Under path dependent consideration, we discuss vulnerable option pricing problem. Two pricing models are proposed: Model(1) use stepwise regression and Monte Carlo simulation, and Model(2) is based on multi-level regression method. Since the option price was approximated by quadratic surface at each time point in Model(1), large mean square errors are induced. Therefore, we further propose a stepwise subset regression method to improve Model(1) approach. At present, this proposed method can compute the option price accurately for no credit risk options. For Model(2), we utilize a multi-level regression method to price vulnerable options, and simulation results show that the method can also obtain accurate option prices.

In recent years, people pay much attention to derivative pricing subject to credit risk. In this paper, we proposed an autoregressive time series model of log odds ratios to price derivatives. Examples of the proposed model are given via the structural and reduced form approaches. Pricing formulae of the proposed time series models are derived for bonds and options. Furthermore, simulation studies are performed to confirm the accuracy of derived formulae.

The various versions of CreditRisk+ have widely been used in the financial industry. We compute the loss distribution under CreditRisk+ model by fast fourier transform technique in order to have faster and more stable results. Moreover, we link the parameters of the model to the exogenously observed variables which could be obtained from the financial markets by the use of Poisson INAR process. It is shown that the estimation of the parameters become available under this setup. This enables us to build a system that allows users to monitor and predict the banks loss characteristics without having specific and current information on banks.

This thesis presents the modeling of credit risk by using structural approach. Three fundamental questions of credit risk literature are analyzed throughout the research: modeling single firm credit risk, modeling portfolio credit risk and credit risk pricing. First we analyze these questions under the assumptions that firm value follows a geometric Brownian motion and the interest rates are constant. We discuss the weaknesses of the geometric brownian motion assumption in explaining empirical properties of real data. Then we propose a new extended model in which asset value, volatility and interest rates follow affine jump diffusion processes. In our extended model volatility is stochastic, asset value and volatility has correlated jumps and interest rates are stochastic and have jumps. Finally, we analyze the modeling of single firm credit risk and credit risk pricing by using our extended model and show how our model can be used as a solution for the problems we encounter with simple models.

<p>The purpose of this thesis is to investigate how well Swedish banks’ follow the interest rate development of Swedish Treasury Bills and Swedish Government Bonds when they are determining the levels for their deposit and lending rates. Individuals’ deposits in a bank serves as one of the banks main assets in the balance sheet, and the spread between the bank’s deposit rate and the short-term market rate is a large source of funding for the bank. If there is a strong relationship of this spread over time, one may assume that this spread is of great importance for financing of the banking firm.</p><p>The spread between the bank’s lending rate and the long-term market rate – credit risk spread – also serves a large source of interest income for the bank, and if this relationship is strong over time, one may assume that this spread is of great importance for financing of the banking firm as well.</p><p>The banks subjected for investigation in this paper are Handelsbanken (SHB) and Föreningssparbanken (FSB). This paper finds a weaker relationship between the banks’ deposit rates and the short-term market rates, than for the lending rates and the long-term market rates. This indicates that the credit risk spread is of greater importance for financing of the banking firm than the funding spread. The weaker relationship between the banks’ deposit rates and the short-term market rate may be due to the great variability of savings alternatives offered in the market place today. The fact that banks today have deposit-deficit may also explain the weaker relationship, which may be explained by the Baumol-Tobin transaction model – where the higher the interest rate, the greater amount is being kept in the account. The stronger relationship between the banks’ lending rate and the long-term market rate may be due to the nature of the credit risk spread to function as a price-discrimination tool between lending clients.</p>

<p>Consumer credit has become increasingly popular in Russia over the past few years. With the rapid growth of lending to individuals and companies, the need for accumulation of credit histories and information, collection services of bad debts, and credit insurance and financing also become of increased importance.</p><p>It was found in this thesis that the larger credit limit given to corporate clients, the greater will the loss be if there is a default and the money cannot be collected. Giving credit to a small number of customers also increases the concentration of the risk.</p><p>The opportunity to diversify in consumer credit is, however, limited because of the geo-graphic concentration of the customers, and the macro economic risk cannot be elimi-nated. Credit periods in consumer credit are in general longer, leading to higher uncertainty of payment and hence higher exposure to risk. Personal relationships are not established with customers in consumer credit, which are argued to act as “insurances” in corporate credit.</p><p>Consumer credit is more common among international companies, leading to better offers and more flexibility in the service. Insurers of corporate credit have a restrictive policy with higher premiums and more administrative work, which is less attractive for companies to take on. Creditors also have to share the risk with insurance companies, often having to pay more than 15 percent of a default.</p><p>With respect to what was mentioned above, it was concluded in this thesis that the risk of giving credit to individuals does not necessary have to be higher than that of corporate cli-ents, but that the terms of the contract is more favourable for the creditor in consumer credit.</p>

Frankfurt (Main), University, Thesis (doctoral), 2001.

This dissertation consists of three essays on credit risk models and their Bayesian estimation. In each essay, defaults or default correlation models are built under one of two main streams. In our first essay, sequential estimation on hidden asset value and model parameters estimation are implemented under the Black-Cox model. To capture short-term autocorrelation in the stock market, we assume that market noise follows a mean reverting process. For estimation, two Bayesian methods are applied in this essay: the particle filter algorithm for sequential estimation of asset value and the generalized Gibbs sampling method for model parameters estimation. The first simulation study shows that sequential hidden asset value estimation using option price and equity price is more efficient and accurate than estimation using only equity price. The second simulation study shows that by applying the generalized Gibbs sampling method, model parameters can be successfully estimated under the model setting that there is no closed-form solution. In an empirical analysis using eight companies, half of which are DowJones30 companies and the other half non-Dow Jones 30 companies, the stock market noise for the firms with more liquid stock is estimated as having smaller volatility in market noise processes. In our second essay, the frailty idea described in Duffie, Eckner, Horel, and Saita (2009) is expanded to industry-specific terms. The MCEM algorithm is used to estimate parameters and random effect processes under the condition of unknown hidden paths and analytically-difficult likelihood functions. The estimate used in the study are based on U.S. public firms between 1990 and 2008. By introducing industry-specific hidden factors and assuming that they are random effects, a comparison is made of the relative scale of within- and between-industries correlations. A comparison study is also developed among a without-hidden-factor model, a common-hiddenfactor model, and our industry-specific common-factor model. The empirical results show that an industry-specific common factor is necessary for adjusting over- or under-estimation of default probabilities and over- or under-estimation of observed common factor effects. Our third essay combines and extends works of the first two essays by proposing a common model frame for both structural and intensity credit risk models. The common model frame combines the merits of several default correlation studies which are independently developed under each model setting. Following the work of Duffie, Eckner, Horel, and Saita (2009), we apply not only observed common factors, but also un-observed hidden factor to explain the correlated defaults. Bayesian techniques are used for estimation and generalized Gibbs sampling and Metropolis-Hasting (MH) algorithms are developed. More than a simple combination of two model approaches (structural and intensity models), we relax the assumptions of equal factor effect across entire firms in previous studies, instead adopting a random coefficients model. Also, a novelty of the approach lies in the fact that CDS and equity prices are used together for estimation. A simulation study shows that the posterior convergence is improved by adding CDS prices in estimation. Empirical results based on daily data of 125 companies comprising CDS.NA.IG13 in 2009 supports the necessity of such relaxations of assumption in previous studies. In order to demonstrate potential practical applications of the proposed framework, we derive the posterior distribution of CDX tranche prices. Our correlated structural model is successfully able to predict all the CDX tranche prices, but our correlated intensity model results suggests the need for further modification of the model. / Statistics

Banks represent one of the most important parts of the economy in the world. As a result, decisions of bank management affect not just the direct bank stakeholders but the state of the economy and society as a whole. This became evident during the latest financial crisis in 2007 where the failure of one bank resulted in the domino falling that affected banks globally. The regulators increase their attention to the risks that bank face and their measures and requirements. Therefore, the research within the banking area has important consequences from both theoretical and practical side.   The purpose of this project is to investigate whether there is a relationship between dividends that Nordic banks pay and different types of risks such as market, credit (including default), liquidity and operational. The results of the research will contribute to the knowledge in finance and help different stakeholders to understand possible reasons for different dividends level.   The methodological position works as a foundation for the conduction of the research. The epistemological and ontological views applied in this project are positivism and objectivism. The deductive research approach and quantitative research strategy are used for the research and thus the collection and analysis of the archival data of 19 Nordic banks over five year time horizon. The research can therefore be described as a panel study.   Based on the previous research papers the following proxies for risks have been used in the research: market risk – capital requirement for market risk to total assets, credit risk – loan loss provisions to total assets, default risk – Altman Z-score, liquidity risk –liquidity coverage ratio, operational risk – economic capital (capital requirement) for operational risk to total asset.   Ordinary Least Square regression analysis is performed over the collected data in order to fulfil the purpose of the project. The tests results identify that there are no statistically significant relationship between dividends and market, credit, default and liquidity risks and the statistically significant negative relationship between the dividends and operational risk in Nordic banks. These findings contribute to a new knowledge within the finance and banking area in particular. Additionally, this project might be used as a foundation for the further research within the field. The findings are also useful for stakeholders in understanding banks risk level.

Credit derivative market has experienced an exponential growth during the last 10 years with credit default swap (CDS) as an undoubted leader within this group. CDS contract is a bilateral agreement where the seller of the financial instrument provides the buyer the right to get reimbursed in case of the default in exchange for a continuous payment expressed as a CDS spread multiplied by the notional amount of the underlying debt. Originally invented to transfer the credit risk from the risk-averse investor to that one who is more prone to take on an additional risk, recently the instrument has been actively employed by the speculators betting on the financial health of the underlying obligation. It is believed that CDS contributed to the recent turmoil on financial markets and served as a weapon of mass destruction exaggerating the systematic risk. However, the latest attempts to curb the destructive force of the credit derivative for the market by means of enhancing the regulation over the instrument, bringing it on the stock-exchange and solving the transparency issue might approve CDS in the face of investor who seeks to diminish the risk of his financial portfolio. In our thesis we provide empirical evidence of CDS ability to fulfil the diversification function in the portfolio of such credit sensitive claims as bonds and stocks. Our data for the empirical analysis consist of 12 European companies whose debt underlies the most frequently traded single-name CDS with the maturity of 5 years. Through multivariate vector autoregressive models we have tested the intertemporal relation between stock returns, CDS and bond spreads changes as well as the magnitude of this relation depending on the stock market state.   The results we have achieved for our sample are the following: 1) stock returns are mainly negatively related to the CDS and bond spread changes; 2) stock returns are the least affected by both credit spread changes, whereas changes in bond spreads are the best explained by the stock and CDS market movements; 3) the strength of the relation between three variables differs over the time: the relationship between stock returns and CDS spreads is the most dominant during the pre and post-crisis periods, while during the financial crisis time the relation between stock returns and bond spread changes as well as that of between both credit spreads comes to the foreground.   The above described relations between the three markets serve as a proof of the possibility to work out diversification strategies employing CDS. During the time of turbulence on the markets the investor may exert bigger diversification gains with the help of CDS. Thus, in spite of all the recent blame of the instrument from the investor perspective it is still remains one of the sources of profit.