ICTS

TALK DETAILS

Speaker: Gopal Basak

Title: Foreign capital inflow, exchange rate dynamics and potential financial crisis

We construct a model of capital inflow in a two country framework. A capital scarce country, typically the developing country with a high return on capital borrows from capital rich country, typically developed country to finance domestic investment. We investigate the potential regimes of foreign exchange crisis under different scenarios of the model through the exchange rate dynamics. (↑)

Speaker: Vivek Borkar

Title: Risk-constrained Markov decision processes

We propose a new constrained Markov decision process framework with risk-type constraints. The risk metric we use is Conditional Value-at-Risk (CVaR), which is gaining popularity in finance. It is a conditional expectation but the conditioning is defined in terms of the level of the tail probability. We propose an iterative offine algorithm to find the risk-contrained optimal control policy. This is joint work with Rahul Jain. (↑)

Speaker: Peter Carr

Titlte: Recent developments in static hedging

Speaker: Freddy Delbaen

Title: BSDE with unbounded terminal value: the boundary case

This will be an extension of work with Richou and Hu.  If the driver is bounded by 1/2 z² then there is uniqueness of a sufficiently integrable solution as soon as the final value ξ, satisfies E[exp(- pξ)]<∞ for some p>1. The case p=1 remains open. I will present some progress on this problem. (↑)

Speaker: Kshama Fernandes

Title: Estimating the distribution of default instances for microfinance loans

Beginning with the forming of informal Self Help Groups (SHG) in early 1980s, Indian microfinance sector has grown significantly in the past decades. However, little research work in credit risk analysis has been done oriented to microcredit in India and worldwide. In this paper, we present a new performance indicator for microfinance portfolios. This risk indicator, called ‘default instance’, calculates the number of payment failures for a portfolio during each repayment period unlike traditional risk measures which are based on days-past-due. Based on default data collected from 19 microfinance loan portfolios, the paper also seek to find appropriate probability distribution for observed default instances. The fitted distributions are used to calculate risk quantities like expected and unexpected defaults and potential tail defaults at a given confidence level. (↑)

Speaker: Kay Giesecke

Title: Large portfolio asymptotics for loss from default

We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinite system of SDEs. The solution to this system leads to the distribution of the limiting portfolio loss, which we propose as an approximation to the loss distribution for a large portfolio. Numerical tests illustrate the accuracy of the approximation, and highlight its computational advantages over a naive Monte Carlo simulation of the original stochastic system. This is joint work with Konstantinos Spiliopoulos (Brown) and Richard Sowers (Illinois at Urbana-Champaign). (↑)

Speaker: Garud Iyengar

Title: An axiomatic approach to systemic risk

Systemic risk is an issue of great concern in modern financial markets as well as, more broadly, in the management of complex systems. We propose an axiomatic framework for systemic risk. Our framework allows for an independent specification of (1) a functional of the cross-sectional profile of outcomes across agents in the system in a single scenario of nature, and (2) a functional of the profile of aggregated outcomes across scenarios of nature. This general class of systemic risk measures captures many specific measures of systemic risk that have recently been proposed as special cases, and highlights their implicit assumptions. Moreover, the systemic risk measures that satisfy our conditions yield decentralized decompositions, i.e., the systemic risk can be decomposed into risk due to individual agents. Furthermore, one can associate a shadow price for risk to each agent that correctly accounts for the externalities of the agent’s individual decision-making on the entire economy. (↑)

 http://moallemi.com/ciamac/papers/systemic-risk-2011.pdf

Speaker: Srikanth Iyer

Title: Pricing Credit Derivatives in a Markov modulated reduced form model

Numerous incidents in the financial world have exposed the need for the design and analysis of models for correlated default timings. Some models have been studied in this regard which can capture the feedback in case of a major credit event. We extend the research in the same direction by proposing a new family of models having the feedback phenomena and capturing the effects of regime switching economy on the market. The regime switching economy is modeled by a continuous time Markov chain. We model the default intensity in a pool of firms using the Markov chain and a risk factor process. We price some single-name and multi-name credit derivatives in terms of certain transforms of the default process. These transforms can be calculated explicitly in case the default intensity is modeled by a conditionally affine point process. In such a case, under suitable technical conditions, the price of credit derivatives are obtained as solutions to a system of ODEs with weak coupling, subject to appropriate terminal conditions. We show that the pricing formulas in our model are computationally tractable. Solving the system of ODEs numerically, we analyze the credit derivative spreads and compare their behavior with the non-switching counterparts. We show that our model can easily incorporate the effects of business cycle. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low floating interest rate, high default intensity rate and high volatility.

Speaker: Suresh Kumar

Title: Credit portfolio management using exponential utility

In this talk we propose a new model for credit portfolio management. Also we prove the existence and characterization of optimal portfolio under this model. It is a joint work with Chandan Pal. (↑)

Speaker: Ratul Lahkar

Title: Logit dynamic and price dispersion

We adopt an evolutionary framework to explain empirical and experimental evidence that price dispersion is a time varying phenomenon. We develop a finite strategy analog of the Burdett and Judd (1983) model of price dispersion. We show that all dispersed price equilibria are unstable in this finite model under the class of perturbed best response dynamics. Using numerical simulations, we show that instead, under the logit dynamic, price dispersion manifests itself as a limit cycle. We verify that limit cycles persist even when the finite strategy model approaches the original continuous strategy model. For a particularly simple case of the model, we also prove the existence of a limit cycle. (↑)

Speaker: Dilip B. Madan

Title: On pricing contingent capital notes

A bank’s stock price is modeled as a call option on the spread of random assets over random liabilities. The logarithm of assets and liabilities are jointly modeled as driven by four variance gamma processes and this model is estimated by calibrating to quoted equity options seen as compound spread options. On defining riskweighted assets as asset value less the bid price plus the ask price of liabilities less the liability value we endogenize capital adequacy ratios following the methods of conic finance for the bid and ask prices. All computations are illustrated on CSGN.VX, ADRed into USD on March 29 2011. (↑)

Talk slides

Speaker: Krishanu Maulik

Title: Tail behavior of randomly weighted sums

Randomly weighted sums come up naturally in the context of the linear processes, including ARIMA and FARIMA processes and they have wide appliacations in actuarial and economic situations and stochastic recurrence equations, especially when the weights are random. In this talk, we consider how the regularly varying tail behavior of the summands affect that of the sum.

We consider a sequence of identically distributed and asymptotically pairwise independent summands $\{X_t, t\geq 1\}$ with regularly varying tails, which are independent of the sequence of positive weights $\{\Theta_t, t\geq 1\}$. We weaken the moment conditions proposed by Resnick and Willekens (1991) for the sum to have regularly varying tails. We also prove a converse result under the extra assumption that the summands are i.i.d. More precisely, we provide sufficient moment conditions, including nonvanishing Mellin transform, for the weights, so that the regularly varying tail of the sum implies that of the summands. This is a joint work with Rajat Subhra Hazra. (↑)