Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.

Monetary policy rules and estimated reaction functions for the European Central Bank

This thesis studies the interest-rate policy of the ECB by estimating monetary policy rules using real-time data and central bank forecasts. The aim of the estimations is to try to characterize a decade of common monetary policy and to look at how different models perform at this task.The estimated rules include: contemporary Taylor rules, forward-looking Taylor rules, nonlinearrules and forecast-based rules. The nonlinear models allow for the possibility of zone-like preferences and an asymmetric response to key variables. The models therefore encompass the most popular sub-group of simple models used for policy analysis as well as the more unusual non-linear approach. In addition to the empirical work, this thesis also contains a more general discussion of monetary policy rules mostly from a New Keynesian perspective. This discussion includes an overview of some notable related studies, optimal policy, policy gradualism and several other related subjects. The regression estimations are performed with either least squares or the generalized method of moments depending on the requirements of the estimations. The estimations use data from both the Euro Area Real-Time Database and the central bank forecasts published in ECB Monthly Bulletins. These data sources represent some of the best data that is available for this kind of analysis. The main results of this thesis are that forward-looking behavior appears highly prevalent, but that standard forward-looking Taylor rules offer only ambivalent results with regard to inflation. Nonlinear models are shown to work, but on the other hand do not have a strong rationale over a simpler linear formulation. However, the forecasts appear to be highly useful in characterizing policy and may offer the most accurate depiction of a predominantly forward-looking central bank. In particular the inflation response appears much stronger while the output response becomes highly forward-looking as well.