In the first part of this thesis, I make use of the notion of excursion and occu-pation time of a diffusion process to study the effect of different repricing mech-anisms in the employee stock options and to price the α-quantile options. By modeling the repricing mechanisms of the employee stock options based on the excursion and occupation time, I investigate the impact of the embedded repric-ing flexibility on the market value of the employee stock options. The analytic representation of the price functions of the repriceable options are derived. To value the option numerically, the forward shooting grid technique in the lattice tree algorithm is used to handle the path dependent features in the repriceable option model. My calculations show that the repricing flexibility may have va...[ Read more ]

In the first part of this thesis, I make use of the notion of excursion and occu-pation time of a diffusion process to study the effect of different repricing mech-anisms in the employee stock options and to price the α-quantile options. By modeling the repricing mechanisms of the employee stock options based on the excursion and occupation time, I investigate the impact of the embedded repric-ing flexibility on the market value of the employee stock options. The analytic representation of the price functions of the repriceable options are derived. To value the option numerically, the forward shooting grid technique in the lattice tree algorithm is used to handle the path dependent features in the repriceable option model. My calculations show that the repricing flexibility may have vary-ing degrees of impact on the option values and their comparative statics. On the other hand, the distribution functions of occupation times under the constant elasticity of variance (CEV) process are also derived. The distribution functions can then be used to price the α-quantile options. I also derive the fixed-floating symmetry relation for α-quantile options when the underlying asset price process follows the Geometric Brownian motion.

In the second part of the thesis, I consider the finite time horizon dividend-ruin model. The asset value process is modeled as a restricted Geometric Brownian process with an upper reflecting (dividend) barrier and a lower absorbing (ruin) barrier. Analytic solutions to the value function of the restricted asset value process are provided. I also solve for the survival probability and the expected present value of future dividend payouts over a given time horizon. The sen-sitivities of the firm asset value and dividend payouts to the dividend barrier, volatility of the firm asset value and firm's credit quality are also examined.

Finally, I present the Markov chain formulation of the credit contagion model with interacting intensities. The Markov chain framework is applied to calculate the joint default distributions of default times. Properties of various dependence measures on pairwise default correlation arising from credit contagion are ex-amined. I also apply the interacting intensities model to study the impact of counterparty risk on the swap premium of a credit default swap.