Systemic Contingent Claims Analysis

Systemic Contingent Claims Analysis

Author: Mr.Andreas A. Jobst

Publisher: International Monetary Fund

Published: 2013-02-27

Total Pages: 93

ISBN-13: 1475557531

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The recent global financial crisis has forced a re-examination of risk transmission in the financial sector and how it affects financial stability. Current macroprudential policy and surveillance (MPS) efforts are aimed establishing a regulatory framework that helps mitigate the risk from systemic linkages with a view towards enhancing the resilience of the financial sector. This paper presents a forward-looking framework ("Systemic CCA") to measure systemic solvency risk based on market-implied expected losses of financial institutions with practical applications for the financial sector risk management and the system-wide capital assessment in top-down stress testing. The suggested approach uses advanced contingent claims analysis (CCA) to generate aggregate estimates of the joint default risk of multiple institutions as a conditional tail expectation using multivariate extreme value theory (EVT). In addition, the framework also helps quantify the individual contributions to systemic risk and contingent liabilities of the financial sector during times of stress.


An Analytic Valuation Method for Multivariate Contingent Claims with Regime-Switching Volatilities

An Analytic Valuation Method for Multivariate Contingent Claims with Regime-Switching Volatilities

Author: Bong-Gyu Jang

Publisher:

Published: 2011

Total Pages:

ISBN-13:

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In this paper, we provide an analytic valuation method for European-type contingent claims written on multiple assets in a stochastic market environment. We employ a two-state Markov regime-switching volatility in order to reflect the stochastically-changing market condition. The method is developed by exploiting the probability density of the occupation time for which the underlying asset processes are in a certain regime during a time period. In order to show its usefulness, we derive closed-form valuation formulas for quanto options and exchange options with two underlying assets, as examples. In addition, we develop an approximation formula for valuing a wide range of financial contingent claims written on more than two underlying assets.


Three Essays on Contingent Claims Pricing

Three Essays on Contingent Claims Pricing

Author: Anlong Li

Publisher:

Published: 2006

Total Pages: 139

ISBN-13:

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This dissertation consists of three research topics in contemporary financial option pricing theories and their applications. The common theme of those topics involves the pricing of financial claims whose value become path-dependent when using the usual lattice approximating schemes.The first essay explores the potential of transformation and other schemes in constructing a sequence of simple binomial processes that weakly converges to the desired diffusion limit. Convergence results are established for the valuation of both European and American contingent claims when the underlying asset prices are approximated by simple binomial processes. It is also demonstrated how to construct reflecting or absorbing binomial processes to approximate diffusions with boundaries. Numerical examples demonstrate that the proposed simple approximations not only converge, but also give more accurate results then existing methods such as Nelson and Ramaswamy (1990), especially for longer maturities.Our purpose in essay 2 is two-fold. First we extend some of the simple lattice-approximation methods for one-dimensional diffusions to higher dimensions and develop special lattices to approximate perfectly correlated diffusions. We then examine current modelling issues of the term structure of interest rates, and demonstrate how to apply the approximation techniques developed here to handle path-dependence and multi-sources of uncertainty in these models.The last essay analyzes the investment decisions of insured banks under fixed-rate deposit insurance. The model takes into account the charter value and allows banks to dynamically revise their asset portfolios. Trade-offs exists between preserving the charter and exploiting deposit insurance. The optimal bank portfolio problem is solved analytically for a constant charter value. In any audit period, banks maximize their risk exposure before some critical time and act cautiously thereafter. The corresponding deposit insurance is shown to be a put option that matures at this critical time rather than at the audit date.


Universal Contingent Claims in a General Market Environment and Multiplicative Measures

Universal Contingent Claims in a General Market Environment and Multiplicative Measures

Author: Valery Kholodnyi

Publisher:

Published: 2018

Total Pages: 14

ISBN-13:

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We present the concept of a universal contingent claim introduced by the author in 1995. This concept provides a unified framework for the analysis of a wide class of financial derivatives.A universal contingent claim describes the time evolution of a contingent payoff. In the simplest case of a European contingent claim this time evolution is given by a family of nonnegative linear operators, the valuation operators. For more complex contingent claims, this time evolution that is given by the valuation operators, can be interrupted by discrete or continuous activation of external influences that are described by, generally speaking, nonlinear operators, the activation operators. For example, Bermudan and American contingent claims represent discretely and continuously activated universal contingent claims with the activation operators being the nonlinear maximum operators.We show that the value of a universal contingent claim is given by a multiplicative measure introduced by the author in 1995. Roughly speaking, a multiplicative measure is an operator-valued (in general, an abstract measure with values in a partial monoid) function on a semiring of sets which is multiplicative on the union of disjoint sets. We also show that the value of a universal contingent claim is determined by a, generally speaking, impulsive semilinear evolution equation.


Contingency Approaches to Corporate Finance

Contingency Approaches to Corporate Finance

Author: Dan Galai

Publisher: World Scientific Publishing Company

Published: 2019-01-30

Total Pages: 2036

ISBN-13: 9789814730723

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Black and Scholes (1973) and Merton (1974) (hereafter referred to as BSM) introduced the contingent claim approach (CCA) to the valuation of corporate debt and equity. The BSM modeling framework is also named the 'structural' approach to risky debt valuation. The CCA approach considers all stakeholders of the corporation as holding contingent claims on the assets of the corporation. Each claim holder has different priorities, maturities and conditions for payouts. It is based on the principle that all the assets belong to all the liability holders.In the structural approach the arrival of the default event relies on economic arguments for why firms default as it is explicitly related to the dynamics of the economic value of the firm. A standard structural model of default timing assumes that a corporation defaults when its assets drop to a sufficiently low level relative to its liabilities.The BSM modeling framework gives the basic fundamental version of the structural model where default is assumed to occur when the net asset value of the firm at the maturity of the pure-discount debt becomes negative, i.e., market value of the assets of the firm falls below the market value of the firm's liabilities. In a regime of limited liability, the shareholders of the firm have the option to default on the firm's debt. Equity can be viewed as a European call option on the firm's assets with a strike price equal to the face value of the firm's debt. Actually, CCA can be used to value all the components of the firm's liabilities. Option pricing models are used to value stocks, bonds, and many other types of corporate claims.Different versions of the model correspond to different assumptions about the conditions when a firm defaults. Merton (1974) assumes that the firm only defaults at the maturity date of the firm's outstanding debt when the net asset value of the firm, in market value terms, is negative. Others introduce other conditions for default. Also, different authors introduce more complicated capital structure with different kinds of bonds (e.g. senior and junior), warrants, corporate taxes, ESOP, and more. Volume 1: Foundations of CCA and Equity ValuationVolume 1 presents the seminal papers of Black and Scholes (1973) and Merton (1973, 1974). This volume also includes papers that specifically price equity as a call option on the corporation. It introduces warrants, convertible bonds and taxation as contingent claims on the corporation. It highlights the strong relationship between the CCA and the Modigliani-Miller (M&M) Theorems, and the relation to the Capital Assets Pricing Model (CAPM). Volume 2: CCA Approach to Corporate Debt ValuationVolume 2 concentrates on corporate bond valuation by introducing various types of bonds with different covenants as well as introducing various conditions that trigger default. While empirical evidence indicates that the simple Merton's model underestimates the credit spreads, additional risk factors like jumps can be used to resolve it. Volume 3: Issues in Corporate Finance with CCA ApproachVolume 3 includes papers that look at issues in corporate finance that can be explained with the CCA approach. These issues include the effect of dividend policy on the valuation of debt and equity, the pricing of employee stock options and many other issues of corporate governance. Volume 4: CCA Approach to Banking and Financial IntermediationVolume 4 focuses on the application of the contingent claim approach to banks and other financial intermediaries. Regulation of the banking industry led to the creation of new financial securities (e.g., CoCos) and new types of stakeholders (e.g., deposit insurers).


A Chaos Expansion Approach for the Pricing of Contingent Claims

A Chaos Expansion Approach for the Pricing of Contingent Claims

Author: Hideharu Funahashi

Publisher:

Published: 2015

Total Pages:

ISBN-13:

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In this paper, we propose an approximation method based on the Wiener-Ito chaos expansion for the pricing of European-style contingent claims. Our method is applicable to the general class of continuous Markov processes. The resulting approximation formula requires at most three-dimensional numerical integration. It will be shown through numerical examples that the accuracy of our approximation remains quite high even for the case of high volatility and long maturity.