A Probabilistic Monte Carlo model for pricing discrete barrier options

We present an original Probabilistic Monte Carlo (PMC) model for pricing European discrete barrier options. Based on Monte Carlo simulation, the PMC model computes the probability of not crossing the barrier for knock-out options and crossing the barrier for knock-in options. This probability is then multiplied by an average sample discounted payoff of a plain vanilla option that has the same inputs as the barrier option but without barrier and to which we have applied a filter. We test the consistency of our model with an analytical solution (Merton 1973 and Reiner & Rubinstein 1991) adjusted for discretization by Broadie et al. (1997) and a naïve numerical model using Monte Carlo simulation presented by Clewlow & Strickland (2000). We show that the PMC model accurately price barrier equity options. Market participants in need of selecting a reliable and simple numerical method for pricing discrete barrier options will find our paper appealing. Moreover, the idea behind the method is so elementary that it can be applied to the pricing of complex derivatives involving barriers, easing the valuation step significantly. Keywords: Monte Carlo Simulation, Option Pricing; Discrete Barrier Option

Will Saudi Arabia get older? Will its pension system be sustainable? Spectral answers

Purpose - The purpose of this paper is to answer the following two questions: Will Saudi Arabia get older? Will its pension system be sustainable? Design/methodology/approach - The methodology/approach is to forecast KSA’s population with wavelet analysis combined with the Burg model which fits a pt h order autoregressive model to the input signal by minimizing (least squares) the forward and backward prediction errors while constraining the autoregressive parameters to satisfy the Levinson-Durbin recursion, then relies on an infinite impulse response prediction error filter. Findings - Spectral analysis projections of Saudi age groups are more optimistic than the Bayesian probabilistic model sponsored by the United Nations Population Division: Saudi Arabia will not get older as fast as projected by the United Nations model. The KSA’s pension system will stay sustainable based on spectral analysis, whereas it will not based on the U.N. model. Originality/value - Spectral analysis will provide better insight and understanding of population dynamics for Saudi government policymakers, as well as economic, health and pension planners

Cabbage and fermented vegetables : From death rate heterogeneity in countries to candidates for mitigation strategies of severe COVID-19

Large differences in COVID-19 death rates exist between countries and between regions of the same country. Some very low death rate countries such as Eastern Asia, Central Europe, or the Balkans have a common feature of eating large quantities of fermented foods. Although biases exist when examining ecological studies, fermented vegetables or cabbage have been associated with low death rates in European countries. SARS-CoV-2 binds to its receptor, the angiotensin-converting enzyme 2 (ACE2). As a result of SARS-CoV-2 binding, ACE2 downregulation enhances the angiotensin II receptor type 1 (AT(1)R) axis associated with oxidative stress. This leads to insulin resistance as well as lung and endothelial damage, two severe outcomes of COVID-19. The nuclear factor (erythroid-derived 2)-like 2 (Nrf2) is the most potent antioxidant in humans and can block in particular the AT(1)R axis. Cabbage contains precursors of sulforaphane, the most active natural activator of Nrf2. Fermented vegetables contain many lactobacilli, which are also potent Nrf2 activators. Three examples are: kimchi in Korea, westernized foods, and the slum paradox. It is proposed that fermented cabbage is a proof-of-concept of dietary manipulations that may enhance Nrf2-associated antioxidant effects, helpful in mitigating COVID-19 severity.Peer reviewe

Nrf2-interacting nutrients and COVID-19 : time for research to develop adaptation strategies

There are large between- and within-country variations in COVID-19 death rates. Some very low death rate settings such as Eastern Asia, Central Europe, the Balkans and Africa have a common feature of eating large quantities of fermented foods whose intake is associated with the activation of the Nrf2 (Nuclear factor (erythroid-derived 2)-like 2) anti-oxidant transcription factor. There are many Nrf2-interacting nutrients (berberine, curcumin, epigallocatechin gallate, genistein, quercetin, resveratrol, sulforaphane) that all act similarly to reduce insulin resistance, endothelial damage, lung injury and cytokine storm. They also act on the same mechanisms (mTOR: Mammalian target of rapamycin, PPAR gamma:Peroxisome proliferator-activated receptor, NF kappa B: Nuclear factor kappa B, ERK: Extracellular signal-regulated kinases and eIF2 alpha:Elongation initiation factor 2 alpha). They may as a result be important in mitigating the severity of COVID-19, acting through the endoplasmic reticulum stress or ACE-Angiotensin-II-AT(1)R axis (AT(1)R) pathway. Many Nrf2-interacting nutrients are also interacting with TRPA1 and/or TRPV1. Interestingly, geographical areas with very low COVID-19 mortality are those with the lowest prevalence of obesity (Sub-Saharan Africa and Asia). It is tempting to propose that Nrf2-interacting foods and nutrients can re-balance insulin resistance and have a significant effect on COVID-19 severity. It is therefore possible that the intake of these foods may restore an optimal natural balance for the Nrf2 pathway and may be of interest in the mitigation of COVID-19 severity

Fitting the Pareto-lévy distribution on the yield curve: An application to forecasting

Finding the optimal distribution of innovation terms to forecast the yield curve or to price derivatives on fixed-income securities with Monte Carlo simulation is a challenge that not so many authors have taken up. We investigate the Pareto-Lévy distribution that fits the U.S. yield curve when the latter experiences different shapes: normal, inverse, flat and humped and experiences a volatile environment or not. We show that the Pareto-Lévy distribution does not improve significantly yield curve forecasting with Monte Carlo simulation when benchmarked to the Normal distribution but we discovered interesting outcomes concerning the Normal distribution such as its higher performance for fitting the yield curve and its consistency whatever the shape of the yield curve and whether the interest rate environment is volatile or not. We base our findings on 2,707 U.S. Treasury yield curves over the 2001-2012 period. Market participants who use Monte Carlo simulation, in need of a methodological framework to identify an optimal random number generator that fits the yield curve or in need of an accurate short term forecast of the yield curve, will find our paper appealingEncontrar la distribución óptima de los términos de innovación a la hora de predecir la curva de tipos de interés o valorar derivados sobre títulos de renta fija mediante simulación Monte Carlo constituye un reto que ha sido aceptado por un escaso número de investigadores. En este artículo se investiga la distribución de Pareto-Lévy que ajusta la curva de tipos del Tesoro americano bajo diferentes formas de esta última: inversa, plana, encorvada, y tanto en ambientes de volatilidad como en entornos de tipos no volátiles. Se muestra que la distribución de Pareto-Lévy no mejora significativamente la predicción de la curva de tipos con simulación Monte Carlo respecto a la distribución Normal; sin embargo, se han descubierto algunos resultados ciertamente interesantes en lo que se refiere a la distribución Normal, tales como su mejor funcionamiento a la hora de ajustar la curva de tipos y su consistencia, cualquiera que sea la forma de la curva y el entorno (de volatilidad o no) de los tipos de interés. Los resultados que se exponen en este artículo están basados en 2.707 curvas de tipos del Tesoro americano, en el periodo 2001-2012. Los participantes en el mercado que utilicen simulación Monte Carlo, ya sea por la necesidad de un marco metodológico para identificar un generador de números aleatorios óptimos que ajuste la curva de tipos o bien para obtener predicciones precisas a corto plazo, encontrarán este artículo atractiv

Assessing the Predictive Power of Customer Satisfaction for Financial and Market Performances: Price-to-Earnings Ratio is a Better Predictor Overall

Our paper shows that based on the RMSE criteria, Price-to-Earnings ratio is a better predictor of financial and market performances of the firm than the Customer Satisfaction index (CS). This conclusion is based on the choice of five financial and seven market indicators that we consider as proxies for financial and market performances with a sample comprising eighty-six companies: Book value, dividend yield, Gross Profit Margin, Price to Cash-Flows, Price-to-Earnings, Price to Sales, Annual return, ROA, ROE, ROI, Volatility and Tobin’s Q. However, CS clearly outperforms our five benchmarks (Tobin’s Q, Price-to-Cash Flows, Price-to-Earnings, Volatility or the indicator itself) when forecasting Tobin’s Q, Volatility, ROE and ROI. In periods of volatile market such as year 2008, CS is a more stable predictor of Volatility or ROE than the indicators themselves (i.e. Volatility for Volatility, ROE for ROE)

Forecasting Spanish GDPs with Spectral Analysis

The paper emphasizes the recent use of spectral analysis for forecasting financial and economic time series which deserves consideration from econometricians. Time series of Spanish nominal and real GDPs are decomposed in simpler signals called approximations and details in the framework of the one-dimensional discrete wavelet analysis. The simplified signals are recomposed after Burg extension. 2017-2026 forecasts with spectral analysis are less optimistic than the ones of government agencies. Benchmarking spectral analysis to an ARIMA model show the pertinence of adding spectral analysis to the battery of tools used by econometricians and quantitative analysts for the forecast of economic time series.El artículo enfatiza el uso del análisis espectral para labores de predicción con series temporales económicas y financieras, que ha merecido la consideración de los económetras. Las series temporales del PIB nominal y real se descomponen en señales más simples denominadas aproximaciones y detalles en el marco del análisis de wavelets discretas unidimensionales. Las señales simplificadas se recomponen después de la extensión de Burg. Las previsiones para el periodo 2017-2016 derivadas del análisis espectral son menos optimistas que las proporcionadas por la agencia gubernamental. De la comparación del análisis espectral con la modelización ARIMA se deriva la pertinencia de incorporar el análisis espectral a la batería de instrumentos utilizados por los económetras y los analistas cuantitativos para labores de previsión de series temporales económicas

Testing an innovative Variance reduction technique for Pricing Bond Options in the Framework of the CIR Model

We design an innovative variance reduction technique coupled with Monte Carlo (MC) simulation that prices accurately plain-vanilla zero coupon bond options. This technique speeds up the convergence of the simulation and offers better results than MC simulation using antithetic variables. Our benchmark is the closed-form solution of Cox Ingersoll and Ross (CIR, 1985). Our paper shows that, when pricing bond options with MC simulation, we can constrain the Wiener process inside upper and lower bands to speed up the convergence towards the �true� option value (the CIR analytical solution). Furthermore, it works best when the bands are drawn at plus or minus 0.5 standard deviations and our technique is less time consuming than a plain MC simulation. Finally, we introduce an original stochastic fifth-order polynomial model beside the CIR solution. Our contribution is to provide market practitioners with an efficient variance reduction technique, easy to implement. The major challenge of our technique would be to price bond options in times of high market volatility, when option price needs badly to reflect rare events located in the tails of the distribution. However, we can argue that pricing options in times of volatile markets is a challenge for every option pricing modelEn este artículo se diseña una nueva técnica de reducción de la varianza combinada con simulación de Monte Carlo que valora con exactitud las opciones sobre bonos cupón cero �plain vanilla�. Esta técnica acelera la convergencia de la simulación y ofrece mejores resultados que la simulación Monte Carlo con variables antitéticas. El objetivo que se persigue es la solución en forma cerrada de Cox, Ingersoll y Ross (CIR, 1985). Se muestra que cuando se valoran opciones sobre bonos con simulación Monte Carlo, se puede limitar el proceso de Wiener dentro de las bandas superior e inferior para acelerar la convergencia hacia el 'verdadero' valor de la opción (la solución analítica CIR). Además, cuando mejor funciona esta alternativa es cuando las bandas se sitúan a más o menos 0,5 desviaciones típicas y es computacionalmente más rápida que la simulación Monte Carlo normal. Finalmente, se introduce un modelo estocástico original, polinomial de quinto orden, junto con la solución CIR. La contribución de este artículo es proporcionar a los profesionales del mercado una técnica de reducción de la variabilidad eficiente y fácil de implementar. El principal reto de esta técnica es la valoración de opciones sobre bonos en periodos de alta volatilidad, cuando la valoración de opciones necesita imperiosamente reflejar acontecimientos raros localizados en las colas de la distribución. Sin embargo, se puede argüir que la valoración de opciones cuando los mercados tienen elevada volatilidad es un reto para cada modelo de valoración de opcione

Appraising the Financial Sustainability of a Pension System with Signal Processing

One key issue of the Spanish pension system is its financial sustainability in regard to slumping fertility rate and rising longevity of the Spanish population. The paper presents a versatile and robust model that may help pension managers gain insight into the future Spanish pyramid of ages, from which they will appraise cash inflows and outflows of the pension system. The model forecasts ninety years of the Spanish population for each cohort of the pyramid of ages. Borrowed from the signal processing discipline, the model relies on the Burg method which fits a pth order autoregressive (AR) model to the input signal by minimizing (least squares) the forward and backward prediction errors while constrai-ning the AR parameters to satisfy the Levinson-Durbin recursión, then uses an infinite impulse response prediction error filter. Results add better perspective and insight to the Spanish population projection forecasted by the United Nations Population DivisionUna de las cuestiones clave del sistema de pensiones español es su sostenibilidad financiera en lo que respecta a caída tasa de fecundidad y el aumento de la longevidad de la población española. El artículo presenta un modelo versátil y robusto que puede ayudar a los administradores de pensiones ganan la penetración en el futuro pirámide española de los siglos, de la que evaluarán las entradas y salidas de efectivo del sistema de pensiones. El modelo pronostica noventa años de la población española para cada cohorte de la pirámide de edades. Tomado de la disciplina de procesamiento de señales, el modelo se basa en el método de Burg que se ajusta un modelo autorregresivo de orden p (AR) para la señal de entrada, reduciendo al mínimo (mínimos cuadrados) los errores de predicción hacia delante y hacia atrás mientras que restringir los parámetros AR para satisfacer las Levinson- Durbin, a continuación, se basa en un filtro de impulso infinito error de predicción de respuesta. Los resultados proporcionan una mejor perspectiva y una visión de la proyección de la población española prevista por la División de Población de las Naciones Unidas