The White information matrix (IM) test is applied to the linear regression model with autoregressive conditional heteroskedastic (ARCH) errors. ARCH models are used widely in analyzing economic and financial time series data. However, in practice, the models are not often thoroughly tested. We...

In this thesis, the research focuses on the development and implementation of two hybrid models for pricing variance swaps and variance options. Some variance derivatives (i.e., variance swap) are priced using portfolios of put and call options. However, longer-term options price not only stock...

In this thesis two contributions are made to the area of mathematical finance. First, in order to explain the non-trivial skewness and kurtosis that is observed in the time series data of constant maturity swap (CMS) rates, we employ the pure jump Levy processes, i.e. in particular Variance...

There is ample historical data to suggest that log returns of stocks and indices are not independent and identically distributed Normally, as is commonly assumed. Instead, the returns of financial assets are skewed and have higher kurtosis. To account for skewness and excess kurtosis, it is...

The VIX index measures the one-month risk-neutral forward volatility of the S&P500 (SPX) index. While Lévy processes such as the CGMY process can price options on the underlying stock or index, they implicitly assume a constant forward volatility. This makes them unsuitable for pricing options...

In this paper, we introduce DSPMD, discretely sampled process with pre-specified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified marginals and pre-specified dependence. In the DSPMD for Levy processes, some regular copula can be...

In this thesis, stochastic volatility models with Levy processes are treatedin parameter calibration by the Carr-Madan fast Fourier transform (FFT) method and pricingthrough the partial integro-differential equation (PIDE) approach. First, different models where the underlying log stock price or...