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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.

Abstract According to a survey conducted by Rock (1984), the major factors of influenced credit risk are (1) the relationship with other creditor, (2) income, (3) loan-income ration, (4) profession, (5) immovable property, (6) check & deposit account. And, the sure way to score with lenders are (1) rules of thumb & subjective judgment, (2) credit rating system, (3) credit scoring system, and (4) expert system. The purpose of the present study is to examine the relationships between sex, age, income, profession, assets, the purpose of loan, employment information, credit references, credit limit, total installment loan account by the consumer, total number of inquiries and the consumer¡¦s payment records. The results of this search indicate that: 1. The previous stereo type thinking of banking industry always treat the military officials as wall as police officials are risky groups to consumer credit loan. However, this study found the contrary result. The payment over due rate is comparatively lower than that of other customer groups. The conclusion is that military officials and police officials are potentially good customers to banking system in terms of profit margin against risk. 2. From the credit scoring system of banking industry. That the customers are between 35 to 50s should be better than those age between 20 to 30s. However, this study demonstrates the other direction that customers with age below 35years old always better than those who over 35years old to the banking creditability actual performance. 3. The banking industry assume the married people will be a better group compared with non-married group on the money collect of the loan they made. However this study proves that creditability performance in sequence is (i) age below 35 and singer is the best. (ii) those married is the second while.(iii)age over 35 and non- married group is the worst one. 4. Most of people think those who have consumer credit loan from bank and would not want their family to be aware of their personal loan may have higher chance of payment over due. However, the statistics study from bank branch A indicates that this kind of customers (don¡¦t want family member know about loan) are the best group on payment over due (only 5.5%). While those who agree to let family member aware are the second (7.5%), and others with no comment are the worst.

<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