For a given threshold l0 < LGD, compute [(L â l0)+]. ... consists in the securitization of a portfolio of mortgage loans which have the same ... Loan to value: 75 %;.
Portfolio Models and ABS École Nationale des Ponts et Chausées Département Ingénieurie Mathématique et Informatique – Master II Loïc BRIN • François CRENIN
Exercice 1: From granular homogeneous portfolio to non-homogeneous portfolio. First, we consider a granular homogeneous pool, with internal risk parameters : PD = N (s), LGD and ρ for the correlation. 1. Compute the standard deviation of losses on the portfolio (Hint: consider a finite number, N , of assets first and then generalize). 2. For each α ∈ [0; 1], compute the α loss quantile. 3. For a given threshold l0 < LGD, compute E[(L − l0 )+ ]. 4. We now relax the homogeneiy assumption and p consider that each asset has its own default probability asset i p defaults as soon as its asset return R i = ρF + 1 − ρεi < s + σε¯i , where all random variables (F, (εi )i , (ε¯i )i ) are normal, centered, reduced, independent variables. Show that the loss distribution remains a Vasicek loss distribution, with modified parameters. s s0 = p 1 + σ2 ρ ρ0 = p 1 + σ2
Comment.
Exercice 2: Analysis of a securitization deal. You are working in a bank and want to compute the required regulatory capital of a securitization deal. The deal consists in the securitization of a portfolio of mortgage loans which have the same size and the same maturity (7 years). In this tutorial, we are going to use a simplified version of rating agencies methodologies. It consists in estimating for each loan a probability of default and an hypothesis in case of major changes in the market. These depend on the initial amount provided (1 - Loan To Value), the ratio Debt-to-Income, the geographical zone and data to assess a trend and volatility on the real estate market. The tranching of the deal is as follows: We will use the following parameters: • Pobability of default for each borrower : 2 %; • Loan to value: 75 %; ENPC – Département IMI – Master II
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Loïc BRIN • François CRENIN
Tutorial 4 – Portfolio Models and ABS
Class A B C TOTAL
Amount 900 70 30 1000
Owner Investors Investors Bank
• Market-Value-Decline: 30 %; • Repossession costs: 10 %. 1. What is the SFA capital on the pool before securitization?
2. A rating is given by agency ratings under the following conditions: Number of time the expected loss is covered 1 2 3 4 5 or more
Rating BB BBB A AA AAA
What are the ratings of the different tranches? What can you say about the methodology? 3. Propose another model to rate the tranches, assuming that you know the probabilities of default of all the corporate ratings.
4. Same question but assuming that there is an excess spread of 50 bp on the pool.
6. Let us suppose that the senior tranche pays: EURIBOR(1y) + 30 bp and that the Asset Swap Spread is 10 bp (on 1 year). Maturity 1 year 2 years 3 years 4 years 5 years 6 years 7 years
the common threshold and Ri a normal variable equal to: Ri = ÏF + 1 â Ïεi, where F and ... consists in the securitization of a portfolio of mortgage loans which have the same ... depend on the initial amount provided (1 - Loan To Value), the rat
This exercise is based on the following S&P transition matrix: .... order to make the results reproducible, we set the seed of the random number generator before.
Swap: the reference is a reference pool (usually between 5 and 10 reference entities) ..... The CRM is a risk metrics that, as the IRC, captures the risks due to.
Write the value of the debt of the firm for the debt-holders, of the shares of the firm for the shareholders, as an option on the value of the firm and with maturity the ...
counterparty risk management: for internal purpose and for regulatory capital .... An airline usually protects itself against a rise in fuel prices by entering into long.
1 Credit risk models to fulfill regulatory requirements and prevent the bank from failure .... IRB Advanced: modeling of PD, LGD and EAD. .... Asset Management.
Lecture 2 â Statistical tools for scoring and default modeling. François CRENIN .... The logistic regression model can be defined the following ways: ... therefore lead to different estimations depending on the algorithm/software chosen. .... Ther
With a barrier option approach and stochastic interest rate [Brys et al., 1997];. â· Taking into account ..... Journal Of Finance. Link. Modigliani and Miller (1958).
that PD = Q(Ri < s) = Φ. ︸︷︷︸. Normal cdf ... A copula C, is a function that is used to model dependencies: â(x1, ..., xd ) .... Gumbel compulas, Student copulas, grouped t-copulas, individual t-copulas, etc.;. â· the so-called ..... Delt
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Let us consider the loan portfolio of a bank made of 200 000 loans for an average amount of 100 000 EUR. ... default occurs when the value of equity is smaller that a threshold. .... Exercise 3: The subprime mortgage crisis: a model risk crisis?
year conditional on no earlier default is 3 %. 1. Estimate the ... that buys protection on A during the period starting in 3 years and ending in 7 years. We assume ...
2 Banks are financial intermediaries which fill the gap between supply and demand on money market and the risk ..... Banking services. Proprietary Trading.
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For details of our global editorial offices, for customer services and for ..... spelling mistakes and bad grammar to provide some invaluable suggestions. .... A lack of proper assessment of credit exposure and default probability was a key ...... In
Credit derivatives. OTC derivatives. Corporate. Retail. Basket default swaps. Contingent ... one can easily deal with a large number of names,. â« Tackle with ...
announcements, should lead to a drop in the company's bond prices. .... associated with the names in the credit portfolio, that can be either historical or market.
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