In the exponential copula model, the joint survival of two obligors is given by S(t,)= S...
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In the exponential copula model, the joint survival of two obligors is given by S(t₁,₂)= S₁ (₁)S2 (2)min(e31, e312), where. U₁ = Si (ti) = e (Ai+A³)t₁, i = 1,2. Here, A, is the idiosyncratic shock intensity of firm i, i = 1,2, and A3 is the intensity of the macro-economic shock affecting both firms simultaneously. (a) Express S(t₁, t2) in the form of the copula function C (₁, u₂) and verify that CT (u₁, 1) = u₁ and CT (1, ₂) = ₂. (b) Let T be the random arrival time of the kth shock, k = 1,2,3, in the current two obligor exponential copula model. Explain why we can simulate the arrival times of these shocks based on simulation of uniform distribution variable Vk over [0, 1], where Hint Recall Tk -In Vk, k 1,2,3. = P[Tk ≤tk] = 1−e¯λ¹, k = 1,2,3. In the exponential copula model, the joint survival of two obligors is given by S(t₁,₂)= S₁ (₁)S2 (2)min(e31, e312), where. U₁ = Si (ti) = e (Ai+A³)t₁, i = 1,2. Here, A, is the idiosyncratic shock intensity of firm i, i = 1,2, and A3 is the intensity of the macro-economic shock affecting both firms simultaneously. (a) Express S(t₁, t2) in the form of the copula function C (₁, u₂) and verify that CT (u₁, 1) = u₁ and CT (1, ₂) = ₂. (b) Let T be the random arrival time of the kth shock, k = 1,2,3, in the current two obligor exponential copula model. Explain why we can simulate the arrival times of these shocks based on simulation of uniform distribution variable Vk over [0, 1], where Hint Recall Tk -In Vk, k 1,2,3. = P[Tk ≤tk] = 1−e¯λ¹, k = 1,2,3.
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a Given St1 t2 S1t1S2t2 mine3t1 e3t2 Where Siti ei 3ti ui survival function of firm i ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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