Essays on Financial Markets
Abstract: This thesis consists of five empirical essays dealing with different issues related to financial markets. Chapter 2 studies a new multivariate technique, Orthogonal GARCH, of forecasting large covariance matrices based on GARCH models. Orthogonal GARCH is built on principal component analysis and makes the creation of positive definite covariance matrices of arbitrary size possible. An important drawback with Orthogonal GARCH is that it builds on assumptions that sometimes break down when some of the assets we model behave differently than the other assets, or when the time period considered is very volatile. For that reason, I have chosen to apply the Orthogonal GARCH model to the highly volatile Nordic stock markets during the Asian Crisis 1997-1998, using a number of different forecast evaluation techniques. The results from the different evaluation methods all indicate a better performance of the Orthogonal GARCH model compared to traditional unconditional forecasting techniques. Chapter 3 investigates the first multinational power exchange in the world, ''Nord Pool''. Nord Pool has existed since 1996 and has participants from Norway, Sweden, Finland, Denmark, and England. Both spot and futures are traded on the exchange and in this thesis, I investigate whether the futures contracts can be used to hedge short-term positions in the underlying spot market. This question is of particular interest in the electricity market, both because electricity cannot be stored, and because of the high volatility in the electricity markets compared to other financial markets. Minimum variance hedges are estimated in a number of different ways, and standard unconditional hedges are compared to conditional GARCH and moving average hedges in an out-of-sample fashion. The empirical results indicate some gains from hedging with futures, despite the lack of straightforward arbitrage possibilities in the electricity market. Chapter 4 searches for evidence of chaos and other nonlinearities in Swedish stock return series. Empirical evidence suggests that nonlinear models, including chaotic models, might explain the dynamics of a financial return series. In this thesis, we use the BDS test to determine which linear or nonlinear dependences are responsible for the observed rejection of the IID-hypothesis in the Swedish stock market. We look at monthly, daily and 15-minute return series and find clear evidence of nonlinearities in general but no evidence of chaos. Instead, most of the nonlinearities seem to be due to GARCH effects. Chapter 5 investigates the discrete nature of stock prices and how the minimum ''tick size'' on a stock exchange creates a ''compass rose'' pattern in a scatter plot of stock returns. The effect of the compass rose on estimates/forecasts as well as on tests for chaos is further studied. Simulations reveal some effects on AR-GARCH estimates as well as forecasts due to the discreteness. The same holds for correlation integral based tests for dependences; we find that large shifts in the null-distributions of the tests render these useless in detecting chaos and other dependences. We also show how non-stationarities and ''spurious'' dependences in the series are created by the discreteness, and how this gives rise to shifts in the null-distributions of the statistical tests. Chapter 6 studies the pricing of European call options when the underlying stock index (OMX-Index) volatility changes randomly over time. This differs from the Black-Scholes approach, where volatility is assumed to be constant. Stochastic Volatility option prices are calculated with the Fourier-Inversion method and process parameters are backed out from empirical market prices on the Swedish Exchange for Options and Other Derivative Securities (OM). Stochastic Volatility option prices are compared to Black-Scholes prices as well as to market prices, and both models overprice out-of-the-money and underprice in-the-money. A dynamic hedging strategy reveals some mispricing in this market, and risk-free profit possibilities exist if transaction costs are neglected.
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