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 ...
Structural models École Nationale des Ponts et Chausées Département Ingénieurie Mathématique et Informatique – Master II Loïc BRIN • François CRENIN
Exercise 1: Term structure of spreads in Merton’s model. 1. 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 maturity of the debt 2. Prove the Call-Put parity in that case. 3. Give the formula of the price of the shares and the one of the debt of the firm. 4. Compute the sensitivity of the price of the share with all the parameters of the problem. 5. Compute the term structure of spreads in Merton’s model and comment the results.
Exercise 2: Leland’s model (1994). In the following exercise, the underlying model is Leland’s, in its easiest form (1994). Let us consider a firm which asset value follows, under the historical probability, the following diffusion: dVt = (µ − δ)d t + σdWt Vt where Wt is a standard brownian motion. The firm is financed through debt and equity that are exchanged on financial markets. Debt has a simple structure: the nominal is D, it was borrowed at t = 0 until the end of time, and the firm has to pay a coupon, C , until the end of time. The firm is managed by the shareholders. These can, at any moment, decide to stop the activity and trigger the bankruptcy. r is the risk free rate.
1. In the case the firm will never default, what is the value of the debt? 2. We now consider a financial asset F on which is paid a continuous coupon C for each period of time. Write the SDE (Stochastic Differential Equation) that follows F and the boundary conditions. Discuss the SDE of Leland’s model. 3. 4. 5. 6. 7. 8.
Compute the market value of the fiscal abatement, and its bankruptcy costs. What is the value of a zero-coupon that pays 1 EUR in case of failure of the firm. Give the total market value of the firm. Debt was sold at par, that is P = Cr . Compute the market value of the firm. Compute the market value of the shares. Compute the distribution of the bankruptcy time.
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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.
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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 ...
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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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