Stochastic Volatility and Pricing Bias in the Swedish OMX-Index Call Option Market

This paper investigates the pricing bias in the Swedish OMX-Index Option market and how a stochastic volatility affects European call option prices. The market is purely European and without dividends for the period studied. A CIR square-root process for the volatility is estimated with non-linear least square minimization, and stochastic volatility option prices are calculated through Fourier-Inversion. These call option prices are compared to Black-Scholes prices as well as observed market prices, and a well-defined bias structure between Stochastic Volatility prices and Black-Scholes prices is observed. With a dynamic hedging scheme, I demonstrate larger (ex ante) profits, excluding transaction costs, for traders using the stochastic volatility model rather than the Black-Scholes modelderivatives pricing; stochastic volatility; Fourier inversion

The Market's View on the Probability of Banking Sector Failure: Cross-Country Comparisons

Considering the increasingly international banks of today, the health of a country's banking sector is crucial not only to the country's growth and prosperity but also to the rest of the international financial community. Early warning signals of a banking sector in trouble or a pending banking crisis would therefore be of great value to both banks, investors and banking regulators/supervisors world wide. Different warning signals exist and in this paper we investigate how the stock market can provide a market-based indicator of banking sector health. Hall and Miles (1990) suggests an approach of estimating default probabilities of individual banks using only their stock market valuations and volatilities. In this paper we apply an aggregated version of their approach to banking sectors around the world in both developed and emerging economies and study the market's assessment of the probability of systemic banking crises in these countries over the last decade, including the Asian Crisis 1997-98. In addition, we investigate whether there is a relationship between the probability of banking sector failure and institutional/structural features of the actual banking sector. The quality of governance and the degree of law and order in a country is found to be significantly negatively related to the market based failure probabilities as is an explicit deposit insurance during periods of crisis.banking sector; banking crisis; default probability; market discipline

Estimating Default Probabilities Using Stock Prices: The Swedish Banking Sector During the 1990s Banking Crisis

The growing interest in management of credit risk and estimation of default probabilities has given rise to a range of more or less elaborate credit risk models. Hall and Miles (1990) suggests an approach of estimating failure probabilities based solely on stock market prices. The approach has the advantage of simplicity but relies on market efficiency to hold. In this paper we suggest an extension to the Hall and Miles (1990) model using extreme value theory and apply the extended model to the Swedish financial sector and to individual Swedish banks. The 15 year long sample in our study covers the period of the Swedish banking crisis of the early 1990s. We find a close correspondence between changes in the estimated probabilities of failure and the actual credit events occuring. Credit ratings from major credit rating agencies, on the other hand, are shown to react much less and much slower to credit quality changes.banking crisis; default; credit risk; extreme value theory

The Compass Rose Pattern of the Stock Market: How Does it Affect Parameter Estimates, Forecasts, and Statistical Tests?

A "compass rose" pattern sometimes appears when stock returns are plotted against themselves with a one-day lag, since stock prices move in discrete steps. In this paper, we perform a Monte Carlo study on simulated stock price series rounded in different ways to mirror the behavior of stocks on the Stockholm Stock Exchange. We find AR-GARCH parameter estimates to be affected by the discreteness imposed by rounding. Based on the compass rose and the discreteness, we investigate, theoretically and empirically, different possibilities of improving predictions of stock returns. The distributions of the BDS test as well as Savit and Green's dependability index are also influenced by the compass rose pattern. However, throughout the paper, we must impose unrealistically heavy rounding of the stock prices to find significant effects on our estimates, forecasts, and statistical tests.discrete prices; GARCH; forecasts; correlation integral statistics

A Simple Continuous Measure of Credit Risk

This paper introduces a simple continuous measure of credit risk that associates to each firm a risk parameter related to the firm's risk-neutral default intensity. These parameters can be computed from quoted bond prices and allow assignment of credit ratings much finer than those provided by various rating agencies. We estimate the risk measures on a daily basis for a sample of US firms and compare them with the corresponding ratings provided by Moody's and the distance to default measures calculated using the Merton (1974) model. The three measures group the sample of firms into various risk classes in a similar but far from identical way, possibly reflecting the models' different forecasting horizons. Among the three measures, the highest rank correlation is found between our continuous measure and Moody's ratings. The techniques in this paper can be used to extract the entire distribution of inter-temporal risk-neutral default intensities which is useful for time-to-default estimators as well as for pricing credit derivatives.

Essays on Financial Markets

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

The Impact of Currency Movements on Asset Value Correlations

This paper looks at the asset correlation bias resulting from firms’ assets and liabilities being denominated in different currencies. It focuses on the time-variation in the bias and on the dependency of the bias on currency movements. Overall, we find that the asset correlation bias for the average pair of firms in the Dow Jones Industrial Average index is significant. The bias fluctuates widely, however, and it has turned negative for shorter periods. The policy implication of the paper is that by ignoring the exchange rate component when computing portfolio credit risk one may materially underestimate the actual risk

Merton for Dummies: A Flexible Way of Modelling Default Risk

One of the most popular approaches to default probability estimation using market information is the Merton [1974] approach. By explicitly modelling a firm's market value, market value volatility and liability structure over time using contingent claims analysis the Merton model defines a firm as defaulted when the firm's value falls below its debt. In this paper we show how a simplified "spread sheet" version of the Merton model produces distance to default measures similar to the original Merton model. Moreover, when applied to a sample of US firms, the simplified model gives a relative ranking of firms that is essentially unchanged compared to the Merton model. Our paper has three main implications. First, the simplicity of our model makes it suitable as a framework for a more elaborate dynamic modelling of volatility and leverage ratios with the aim of capturing the dynamic nature of default risk suggested by empirical evidence. At the same time, in the model's most simple version, distance to default can be calculated very quickly and intuitively (on the back of an envelope). Second, the default probability's insensitivity to the leverage ration at high levels of debt makes it possible to apply the model to banks and other highly leveraged firms without exact knowledge of their leverage ratios. Third, the model can be applied to any firm regardless of its level of riskiness without estimation problems.