We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model (HEM). Similar results are only available previously in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as we essentially use only Itô’s formula and do not need more advanced results such as those of Bessel pr...

In this paper we discuss the approximate basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated diffusion processes with idiosyncratic and systematic jumps. We suggest a new approximate pricing formula which is the weighted sum of Roger and Shi’s lower bound and the conditional second moment adjustments. We show the approximate value is always wi...

We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model (HEM). Similar results are only available previously in the special case of Black-Scholes model (BSM). Even in the case of BSM, our approach is simpler as we essentially use only the Ito's formula and do not need more advanced results such as those of Bessel proces...

This paper studies the question of maximizing terminal wealth from expected utility in a multidimensional jump-diffusion model. The special feature of our approach is that the investor only observes the vector of stock prices, therefore leading to a partial information framework. Using non-linear filtering and change of measure techniques, we show that the optimization problem can be rewritten ...

In this paper we demonstrate the efficacy of a stochastic modelling approach involving both diffusion and a jump processes to describe the evolution of spot electricity prices in New South Wales. The model allows a deterministic time trend component and an unobserved process driven by both time varying volatility and occasional jumps. The structure allows us to cast the problem in a state space...

Acknowledgements I would like to extend my gratitude to my supervisor Sam Howison for his guidance and advice throughout the preparation and writing of this dissertation. I would also like to thank Christoph Reisinger for his advice whilst Dr Howison was away. Finally and most importantly I would like to thank my parents for their continued emotional and financial support, without which I would...

We study a practical optimization problems for venture capital investments and/or Research and Development (R&D) investments. The first problem is that, given the amount of the initial investment and the reward function at the initial public offering (IPO) market, the venture capitalist wants to maximize overall discounted cash flows after subtracting subsequent (if needed) investments. We desc...

Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We ad...