Essays in exotic derivative pricing and time series analysis

The first essay presents a closed-form pricing formula for a European call warrant issued by a leveraged firm and demonstrates there are significant pricing errors if the formula derived under the all-equity firm assumption in Schulz & Trautmann (Journal of Banking and Finance, 1994) and the formula developed for pricing regular options in Black & Scholes (Journal of Political Economy, 1973) are used to price such a warrant. The second essay is on pricing a Catastrophic Put Option (Cat-E-Put). A Cat-E-Put is a catastrophic event triggered equity option, designed as a post-loss refinancing tool for a primary insurance company. The objective of this paper is to develop a pricing formula that factors in both 'feedback effect' and 'dilution effect'' to the share price due to the exercise of the put. We successfully derive a pricing formula and illustrate in numerical examples that the failure to price a Cat-E-Put as on-your-own stock option (option written on buyer or seller's stock) could lead to relative pricing error in a factor close to the hedge ratio (the number of new shares to be issued upon the exercise of the Cat-E-Put divided by the number of current outstanding shares). The third essay is about time series modeling of temperature processes for weather derivatives pricing and it compares the performance of three classes of time series models. The fractional AR-GARCH model is favored in most of cases over another two models, AR-GARCH and fractional AR by AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion). We also use the three models to forecast densities of two weather indices. Relative to volatility calculated based on historical realized index values and volatilities based on simulated index values, AR-GARCH tends to give the lowest volatility estimate for each city and each index, with only two exceptions out of 20 cases considered.