2-Factor Models in Credit and Energy Markets

This thesis is divided in two main parts. Part A is focusing on assessing the ability of structural – form framework to predict the spreads and the prices in two different market regimes before and during the credit crisis. In Part B a 2 – factor model with local volatility for oil market is developed. For the first part three structural form models; Merton’s (1974), Leland – Toft (1996) and Longstaff – Schwartz (1995); were implemented using different assumptions for volatility and debt maturity (i) exogenous volatility and actual bond maturity, (ii) exogenous volatility and adjusted maturity, (iii) model determined volatility and actual bond maturity and (iv) model determined volatility and adjusted maturity. To our knowledge it is the first time that the model is calibrated against such four alternatives. Another novel feature of our work is the usage of historical implied volatility was used for equity. Results were in contrast with Lyden and Saraniti (2000) and Wei and Guo (1997) who argued that Merton’s model dominates Longstaff and Schwartz in predictive accuracy as Longstaff and Schwartz model revealed a very good performance. The encouraging results during the first period (January 1998 - April 2006) led to a very critical element of this research – the implementation of the Longstaff and Schwartz (1995) model on 2007 – 2008 bond data. The assumption of simple capital structure is relaxed and a composite implied volatility is calculated. Again the model indicated very good performance in all cases proving an average predicted over actual credit spread ratio of 57%. The second part of this research proposes a 2 – factor model with local volatility to price Oil Exotic Structures. The proposed approach utilizes the general multi – factor model framework and the interest ate modeling developments as described by Clewlow and Strickland (1999b) and Brigo and Mercurio (2006) respectively. The model has the flexibility to generate different local volatility surfaces depending on the calibrated data. Moreover the model allows different correlation surface. The model is used to price a number of exotic structures – barrier options, Target Redemption Notes and European and Bermudan Swaptions – that are common in the oil market. Based on the results it is clear that being able to capture the smile dynamics is very important not only for valuation reasons but also for risk management purposes. The model can be calibrated directly and match market traded instruments such us swaptions and monthly strip options