scholarly journals CREDIT RISK MODELING USING TIME-CHANGED BROWNIAN MOTION

2009 ◽  
Vol 12 (08) ◽  
pp. 1213-1230 ◽  
Author(s):  
T. R. HURD
Keyword(s):  
Brownian Motion ◽  
Firm Value ◽  
Credit Derivatives ◽  
Distribution Functions ◽  
Reduced Form ◽  
Risk Modeling ◽  
First Passage ◽  
Wide Range ◽  
Time Changes ◽  
First Passage Problem

Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard first passage problem for stochastic processes to capitalize on this time change structure and find that the distribution functions of such "first passage times of the second kind" are efficiently computable in a wide range of useful examples. Thus this new notion of first passage can be used to define the time of default in generalized structural credit models. Formulas for defaultable bonds and credit default swaps are given that are both efficiently computable and lead to realistic spread curves. Finally, we show that by treating joint firm value processes as dependent time changes of independent Brownian motions, one can obtain multifirm credit models with rich and plausible dynamics and enjoying the possibility of efficient valuation of portfolio credit derivatives.

A MODELING SYSTEM FOR CLIMATE CHANGE RISK ASSESSMENT, MANAGEMENT AND HEDGING IN COASTAL AREAS

2017 ◽  
Author(s):  
Sergei Soldatenko ◽  
Sergei Soldatenko ◽  
Genrikh Alekseev ◽  
Genrikh Alekseev ◽  
Alexander Danilov ◽  
...  
Keyword(s):  
Climate Change ◽  
Risk Assessment ◽  
Coastal Areas ◽  
Mitigation Strategies ◽  
System Structure ◽  
The Arctic ◽  
Risk Modeling ◽  
Wide Range ◽  
Adverse Weather ◽  
The Impact

Every aspect of human operations faces a wide range of risks, some of which can cause serious consequences. By the start of 21st century, mankind has recognized a new class of risks posed by climate change. It is obvious, that the global climate is changing, and will continue to change, in ways that affect the planning and day to day operations of businesses, government agencies and other organizations and institutions. The manifestations of climate change include but not limited to rising sea levels, increasing temperature, flooding, melting polar sea ice, adverse weather events (e.g. heatwaves, drought, and storms) and a rise in related problems (e.g. health and environmental). Assessing and managing climate risks represent one of the most challenging issues of today and for the future. The purpose of the risk modeling system discussed in this paper is to provide a framework and methodology to quantify risks caused by climate change, to facilitate estimates of the impact of climate change on various spheres of human activities and to compare eventual adaptation and risk mitigation strategies. The system integrates both physical climate system and economic models together with knowledge-based subsystem, which can help support proactive risk management. System structure and its main components are considered. Special attention is paid to climate risk assessment, management and hedging in the Arctic coastal areas.

scholarly journals On the First Passage time for Brownian Motion Subordinated by a Lévy Process

2009 ◽  
Vol 46 (1) ◽  
pp. 181-198 ◽  
Author(s):  
T. R. Hurd ◽  
A. Kuznetsov
Keyword(s):  
Brownian Motion ◽  
Approximation Scheme ◽  
First Passage Time ◽  
Gaussian Model ◽  
Passage Time ◽  
Financial Mathematics ◽  
First Passage ◽  
Financial Modeling ◽  
Motion Time ◽  
Normal Inverse Gaussian

In this paper we consider the class of Lévy processes that can be written as a Brownian motion time changed by an independent Lévy subordinator. Examples in this class include the variance-gamma (VG) model, the normal-inverse Gaussian model, and other processes popular in financial modeling. The question addressed is the precise relation between the standard first passage time and an alternative notion, which we call the first passage of the second kind, as suggested by Hurd (2007) and others. We are able to prove that the standard first passage time is the almost-sure limit of iterations of the first passage of the second kind. Many different problems arising in financial mathematics are posed as first passage problems, and motivated by this fact, we are led to consider the implications of the approximation scheme for fast numerical methods for computing first passage. We find that the generic form of the iteration can be competitive with other numerical techniques. In the particular case of the VG model, the scheme can be further refined to give very fast algorithms.

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