In this project, we study an asymptotic expansion method for solving stochastic volatility European option pricing problems. We explain the backgrounds and details associated with the method. Specifically, we present in full detail the arguments behind the derivation of the pricing PDEs and detailed calculation in deriving asymptotic option pricing formulas using our own model specifications. Finally, we discuss potential difficulties and problems in the implementation of the methods.

Volatility plays an important role in option pricing and risk management. It is crucial that volatility is modelled as accurately as possible in order to forecast with confidence. The challenge is in the selection of the ‘best’ model with so many available models and selection criteria. The Model Confidence Set (MCS) solves this problem by choosing a group of models that are equally good. A set of GARCH models were estimated for several JSE indices and the MCS was used to trim the group of models to a subset of equally superior models. Using the Mean Squared Error to evaluate the relative performance of the MCS, GARCH (1,1) and Random Walk, it was found that the MCS, with an equally weighted combination of models, performed better than the GARCH (1,1) and Random Walk for instances where volatility in the returns data was high. For instances of low volatility in the returns, the GARCH (1,1) had superior 5-day forecasts but the MCS had better performance for 10-days and greater. The EGARCH (2,1) volatility model was selected by the MCS for 5 out of the 6 indices as the most superior model. The Random Walk was shown to have better long term forecasting performance.

Introduction – The introduction gives background to exchange rate volatility and the negative effects on economic growth that emerges when the exchange rate volatility is high.  Exchange rate volatility can affect economic growth in different ways such as establishing trade barriers or investment uncertainty. Previous studies have become quite outdated and the studies that have focused around the EMU have only compared smaller economies, hence this paper investigates the topic for developed economies and with new up-to-date data. The paper also examines two different types of exchange rate volatility, effective nominal exchange rate volatility and nominal exchange rate volatility to test if the choice of exchange rate volatility has an impact on the results. The sample for the paper contains the 36 OECD countries and the time period is 2000-2016.   Purpose – The purpose of this study is to explore how exchange rate volatility affects growth for the OECD countries. The paper also looks at what the effect of adopting the Euro as a primary currency has been for the countries in the OECD sample when looking at the exchange rate volatility and economic growth. Method – This study is conducted with a quantitative methodology, investigating a sample of 36 countries over 17 time periods from 2000-2016. The effect from exchange rate volatility on growth is analyzed through a content analysis and four panel-data regressions. This study also introduces a causality test to see if the exchange rate affects the economic growth or if economic growth affects the exchange rate volatility. Conclusion – The paper finds that both measures of exchange rate volatility have a negative effect on economic growth. There is also evidence that adopting the Euro as your currency for the time period has been negative for economic growth. Regarding the causality between exchange rate volatility and economic growth the paper finds evidence for a bidirectional causality, meaning that exchange rate volatility affects economic growth and economic growth affects exchange rate volatility.

Thesis (Ph.D.)--Boston University / This dissertation comprises three chapters on the network structure of the economy and its macroeconomic consequences. In the first two chapters, I analyze the relationship between macroeconomic volatility of individual countries and the international trade network the countries are embedded in. In the third chapter, I study the international migration network. In the first chapter, I show a regularity that European countries occupying more central positions in the intra-Europe trade network exhibit lower macroeconomic volatility. Intuitively the trade network has a core-periphery structure and the core is more stable than the periphery. This is puzzling because the core country is also more open to shocks coming from all other countries, which increases volatility. This relationship is informative in the context of the unsettled, classic debate on whether trade openness increases or decreases country-level volatility. Rather than considering an aggregate measure like trade openness, the idea of centrality provides a more comprehensive measure of the nature and strength of trade linkages as well as the identity of the trade partners, all of which have important effects on volatility. I construct a multi-country, multi-sector model subject to idiosyncratic productivity and liquidity shocks, and fully characterize the trade network generated in equilibrium. I calibrate the model to the European Union and I show that it closely replicates the observed negative relationship. Next, I extend the theory presented to incorporate a general network structure and its effects on volatility. From an empirical perspective, I construct an instrument based on geographic distance to establish the finding. From a theoretical perspective, I consider the possibilities of missing linkages and stochastic weights in the trade networks. The third chapter studies the European immobility puzzle. A theory of cross-country migration is devised in the form of labor mobility based on regional and sectoral productivity shocks in a multi-country, multi-sector setting. Differences across countries in socio-cultural and institutional factors induce a friction on such labor reallocation process. The model explains interstate migration network within the U. S. (frictionless benchmark) well. When applied to Europe, the model predicts a sizeable missing mass of migrants. Our estimates show this to be due to socio-cultural barriers.

We will begin with a review of key financial topics and outline many of the crucial ideas utilized in the latter half of the paper. Formal notation for important variables will also be established. Then, a derivation of the Black-Scholes equation will lead to a discussion of its shortcomings, and the introduction of stochastic volatility models. Chapter 2 will focus on a variation of the CIR Model using stock price in the volatility driving process, and its behavior to a greater degree. The key area of discussion will be to approximate a hedging function for European call option prices by Taylor Expansion. We will apply this estimation to real data, and analyze the behavior of the price correction. Then make conclusions about whether stock price has any positive effects on the model.

This thesis consists of three main empirical chapters on the effect of stock liquidity on exchange markets. The first (Chapter 2) investigates the pricing ability of an illiquidity measure, namely the Amihud measure (Amihud, 2002), in different sample periods. The second (Chapter 3) determines the causal link between two well-known market quality factors liquidity and idiosyncratic volatility adopting two-stage least squares methodology (2SLS). The last empirical chapter (Chapter 4) revisits the limits to arbitrage theory and studies the link between stock liquidity and momentum anomaly profit, employing the difference-in-differences approach. The overall contribution of this thesis is to employ causal techniques in the context of asset pricing in order to eliminate potential endogeneity problems while investigating the relation between stock liquidity and exchange markets. Chapter 2 investigates whether the Amihud measure is priced differently if the investor is optimistic or, conversely, pessimistic about the future of the stock markets. The results of the chapter show that Amihud measure is priced in the low-sentiment period and that there is illiquidity premium when investor sentiment is low. Chapter 3 studies whether a change in stock liquidity has an impact on idiosyncratic volatility, employing causal techniques. Prior studies investigate the link between liquidity and idiosyncratic volatility but none focus on the potential problem of reverse causality. To overcome this reverse causality problem, I use the exogenous event of decimalisation as an instrumental variable and employ two-stage least squares approach to identify the impact of liquidity on idiosyncratic volatility. The results of the chapter suggest that an increase in illiquidity causes an increase in idiosyncratic volatility. As an additional result, my study shows that reduction in the tick size as a result of decimalisation improves firm-level stock liquidity. Chapter 4 examines whether liquid stocks earn more momentum anomaly profits compare to illiquid stocks, using the implementation of different tick sizes for different price ranges in the American Stock Exchange (AMEX) between February 1995 and April 1997. This programme provides a plausibly exogenous variation to disentangle the endogeneity issue and allows me to examine the impact of liquidity on momentum, by clearly exploiting the difference-in-difference framework. The results of the chapter show that liquid stocks earn more momentum profit than illiquid stocks.

This diploma thesis deals with the impact of real exchange rate volatility on real export of the Czech Republic. In the first part, theoretical aspects of this relationship are examined, explaining both - positive and negative ? effects on bilateral and aggregate trade flows. Further on, empirical data and econometric tools are employed to capture the relationship between real export and its main determinants for the case of Czech Republic in the past decade. After the brief theoretical introduction to time series econometrics, the particular export demand model is proposed and various cointegration techniques are explained and applied to examine the long-run equilibrium but also short-run dynamics.

No description available.

The objective of this paper is to examine the impact of implementing the static and dynamic volatility interruption rule on idiosyncratic volatility and stock returns in Nasdaq Stockholm. Using EGARCH and GARCH models to estimate the conditional idiosyncratic volatility, we find that the conditional idiosyncratic volatility and stock returns increase as stock prices hit the upper static or dynamic volatility interruption limits. Conversely, we find that the conditional idiosyncratic volatility and stock returns decrease as stock prices hit the lower static or dynamic volatility interruption limit. We also find that the conditional idiosyncratic volatility is higher when stock prices reach the upper dynamic limit than when they reach the upper static limit. Furthermore, we compare the conditional idiosyncratic volatility and stock returns on the limit hit days to the day before and after the limit hit events and find that the conditional idiosyncratic volatility and stock returns are more volatile on the limits hit days. To test the volatility spill-over hypothesis, we set a range of a two-day window after limit hit events and find no evidence for volatility spill-over one or two days after the limit hit event, indicating that the static and dynamic volatility interruption rule is effective in curbing the volatility. Finally, we sort stocks by their size and find that small market cap stocks gain higher returns than larger market cap stocks upon reaching the upper limits, both static and dynamic.

The dissertation consists of two essays. In the first essay, we investigate the relation of government ownership to the idiosyncratic volatility of Saudi Arabian firms that traded in the Saudi stock exchange between 2010 and 2016. The results show that publicly traded firms with an increase in government ownership have less idiosyncratic volatility. Furthermore, we investigate market leverage ratio, dividend payout ratio, and illiquidity ratio as potential roles in which government ownership influences the idiosyncratic volatility. The results prove the negative relationship between government ownership and idiosyncratic volatility. In the second essay, we investigate the association between government ownership and momentum trading of firms traded in the Saudi stock exchange between 2010 and 2016. The results show that firms with higher state ownership are expected to have greater price momentum. We used two approaches: the portfolio sorting approach and the fixed effect approach, and these two approaches confirm the positive relationship between government ownership and momentum.