Modelling dependence in finance using copulas - Thierry Roncalli's ...

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The First-to-Default (FtoD) option – A first-to-default is a contingent claim that pays at the first of N credit events an amount ϖ (τ). FtoD (t 0 , t) = E [ ϖ (τ) e −r(τ) ] 1 [τ
Numerical illustrations ϖ = 1 — r = 5% — Exponential survival times with hasard rates λ n — the survival copula is a Normal copula with a matrix of parameters of the form ⎡ ⎢ ⎢ ⎢ ⎣ 1 ρ · · · ρ 1 . .. . 1 ρ 1 ⎤ ⎥ ⎥⎥ ⎦ Modelling dependence in finance using copulas New pricing methods with copulas 4-12
Page 1 and 2: Modelling dependence in finance usi
Page 3 and 4: 1 The Gaussian assumption in financ
Page 5: 2.1 Pearson correlation and depende
Page 8: 2.3 Copulas in a nutshell A copula
Page 11 and 12: The copula function C (u; ρ) = Φ
Page 13 and 14: Simulation • Generate a gaussian
Page 15 and 16: We can show that the solution of th
Page 19 and 20: 3 An open field for risk management
Page 21 and 22: Let consider an example of equity p
Page 23 and 24: 3.2 Operational risk Industry defin
Page 25 and 26: For a given target insolvency rate
Page 27: Correlated aggregate loss distribut
Page 31: The limit case λ = lim α→1 λ (
Page 35 and 36: 4.1 Coherent valuation of multi-ass
Page 37 and 38: Relationships between C Q and C P L
Page 39: BS pricing in stochastic volatility
Page 46: An example of the computation of th
Page 49: Some examples ∗ The Default Digit
Page 57 and 58: 6 References (Copulas and Finance)
Page 59 and 60: [18] Georges, P., A-G. Lamy, E. Nic
Page 61: 7 Other references [1] Deheuvels, P

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