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 dissertation we propose a new model which captures observed features of asset prices. The model reproduces the skewness and fat tails of asset returns by introducing a discretized variance gamma process as the driving innovation process, in addition to a double gamma process to reflect...

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...

The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case a Merton-type formula is...

Investors in equilibrium are modeled as facing investor specific risks across the space of assets. Personalized asset pricing models reflect these risks. Averaging across the pool of investors we obtain a market asset pricing model that reflects market risk exposures. It is observed on invoking...

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and...

European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). The incomplete markets equilibrium change of measure is approximated and identified using the log return mean. variance, and kurtosis. An exact equilibrium...