Mathematical Finance/Quantitative Finace

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.

The Markowitz mean-variance portfolio theory posits that the optimal portfolio weights can be chosen based off an efficient tradeoff between profit modeled as the mean and risk measured as the variance-covariance matrix. These values must be historically estimated, occasionally leading to poor portfolio performance and asset misallocation. Moreover, as Brodie et. al. point out, the Markowitz optimization scheme, “is empirically unstable,” making, “the classic Markowitz portfolio optimization an ill-posed (or ill-conditioned) inverse problem.”  Consequently, this paper formulates the global minimum variance portfolio as a regression problem with added penalties. This analysis thus utilizes penalty regularization on training data to more efficiently estimate global minimum variance portfolio weights and resolve many of the classic scheme’s issues.

We build a heuristic that takes a given option price in the tails with strike K and extends (for calls, all strikes > K, for put all strikes < K) assuming the continuation falls into what we define as "Karamata Constant" over which the strong Pareto law holds. The heuristic produces relative prices for options, with for sole parameter the tail index α under some mild arbitrage constraints.
Usual restrictions such as finiteness of variance are not required.
The heuristic allows us to scrutinize the volatility surface and test theories of tail option mispricing and overpricing usually built on thin tailed models and modification of the Black-Scholes formula.

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

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 non-performing 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.

In this note we describe the HJM(LLM) model for pricing Mid-Curve Money Market Future Options. The model is based on assuming a lognormal process for the relevant forward money market (“LIBOR”) rates and imbedding it into the general no-arbitrage HJM interest rate modeling framework (understood in the most general sense as a manifestly self-consistent framework for formulating interest rate models in terms of any type of interest rate, including the observable market rates [2, 3, 4]). The relevant convexity adjustment factor is calculated by leveraging on the known functional form for the discount bond price volatility in any no-arbitrage lognormal “LIBOR” rate model, and approximating it with a leading order deterministic approximation. This makes it possible to derive an analytic expression for the HJM(LLM) model Discount Propagator using the path integral techniques and leads to the explicit analytic pricing formulas for the Mid-Curve futures options.

We present a new term-structure model for commodity futures prices based on Trolle & Schwartz (2009), which we extend by incorporating multiple jump processes. Our work explores the valuation of plain vanilla options on futures prices when the spot price follows a log-normal process, the forward cost of carry curve and the volatility are stochastic variables, and the spot price and the forward cost of carry allow for time-dampening jumps. We obtain an analytical representation of the characteristic function of the futures prices and, hence, also for plain vanilla option prices using the fast Fourier transform (FFT) methodology. We price options on WTI crude oil futures contracts using our model and extant models. We obtain higher accuracy than earlier models and save significantly in computing time.

“Credit aggregates contain valuable information about the likelihood of future financial crises.”1 The seminal 2012 paper by Schularick and Taylor evaluated impacts of various macroeconomic indicators financial stability, discovering that rather than follow Friedman and Schwartz’s “money view” the post- WWII era has experienced credit decoupling from money supplies, creating more leveraged economies and thus new potential financial risks. Analyzing this fact, they found that lagged credit growth serves as a highly significant predictor of financial crises with virtually no explanatory power added by other macroeconomic indicators.
“
Furthering their work on financial crises prediction, this paper utilizes machine learning classification techniques to evaluate and verify Schularick and Taylor’s findings’ explanatory and predictive power. With regards to credit growth’s financial impacts, this analysis verifies it as the primary macroeconomic indicator for financial crisis; however, further findings reveal that money growth, particularly narrow (M0 or M1) money aggregates, may hold additional explanatory and predictive power. Moreover, it is revealed that the traditional econometric logistic regression method is a superior model to most machine learning techniques, with only neural networks (H=3) having consistent, accurate performance.

In this paper, we try to revisit some of the most fundamental issues lying at the foundation of mathematics in space-time relativistic perspective ,rather than conventional absolute space. We are adding a new dimension "Time" to the mathematics and review it in Space-Time relativistic framework to resolve the major foundational issues and making it in line with physical world realities. We shall look at the famous Cantor's Diagonalization approach in to show the Countability of Real Numbers and explain Infiniteness in that perspective. We shall also look to resolve the famous paradoxes e.g. Richard, Russell,Liar, Skolem. We shall also look at the the foundation of Set theory historically in Space-time to restore the issues that had led to ZFC by elimination and restrictions. As a consequence, we shall also revisit Godel Incompleteness theorems for Real Numbers and also otherwise explain the "inconsistency" in the new framework. This could possibly lead to entirely new way of looking at conventional mathematics in broader sense.

Due to commission fees and tax implications in the trading of equities in the Philippine equities market, the costs of trading equities are higher than their quoted price. In which case, the holding period return (HPR) calculated from the buying point to the selling point of equities cannot be directly calculated from the quoted buying and the selling prices alone.

Software may be used in university teaching both to enhance student learning of discipline-content knowledge and skills, and to equip students with capabilities that will be useful in their future careers. Although research has indicated that software may be used as an effective way of engaging students and enhancing learning in certain scenarios, relatively little is known about academic practices with regard to the use of software more generally or about the extent to which this software is subsequently used by graduates in the workplace. This article reports on the results of a survey of academics in quantitative and financial disciplines, which is part of a broader study also encompassing recent graduates and employers. Results indicate that a variety of software packages are in widespread use in university programmes in quantitative and financial disciplines. Most surveyed academics believe that the use of software enhances learning and enables students to solve otherwise intractable problems. A majority also rate spreadsheet skills in particular as very important for the employability of graduates. A better understanding of the use of software in university teaching points the way to how curricula can be revised to enhance learning and prepare graduates for professional work.

Cryptocurrencies are currently traded worldwide, with hundreds of different currencies in existence and even more on the way. This study implements some statistical and machine learning approaches for cryptocurrency investments. First, we implement GJR-GARCH over the GARCH model to estimate the volatility of ten popular cryptocurrencies based on market capitalization: Bitcoin, Bitcoin Cash, Bitcoin SV, Chainlink, EOS, Ethereum, Litecoin, TETHER, Tezos, and XRP. Then, we use Monte Carlo simulations to generate the conditional variance of the cryptocurrencies using the GJR-GARCH model, and calculate the value at risk (VaR) of the simulations. We also estimate the tail-risk using VaR backtesting. Finally, we use an artificial neural network (ANN) for predicting the prices of the ten cryptocurrencies. The graphical analysis and mean square errors (MSEs) from the ANN models confirmed that the predicted prices are close to the market prices. For some cryptocurrencies, the ANN models perform better than traditional ARIMA models

The prospect of tourism growth as a tool for promoting economic resilience in developing economies, diversifying from dependence on extractive industries is interesting. The purpose of this study is to investigate the relationship between tourism and the economic performance of Zimbabwe. Using a bivariate unrestricted Vector Autoregressive model and granger causality, this study analyzed the short-run relationship between gross domestic product (GDP) and tourism receipts, using annual data from 1990-2018. The lagged values of GDP and tourism receipts were found to be significant in estimating GDP in the short-run. The results also show a unidirectional, positive causal relationship, where tourism receipts granger causes GDP. The study outlines the significance of the tourism sector in improving the economic performance of Zimbabwe, thus interventions to improve the sector will yield positive results in the short-run. Capital investment in tourist areas will lead to an improvement in the quality of service and infrastructure in these areas to boost tourism growth. Further studies are needed to investigate the multiple effects of tourism in Zimbabwe.

Abstract
Behavioural economics points to simultaneity bias and clientele effects in cross sectional regressions of subjective well-being (SWB) and happiness, on income growth, when myopic loss aversion (MLA) to decline in standard of living is not included in their specifications. Thus, extant models overestimate the impact of economic growth on SWB, and inference and policies based on those models may be misdirected. Theory predicts that the relative impact of growth on SWB is inversely proportional to loss aversion. To rectify the specification problem, we introduce an econometric theory for embedding and recovering consistent estimates of the MLA index from cross sectional regressions on SWB, and an exact econometric test for the identifying MLA restriction. The asymptotic distribution of the MLA index estimator is in the domain of attraction of a stable law. This implies that large values of the MLA index are admissible, that in some cases its mean and variance do not exist, and that the mode or median MLA index is a consistent estimator. We apply the theory to data from a metastudy on loss aversion index, and to published results on consumption, SWB and happiness around the world. The theory is upheld. Metastudy data support stable law while recovered MLA index estimates are consistent with those reported in the behavioural and experimental economics literature. High income countries have higher MLA indexes than low income countries so they are more likely to report decline in SWB for a fall in income. Aggregation bias masks large disparities in MLA index estimates within countries. To the best of our knowledge, direct estimation of a MLA index for consumption and SWB via recovery from cross-sectional regressions, derivation of its asymptotic distribution, and econometric test for recovered MLA indexes are new to the literature.

En este artículo se estudian diversos enfoques para definir promedios móviles y volatilidades desde el punto de vista exponencial, es decir, dando mas ponderación a los datos más
recientes. Se ve que varios de los que enfoques usados en la literatura adolecen de varios
problemas de definición. Se propone una manera de definir un sistema completo de pesos y de esta manera corregir algunos de los problemas que presentan esos enfoques. Además, se
propone una fórmula recurrente que converge al promedio móvil y la volatilidad exponencial reales. Finalmente, se estudian las cotas para los errores de aproximación que se cometen cuando se usan las fórmulas estudiadas.

In this article we model a financial derivative price as an observable on a market state function, with a view to understanding how some of the non-commutative behaviour of the financial market impacts the dynamics. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model introduces quantum interference effects that can act as either a drag or a boost on the resulting return. The ultimate objective is to investigate the nature of quantum drift in the Accardi-Boukas quantum Black-Scholes framework which involves modelling the financial market as a quantum observable, and introduces randomness through the Hudson-Parthasarathy quantum stochastic calculus. In particular we aim to differentiate randomness that is introduced through external noise (quantum stochastic calculus) and randomness that is fundamental to a quantum system (Heisenberg Equation of Motion).

Conditional value at risk (CVaR) estimates the losses in the tail of the distribution of the scenarios of the market. For example, we simulate return base on normal distribution, the maximum profit is on the right of the normal distribution and the maximum loss is in the left then we define an optimal probability level for defining 95%. The VaR level are highlighted by red in the figure where the CVaR at 95% shows the average of losses for the scenarios. For this study, we used DOW Jones Industrial averages portfolio data (Collected from Bloomberg). In this case we considered 8 stocks and calculate the return data and showed in the histogram. There are two well-known method for simulating distribution of returns based on mean and covariance of the returns after that we simulate covariate distribution that is the try to mimic empirical distribution of each stocks since this method has different steps using Machine Learning toolbox in MATLAB using copula fit to estimate the model parameters. Then we generate random sample by copula scale. Finally, we convert the random variables by copula scale using empirical distributions for scenarios as well as use portfolio object to specify asset scenarios. We plot the efficient frontier (EF), to show the mean portfolio return against the CVaR and show portfolio weights for 10 portfolios along the EF. Finally, we compare the portfolio returns between CVaR and Mean-Variance optimization method (which is normally distributed returns). To differentiate both EF, we convert one risk measure to another, for this we use estimate port returns and risk method to calculate optimal portfolio returns and portfolio CVaR respectively as well as represent the performance graphically.

An agent can distribute his wealth between two investments, one with a fixed rate of return r and the other with a random rate of return (modeled as a diffusion) with mean r. The agent seeks to maximize total discounted utility from consumption over an infinite horizon. Consumption may be constrained from below. Various models for bankruptcy, including welfare, are considered. The agent has a strictly concave utility function for consumption; however, it is shown that the utility function for wealth may have convex portions, thus the agent may be risk seeking. The paper gives a complete treatment of the existence and nonexistence of optimal policies. New theorems for the optimal control of degenerate diffusions are given, as well as explicit formulas for the value function. * This paper also gives a careful treatment of this decision problem with two important additional features generalizing the original work of Samuelson or Merton [11], . The reader should consult the volume edited by Ziemba and Vickson [18] for a collection of papers related to this topic. First, the analysis allows consumption to be constrained from below by a nonnegative constant, c. When c = 0, this constraint merely represents the fact that consumption must be nonnegative, a tacit assumption in all previous work. Second, the analysis allows the agent to pursue consumption and investment policies which result in the agent's wealth reaching level 0 (bankruptcy) in finite time.

The cross-section of options bid–ask spreads with their strikes are modelled by maximis- ing the Kaniadakis entropy. A theoretical model results with the bid–ask spread depending explicitly on the implied volatility; the probability of expiring at-the-money and an asym- metric information parameter (κ). Considering AIG as a test case for the period between January 2006 and October 2008, we find that information flows uniquely from the trading activity in the underlying asset to its derivatives. Suggesting that κ is possibly an option implied measure of the current state of trading liquidity in the underlying asset.