simulated and any parameter spaces to be tested and optimized with minimal adjustments. Also, arbitrary trading frequencies can be tested, from intraday to long-term strategies. Many standard return metrics, risk metrics, and robustness test functionalities come out-of-the-box in CSV format and as diagrams. Users can provide signals and price data via CSV or Excel files. Signal processing does not require a technical (code-level) understanding of the backtesting tool on behalf of the user.

There has been significant evidence on the forecasting ability of Regime switching regression models. Smart beta or alternative beta indices are gaining wide popularity among investment community. Smart beta indices constructed based on fundamental weighing are proven to outperform cap-weighted portfolios in the long run. At the same time, smart beta indices have significant exposure to risk factors such as size, value, momentum and volatility. The risk factors exhibit different behaviour in different regimes. In this research we examine and present evidence of the presence of regimes in smart beta indices. We also examine the possibility of adding value to a portfolio by switching between regime dependent portfolios of smart beta indices exploiting factor exposures.

(http://dx.doi.org/10.2139/ssrn.2933193)

The Spearman Correlation is a well known approach to assess the rank correlation of two data sets. One of the advantages choosing Spearman over other correlation coefficients such as the Pearson is that the difference in original value series is less important while the relative rank of the value is what matters most in this coefficient. The Spearman correlation coefficient is often used to assess and validate the performance of models that require less accuracy in absolute value estimate, e.g. the loss prediction models or exposure models. Although other measures such as the Kendall's τ and Somer's D are used to measure rank ordering with tied observations, the Spearman's ρ is often calculated as an initial step of correlation analysis. In this short note we look into the tied observations in the target data set and investigate the impact on the Spearman Correlation coefficient in three different scenarios: single value ties, random multi-value ties, and bounded random ties.

Financial planning is the process of assessing the financial goals of an individual, its taking money that he is owing, determine life goals, and then take necessary steps in order to achieve goals in the determining period. It is a technique of quantifying a person's requirements in terms of money. This study aims at answering these questions; Q1: how can the investor plan for his financial resources? Q2: What is the overview of the investor in short and long term goals? For data collection, the researcher has collected primary data by surveying investor's investment objectives and risk profile. The result found that the comprehensive study about each aspect of this topic has shown that the Financial Planning is a dynamic and flexible concept which involves regular and systematic analysis, proper management, judgment, and actions.

We propose a general class of analytically tractable models for the dynamics of an asset price leading to smiles or skews in the implied volatility structure. The considered asset can be an exchange rate, a stock index, or even a forward Libor rate. The class is based on an explicit SDE under a given forward measure. The models we propose feature i) explicit asset-price dynamics, ii) virtually unlimited number of parameters, iii) analytical formulas for European options.

Phronetic organizational research is an approach to the study of management and organizations focusing on ethics and power. It is based on a contemporary interpretation of the Aristotelian concept phronesis, usually as ‘prudence’. Phronesis is the ability to think and act in relation to values, to deliberate about ‘things that are good or bad for humans’ in the words of Aristotle (1976:1140a24–b12). Phronetic organizational research effectively provides answers to the following four value-rational questions, for specific problematics in management and organization studies: 1. Where are we going with this specific management problematic? 2. Who gains and who loses, and by which mechanisms of power? 3. Is this development desirable? 4. What, if anything, should we do about it?

The efficient frontier is a core concept in Modern Portfolio Theory. Based on this idea, we will construct optimal trading curves for different types of portfolios. These curves correspond to the algorithmic trading strategies that minimize the expected transaction costs, i.e. the joint effect of market impact and market risk. We will study five portfolio trading strategies. For the first three (single-asset, general multi-asseet and balanced portfolios) we will assume that the underlyings follow a Gaussian diffusion, whereas for the last two portfolios we will suppose that there exists a combination of assets such that the corresponding portfolio follows a mean-reverting dynamics. The optimal trading curves can be computed by solving an N-dimensional optimization problem, where N is the (pre-determined) number of trading times. We will solve the recursive algorithm using the &quot;shooting method&quot;, a numerical technique for differential equations. This method has the advantage...

This paper examines the return predictability of the US stock market using portfolios sorted by size, book-to-market ratio and industry. We use novel panel variance ratio tests, based on the wild bootstrap proposed in this paper, which exhibit desirable size and power properties in small samples. We have found evidence that stock returns have been highly predictable from 1964 to 1996, except for a period leading to the 1987 crash and its aftermath. After 1997, stock returns have been unpredictable overall. At a disaggregated level, we find evidence that large-cap portfolios have been priced more efficiently than small- or medium-cap portfolios; and that the stock returns from high-tech industries are far less predictable than those from non-high-tech industries.

We derive two new technical indicators for trading systems and risk management. They stem from trends in time series, the existence of which has been recently mathematically demonstrated by the same authors (A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009), and from higher order quantities which replace the familiar statistical tools. Recent fast estimation techniques of algebraic flavor are utilized. The first indicator tells us if the future price will be above or below the forecasted trendline. The second one predicts abrupt changes. Several promising numerical experiments are detailed and commented.

Although the square-root process has long been used as an alternative to the Black-Scholes geometric Brownian motion model for option valuation, the pricing of Asian options on this diffusion model has never been studied analytically. However, the additivity property of the square-root process makes it a very suitable model for the analysis of Asian options. In this paper, we develop explicit prices for digital and regular Asian options. We also obtain distributional results concerning the square-root process and its average over time, including analytic formulae for their joint density and moments. We also show that the distribution is actually determined by those moments.

Financial planning is the process of assessing the financial goals of an individual, its taking money that he is owing, determine life goals, and then take necessary steps in order to achieve goals in the determining period. It is a technique of quantifying a person&amp;#39;s requirements in terms of money. This study aims at answering these questions; Q1: how can the investor plan for his financial resources? Q2: What is the overview of the investor in short and long term goals? For data collection, the researcher has collected primary data by surveying investor&amp;#39;s investment objectives and risk profile. The result found that the comprehensive study about each aspect of this topic has shown that the Financial Planning is a dynamic and flexible concept which involves regular and systematic analysis, proper management, judgment, and actions.

In the first part of our study, we discuss empirical results regarding data pertaining to high-frequency bitcoin transactions-Recently, cryptocurrencies have been explored as a novel kind of financial asset, and they represent an interesting example, with a current market capitalization of over $500 billion. The current spike in interest in cryptocurrencies among academics and businesses prompted me to provide the first empirical results for high-frequency cryptocurrency data. In the next part of our research, we are studying how the generalized hyperbolic distribution and its subclasses are used to analyze a new generation of cryptocurrencies: Ethereum and its financial risk. Ethereum has garnered considerable attention as the first decentralized platform to allow smart contracts, capturing the interest of a diverse variety of organizations, enthusiasts, and even global leaders. We may think that effective fitting of these variations is critical given the significant price changes and volatility of Ether. Using the fitting of Generalized hyperbolic distribution and its subclasses, I've conducted the first formal statistical analysis of the Ethereum (the second-largest cryptocurrency by market capitalization) exchange rate. Finally, in the last part, we investigate how the adaptive market hypothesis is used in the highfrequency cryptocurrency market-Cryptocurrencies may be viewed as relatively new financial assets that are still in their infancy. One of the main purposes of our research is to determine whether or not the efficient market hypothesis (EMH) holds true at this level. Furthermore, the occurrence of active liquid financial markets shows the presence of profit chances. As such, our contribution was to develop this theory by using the adaptive market hypothesis (AMH) to analyze the high-frequency markets for the two major cryptocurrencies, Bitcoin and Ethereum, in comparison to the Euro and the US Dollar.

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between estimation period T and number of stocks N , on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than the one obtained with the sample covariance method. This is particularly true when T /N is close to one. Moreover many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary when short selling is not allowed and T > N , the considered methods are unable to outperform the sample covariance in terms of realized risk but can give much more diversified portfolios than the one obtained with the sample covariance. When T < N the use of the sample covariance matrix and of the pseudoinverse gives portfolios with very poor performance.

What percentage of their portfolio should investors allocate to hedge funds? The only available answers to the above question are set in a static mean-variance framework, with no explicit accounting for uncertainty on the active manager's ability to generate abnormal return, and usually generate unreasonably high allocations to hedge funds. In this paper, we apply the model introduced in Cvitanić, Lazrak, Martellini and Zapatero (2002b) for optimal investment strategies in the presence of uncertain abnormal returns to a database of hedge funds. We …nd that the presence of model risk signi…cantly decreases an investor's optimal allocation to hedge funds. Another …nding of this paper is that low beta hedge funds may serve as natural substitutes for a signi…cant portion of an investor risk-free asset holdings.

Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets and other strong assumptions. We confirm that the heuristics used by traders for centuries are both more robust, more consistent, and more rigorous than held in the economics literature. We also show that options can be priced using infinite variance (finite mean) distributions. JEL Classification: G13, D81, A14 1. Background Option valuations methodologies have been used by traders for centuries, in an effective way (Haug and Taleb, 2010). In addition, valuations by expectation of terminal payoff forces the mean of the probability distribution used for option prices be be that of the forward, thanks to Put-Call Parity and, should the forward be risk-neutrally priced, so will the option be. The Black Scholes argument (Black and Scholes, 1973; Merton, 1973) is held to allow risk-neutral option pricing thanks to dynamic hedging, as the option becomes redundant (since its payoff can be built as a linear combination of cash and the underlying asset dynamically revised through time). This is a puzzle, since: 1) Dynamic Hedging is not operationally feasible in financial markets owing to the dominance of portfolio changes resulting from jumps, 2) The dynamic hedging argument doesn't stand mathematically under fat tails; it requires a very specific 'Black Scholes world' with many impossible assumptions, one of which requires finite quadratic variations, 3) Traders use the same Black-Scholes 'risk neutral argument' for the valuation of options on assets that do not allow dynamic replication, 4) Traders trade options consistently in domain where

Option traders use a heuristically derived pricing formula which they adapt by fudging and changing the tails and skewness by varying one parameter, the standard deviation of a Gaussian. Such formula is popularly called “Black–Scholes–Merton” owing to an attributed eponymous discovery (though changing the standard deviation parameter is in contra- diction with it). However, we have historical evidence that: (1) the said Black, Scholes and Merton did not invent any formula, just found an argument to make a well known (and used) formula compatible with the economics establishment, by removing the “risk” parameter through “dynamic hedging”, (2) option traders use (and evidently have used since 1902) sophisticated heuristics and tricks more compatible with the previous versions of the for- mula of Louis Bachelier and Edward O. Thorp (that allow a broad choice of probability distributions) and removed the risk parameter using put-call parity, (3) option traders did not use the Black–Scholes–Merton formula or similar formulas after 1973 but continued their bottom-up heuristics more robust to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop using the wrong designation for option pricing.

This research was undertaken during a period in which the Zimbabwean banking sector was facing serious liquidity challenges associated with the management of assets & liabilities and proliferation of non performing loans on bank balance sheets across the sector. This is evidenced by a decline trend in liquidity ratios of most banks since dollarisation of the Zimbabwean economy in 2009. This research seeks to highlight and assess the presence and significance of assets and liabilities risk management for liquidity risk management in Zimbabwean commercial banks as measured by three key variables in assets and liabilities liquidity risk management which are i) assets and liabilities management policies ii ) contingency funding plans and iii ) liquidity stress testing. The research also seeks to identify variables that best describe variability in liquidity risk for commercial banks and come up with models for both individual bank liquidity risk and sectorial liquidity risk. The research through these models seeks to give recommendations for balance sheet restructuring through targeting optimal levels of the descriptive variables to minimise liquidity risk.

has emerged as the standard tool for measuring and managing financial market risk. In this paper, we study the effects of asymmetric long memory volatility models on the accuracy of stock index return VaR estimates. We also investigate the relevance of Student's t and skewed Student's t-distribution innovations in analyzing volatility stylized facts, such as volatility clustering, volatility asymmetry and volatility persistence or long memory in volatilities, in some developed and emerging stock markets. In order to do so, we evaluate and compare the performance of asymmetric, FIEGARCH and FIAPARCH, versus symmetric, FIGARCH, long memory VaR models, respectively with normal, Student's t and skewed Student's t-distributions. Based on individual market indexes for selected developed and emerging stock markets, the empirical results show that, using Kupiec's likelihood ratio tests, the FIAPARCH(1, d, 1) model with skewed Student's t innovation is more accurate in in-sample VaR analysis for long and short trading positions than the other models. For out-of sample VaR analysis, the FIAPARCH(1, d, 1) model with Student's t-distribution innovation provided more accurate VaR calculations in capturing stylized facts in the volatility of our sample returns. Thus, in-sample and out-of-sample VaR values computed using asymmetric long memory volatility models have better accuracy than those generated using the symmetric FIGARCH model and the correct assumption of return distribution might improve the estimated performance of VaR models in the stock markets. Asymmetric long memory volatility models in value-at-risk estimation 59 2 Baillie et al (1996) provide information about the presence of fractionally integrated behavior in the conditional variance of nominal US dollar-deutschmark exchange rates. 3 The lags of the fractional differencing operator are truncated at 1,000, which is large enough to examine the long memory process. have proposed other asymmetric Student's t densities. 15 Giot and Laurent (2003) show that an asymmetric power autoregressive conditional heteroskedasticity (AR-APARCH) model with a skewed Student's t density succeeds in correctly forecasting (both in-and out-of-sample) the one-day-ahead VaR for three international stock indexes and three US stocks of the Dow Jones index. Models based on the normal or Student's t-distributions clearly underperform when applied to the same data sets. 16 The asymmetry coefficient ξ > 0 is defined such that the ratio of probability masses above and below the mean is (P (ε ≥ 0/ξ )/P (ε < 0/ξ )) = ξ 2 .