Learning Options and Binomial Trees

The cryptocurrencies are digital currencies that were initially designated to replace the old ones. However, they act as investment assets and many treat them like stocks. The market for cryptocurrencies counts more than 1600 types and the Bitcoin is the first and foremost of all of them. In one year the price of Bitcoin grew staggering 2000 percent. Other currencies have not seen this type of rising. This study investigates the period of over 4 years of data for 5 cryptocurrencies, the three years before and the last year of hyper-growth of the Bitcoin. We used GARCH model to see if two periods of data may offer some incites for patterns. The findings of this paper show that the Bitcoin in the period of high volatility is more diverged from its counterparts. According to results in the period of high volatility, the factors that influence the price formation of cryptocurrencies may not be the same for all of them. Using the price of the Bitcoin of one day earlier and the price of altcoins today we find spillover effect. Spillover effect is less prominent in the second period of high volatility. It may indicate of relatively independent nature of altcoins during the periods of high volatility.

Calendar anomalies in cash and stock index futures: International evidence

Purpose – The purpose of this paper is to analyze the effect of investor sentiment, measured with Google internet search data, on volatility forecasts of the US REIT market. Design/methodology/approach – The author uses the S & P US REIT index and collects search volume data from Google Trends for all US REIT. Two different Generalized Autoregressive Conditional Heteroskedastic models are then estimated, namely, the baseline model and the Google augmented model. Using these models, one-step-ahead forecasts are conducted and the forecast accuracies of both models are subsequently compared. Findings – The empirical results reveal that search volume data can be used to predict volatility on the REIT market. Especially in periods of high volatility, Google augmented models outperform the baseline model. Practical implications – The results imply that Google data can be used on the REIT market as a market indicator. Investors could use Google as an early warning system, especially in periods of high volatility...

Revisiting stock market index correlations

In this paper we will discuss the estimation of powerline communication (PLC) asynchronous impulsive noise volatility by studying the conditional variance of the noise time series residuals. In our approach, we use the Generalized Autoregressive Conditional Heteroskedastic (GARCH) models on the basis that in our observations, the noise time series residuals indicates heteroskedasticity. By performing an ordinary least squares (OLS) regression of the noise data, the empirical results show that the conditional variance process is highly persistent in the residuals. The variance of the error terms are not uniform, in fact, the error terms are larger at some portions of the data than at other time instances. Thus, PLC impulsive noise often exhibit volatility clustering where the noise time series is comprised of periods of high volatility followed by periods of high volatility and periods of low volatility followed by periods of low volatility. The burstiness of PLC impulsive noise is therefore not spread randomly across the time period, but instead has a degree of autocorrelation. This provides evidence of time-varying conditional second order moment of the noise time series. Based on these properties, the noise time series data is said to suffer from heteroskedasticity. Numerical results provide evidence that the proposed model is capable of providing an accurate stochastic representation of the impulsive noise in the 1-30MHz frequency band. The parameter estimates of the model indicates a high degree of persistence in conditional volatility of impulsive noise which is a strong evidence of explosive volatility.

This dissertation is composed of three loosely related chapters, all of which are empirical.In Chapter 1, I examine whether expectations are formed in a systematically different manner during periods of low volatility versus periods of high volatility. I achieve this by measuring non-linearities in relationship between the SP 500 and the VIX across different market regimes. Three distinct market regimes are identified through a Markov Process, allowing for the capture of non-constant behavior in the relationship between contemporaneous price changes and future volatility expectations. The results indicate that the effect of the underlying asset on the supply and demand dynamics of its derivative is strongest during periods of low volatility and weakest during periods of high volatility. The decrease in magnitude of the SP 500 coefficient as the market switches from low volatility to high, suggests that information scarcity (low volatility) makes additional data (price changes) more impactful. Measures to limit market volatility may make market participant prone to expect changes in the state of the system. The purpose of Chapter 2 is to draw inference from the tail behavior of financial market price volatility in order to compare and contrast volatility expectations with volatility realizations. In doing so, I discuss the implications of slowly decaying tails as they relate to systems susceptible to unpredictable and consequential events. In such cases where fat tails are identified, typical values such as the average and variance, do not properly characterize the risk and unpredictability of the dynamic process under study. Prior research has identified asset prices and asset volatility as being drawn from a power law distribution. This paper aims to quantitatively confirm this characterization, specifically for market volatility. Further, this paper identifies whether or not volatility expectations exhibit similar power law characteristics. Goodness of fit and log likelihood tests indicate that most realized volatility series are plausibly drawn from a power- law distribution. However, none of the studied implied volatility series show evidence of power-law behavior, suggesting that risk premia may exist for lower levels of volatility but does not scale proportionally to the more extreme crisis events. That is, risk premia does not scale proportionally as values move farther into the tail. In Chapter 3, co-authored with Minh Pham, we investigate how economic uncertainty, specifically stock market uncertainty, correlates to individuals' life-satisfaction. Using expected price volatility (VIX) as our anticipatory indicator and life-satisfaction as our measure of utility, our hypothesis is built on the Anticipatory Utility framework, which suggests that people also derive utility from their beliefs. After accounting for associations with the unemployment rate and stock ownership, we find a positive relationship between the VIX and low self-reported life- satisfaction. This analysis captures the contemporaneous effects of future beliefs and indicates that economic sentiment about the future plays an important role in individuals' feelings about the present. This work was inspired by a desire to understand the economic crises that redirect and ultimately redefine our socioeconomic lives, as individuals and as nations. I began my economic studies during one of the most profound crises in recent history, the global financial crisis of the late 2000s. Here again in 2021, as my studies conclude, economies grapple with another, albeit different crisis. Both the Covid-19 pandemic and the subprime financial crisis highlight a salient fact; we never really know when, why, or from where such extreme events arrive. But they do, and do so more frequently than we like or predict. Each of the chapters presented in this dissertation seek to understand the ways in which we anticipate and interact with a characteristic marker of economic and financial crises, uncertainty.

Forecasting stock market in high and low volatility periods: a modified multifractal volatility approach

The impressive rise in commodity prices since 2002 and their subsequent fall since July 2008 have revived the debate on the role of commodities in the strategic and tactical asset allocation process. Commonly accepted benefits include the equity-like return of commodity indexes, the role of commodity futures as risk diversifiers, and their high potential for alpha generation through long-short dynamic trading. This article examines conditional correlations between various commodity futures with stock and fixed-income indices. Conditional correlations with equity returns fell over time, which indicates that commodity futures have become better tools for strategic asset allocation. The correlations between the S&amp;P 500 Index and several commodities also fell in periods of above-average volatility in equity markets. This is desirable for long institutional investors as they need the benefits of diversification most in periods of high volatility in equity markets. Similarly, the results suggest that adding commodity futures to T-bill portfolios reduces risk further in volatile interest rate environments. <b>TOPICS:</b>Commodities, futures and forward contracts, portfolio construction, performance measurement

Wheat, corn, rice, soybeans, and cotton experienced higher volatility in the second half of the 2000s. For the sample at hand, the unit root tests only validate a new period of high volatility for wheat and cotton. If in the next couple of years however, corn, rice and soybeans maintain their higher volatility, a new period of high volatility may also be validated statistically. Regarding the factors driving the intrayear volatility GMM estimates show that “commodity market fundamentals” i.e., the stock‐to‐use ratio and to a lesser extent the degree of internationalization, are the most systematically statistically significant coefficients among commodities. Over time, consecutive low stock‐to‐use ratios and a thin international market provoke typically high volatility. Speculative activity and liquidity in the agricultural derivative market have a stabilizing effect on the spot price, if any. Finally, “common macro” factors significantly impact volatility, especially the volatility of petrol and of exchange rates; their dispersion importance over the sample is quite sizeable. However, it is difficult to establish a link between, on the one hand, loose monetary policy, business cycle and inflation, and, on the other hand, commodity price volatility, as the sign of the estimated coefficient changes depending on the commodity and the estimated elasticities are quite low.

Purpose The purpose of this paper is to study the value effects of hedging in the airline industry during a period of high volatility and high fuel costs. The authors also study the determinants of hedging in the airline industry, most importantly whether managerial ownership affects airlines’ tendency to hedge their fuel price risk. Design/methodology/approach This study’s research design follows closely previous studies in the area. This allows comparison of the results of this study to those reported earlier, and thus the authors can draw conclusions about the effects of the different market conditions during the sample period. Findings The authors find a positive relationship between hedging and firm value, but the relationship is weaker than what is reported in prior studies. The result appears driven by the early part of the sample, whereas in the latter half of the sample, when uncertainty and fuel price are higher, the hedging premium is smaller. The authors also find that hedging premium is larger for firms that follow passive hedging strategies and that managerial ownership increases the firms’ degree of hedging. Originality/value This study provides new results on the old question of whether hedging generates value in the airline industry. The recent period of high volatility and high fuel prices makes this an interesting question to re-visit.

Executive Summary. The paper studies the temporalvariations in the conditional correlations between realestate investment trust (REIT) returns and equity, bond,and commodity returns. The findings reveal that the correlationsbetween REITs and equity returns rose over theperiod analyzed, while the correlations with bonds andcommodities fell. The findings also reveal that the correlationswith REITs rose especially in periods of aboveaverage volatility in equity and bond markets; however,for U.S. government securities and the Goldman SachsCommodity Index, the conditional correlations withREITs fell in periods of high volatility in these markets.This indicates that to reduce the total risk of their portfolio,investors in U.S. government securities and commoditiesshould tilt their asset allocation more towardsreal estate when they anticipate changes in monetarypolicy or abnormal fluctuations in commodity prices.

The recombining binomial tree approach, which has been initiated by Cox et al. (J Financ Econ 7: 229–263, 1979) and extended to arbitrary diffusion models by Nelson and Ramaswamy (Rev Financ Stud 3(3): 393–430, 1990) and Hull and White (J Financ Quant Anal 25: 87–100, 1990a), is applied to the simultaneous evaluation of price and Greeks for the amortized fixed and variable rate mortgage prepayment option. We consider the simplified binomial tree approximation to arbitrary diffusion processes by Costabile and Massabo (J Deriv 17(3): 65–85, 2010) and analyze its numerical applicability to the mortgage valuation problem for some Vasicek and CIR-like interest rate models. For fixed rates and binomial trees with about thousand steps, we obtain very good results. For the Vasicek model, we also compare the closed-form analytical approximation of the callable fixed rate mortgage price by Xie (IAENG Int J Appl Math 39(1): 9, 2009) with its binomial tree counterpart. With respect to the binomial tree values one observes a systematic underestimation (overestimation) of the callable mortgage price (prepayment option price) analytical approximation. This numerical discrepancy increases at longer maturities and becomes impractical for a valuable estimation of the prepayment option price.

This study examines the risk-return dynamics of equity funds in emerging markets with five- and one-globe ratings from Morningstar, with a focus on Brazil, Chile, India, Mexico, and South Korea. This research contributes to the growing body of literature on funds of funds (FoFs) in emerging markets by analyzing synthetic environmental, social, and governance (ESG) and non-ESG portfolios. The findings contribute to the debate on the effectiveness of ESG, showing that its performance depends on the local market structure, policy risk, and economic context. The study offers a novel perspective on how ESG fund performance shifts under macroeconomic stress in emerging markets within the context of global capital allocation, integrating multifactor models with nonlinear regime-switching techniques. Using the FF4 and FF5 models, we compare five- and one-globe fund portfolios (Morningstar Sustainability Rating). We extend these models using GEPU, VIX, and WTI indices to assess economic uncertainty. Finally, we apply Markov-switching regressions to capture regime shifts and nonlinear effects across volatility periods in each market. Using the FF4 and FF5 models, we examine five emerging markets (Brazil, Chile, India, Mexico, and South Korea) from September 2018 to September 2024 (73 observations) and find that market risk dominates across markets while size and value matter in India and Mexico. Brown funds in Brazil and Mexico benefit from oil price shocks, indicating their reliance on fossil fuels. Green funds in Chile and Mexico perform better under stable conditions. ESG funds are more sensitive to volatility, while brown funds are more resilient during crises. In Brazil and India, brown funds outperform, particularly during periods of high volatility (MS model). In Chile and Mexico, green funds perform better in calm markets. In South Korea, no significant differences were found, though green funds outperformed in the FF4 and FF5 models.

We address the problem of modeling commodity forward curves, while preserving empirical features observed in commodity markets. By letting a commodity market to “live” in the tempo of a business rather than calendar clock, we create a model with a rich but realistic set of features, such as stochastic volatility, stochastic rate of mean reversion and various shapes of forward curves such as backwardation and contango. The model, when applied to extensive historical datasets of crude oil and natural gas forward curves, shows a remarkably good fit to the observed futures prices, also in periods of high volatility and negative prices. The model is developed in such a way that it can be used for a wide variety of applications, ranging from exotic derivatives pricing to risk management of commodity portfolios.

The Nonlinear Dynamics of Corporate Bond Spreads: Regime-Dependent Effects of Their Determinants