Topics on strategic games between two asymmetric firms and pricing of credit default swap by multi-variate rational lognormal model

In this thesis, we study two main topics. One is related to Real Options of competing firms and the other on pricing credit default swap (CDS). On real op-tions, we examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows. Under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms, we investigate the value of real investment options and strate-gic interaction of investment decisions. Compared to earlier models that only allow for asymmetry on sunk cost, our model demonstrates a richer set of strate-gic interactions of entry decisions. We provide a complete characterization of pre-emptive, dominant and simultaneous equilibriums by analyzing the relative value of leader's and follower's optimal investment thresholds. In a duopoly mar-ket with negative externalities, a firm may reduce loss on its real options value by selecting appropriate pre-emptive entry. When one firm has a dominant ad-vantage over its competitor, both the dominant firm and dominated firm enter at their respective leader's and follower's optimal thresholds. When the pre-emptive thresholds of both firms happen to coincide, the two firms enter simultaneously. Under positive externalities, firms do not compete to lead. On the second topic, we apply the multi-variate rational lognormal approach to model the interest rate process and default intensity processes of risky obligors. Under the rational lognormal framework, positivity of the default intensities and interest rate are guaranteed. In our model, pairwise correlation of the default processes is introduced through correlation among the stochastic factors. For pricing of single-name credit default swaps and swaptions, we manage to obtain analytic representation of the fair swap premium and option price. For pricing of basket default swaps, we derive the joint survival probabilities of default times and the probability density of the time of the nth-to-default under the assumption of conditional independence. Numerical simulation experiments were performed to demonstrate the dependence of the pricing of basket default swaps on default correlation among the risky obligors in the basket