Expected Shortfall and Value-At-Risk Under a Model with Market Risk and Credit Risk

This dissertation, "Expected Shortfall and Value-at-risk Under a Model With Market Risk and Credit Risk" by Kin-bong, Bonny, Siu, 蕭健邦, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled EXPECTED SHORTFALL AND VALUE-AT-RISK UNDER A MODEL WITH MARKET RISK AND CREDIT RISK Submitted by SIU KIN BONG BONNY for the degree of Master of Philosophy at The University of Hong Kong in October 2006 A model which takes care of both market and credit risks was presented. Asurplusprocesswasproposedwhichmodelsthecreditriskcomponentbyarst order Markov chain on Standard and Poor's credit ratings. Under the Markovian regime switching setup, various risk measures have been considered. Risk mea- sures including natural value at risk and expected shortfall were reviewed and adopted. A risk measure called n-period value at risk which is more conservative than the natural value at risk has also been proposed. Recursive equations were developedfortheseriskmeasures. Inordertodealwithsomekindofdependency on the credit risks, a weak Markov chain was attempted to model the credit rat- ing dynamics in the surplus process. A weak Markov chain is a Markov chain in which transition depends on two or more transition histories. In particular, a second order Markov model was considered for the sake of simplicity. Second order transition probabilities, transition matrix, and transition states have been re-estimated and restated to cope with the dependency structure. The surplus process and recursive equations have also been rederived. By assuming that the market risks follow some known distributions, simulations under both Markov chain models were carried out for three scenarios. Under the rst order model, the results are consistent with expectation and other research works. The pro- posed risk measure n-period value at risk works e(R)ectively in normal distribution scenario. As a contradiction, although the results for second order model are generally consistent with the use of rst order Markov model, there exists some discrepancies between two particular credit state combinations. It was concluded that the estimated second order transition matrix and the length of observation period would be the cause and further investigation is needed to solve the prob- lem. DOI: 10.5353/th_b3772747 Subjects: Risk management - Mathematical models Financial futures - Mathematical models Markov processes