MTL843
| MTL843 | |
|---|---|
| Mathematical Modeling of Credit Risk | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | MTL106/MTL601 |
| Overlaps | |
MTL843 : Mathematical Modeling of Credit Risk
[edit]Review of elementary stochastic calculus and Black - Scholes - Merton theory of option pricing. Corporate liabilities and contingent claims. Risk structure of interest rates. Statistical techniques for analyzing defaults. Credit scoring modeling using logistic regression, Discriminant Analysis and support vector machines. Rating based term structure models. Credit risk and interest rate swaps. Credit default swaps (CDS), collateralized debt obligations (CDO's) and other related products. The copula approach. Portfolio Credit risk analysis using coherant risk measures. MTL 850 Abstract Harmonic Analysis 3 Credits (3-0-0) Fourier transform of L1 functions on Rn, Fourier- Stieltjes transform, Plancherel theorem, convolution on L1 on Rn, Fourier series of L1 functions on Tn, Fourier- Stieltjes series, Plancherel theorem, convolution on L1 on Tn. Banach algebras, spectrum of an element and its properties, spectral radius, ideals in a commutative Banach algebra, spectrum of a commutative Banach algebra, Gelfand transform, Gelfand-Naimark theorem. Topological groups and its properties, Haar measure on a locally compact group, existence and uniqueness, modulator function, convolution, homogeneous spaces, existence of an invariant measure, weil's formula. Unitary representation of locally compact groups, Schur's lemma, relation between unitary representation of groups and the *-representations of the group algebra, positive definite functions, Gelfand-Raikov theorem. Harmonic analysis of LCA groups: Dual group of locally compact abelian group, dual group as a locally compact abelian group, Pontriagin duality theorem, spectrum of the L1 space w.r.t. the convolution, Fourier analysis on locally compact abelian groups, Plancherel theorem, Bochner's theorem. Harmonic analysis on compact groups: Finite dimensionality of the irreducible unitary representations of a compact group, Schur's orthogonality relations, Peter-Weyl thereom, Fourier analysis on compact groups, Plancherel theorem, representations of SU(2) and SO(3).