Present value of firm asset in case of correlated defaults: a generalized structural approach of credit risk

Lietuvos matematikos rinkinys ◽

10.15388/lmr.2007.18188 ◽

2007 ◽

Vol 47 ◽

Author(s):

Mantas Valužis

Keyword(s):

Credit Risk ◽

Financial Market ◽

Structural Approach ◽

Present Value ◽

Brownian Motions ◽

Value Of Firm ◽

Correlated Defaults ◽

Geometric Brownian Motions ◽

The Impact ◽

Implied Correlation

This article investigatesthe present value of a firm’s asset in the case of n \geq 2 correlateddefaults. The structural approach of credit risk is developed in the case when default boundaries follow geometric Brownian motions. Correlated defaults are defined by the implied correlation of Brownian motions. The operational risk and the risk of financial market changes are allowed in this model. Also, the impact of implied correlation to the present value of firm’s asset is shown numerically.

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Behavioural Present Value Defined as Fuzzy Number – a New Approach

Folia Oeconomica Stetinensia ◽

10.1515/foli-2015-0033 ◽

2015 ◽

Vol 15 (2) ◽

pp. 27-41 ◽

Cited By ~ 6

Author(s):

Krzysztof Piasecki ◽

Joanna Siwek

Keyword(s):

Financial Market ◽

Fuzzy Number ◽

Formal Model ◽

Market Equilibrium ◽

Present Value ◽

New Approach ◽

Behavioural Factors ◽

The Impact ◽

Numerical Case Study

Abstract The behavioural present value is defined as a fuzzy number assessed under the impact of chosen behavioural factors. The first formal model turned out to be burdened with some formal defects which are finally corrected in the presented article. In this way a new modified formal model of a behavioural present value is obtained. New model of the behavioural present value is used to explain the phenomenon of market equilibrium on the efficient financial market remaining in the state of financial imbalance. These considerations are illustrated by means of extensive numerical case study.

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PRICING OF CONTINGENT CLAIMS IN A TWO-DIMENSIONAL MODEL WITH RANDOM DIVIDENDS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024909005592 ◽

2009 ◽

Vol 12 (08) ◽

pp. 1091-1104 ◽

Cited By ~ 2

Author(s):

PAVEL V. GAPEEV ◽

MONIQUE JEANBLANC

Keyword(s):

Financial Market ◽

Diffusion Processes ◽

Partial Information ◽

Asset Price ◽

Contingent Claims ◽

Dimensional Model ◽

Random Drift ◽

Brownian Motions ◽

Risky Assets ◽

Geometric Brownian Motions

We study a model of a financial market in which two risky assets are paying dividends with rates changing their initial values to other constant ones when certain events occur. Such events are associated with the first times at which the value processes of issuing firms, modeled by geometric Brownian motions, fall to some prescribed levels. The asset price dynamics are described by exponential diffusion processes with random drift rates and independent driving Brownian motions. We derive closed form expressions for rational values of European contingent claims, under full and partial information.

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MAXIMIZING THE PROBABILITY OF A PERFECT HEDGE USING AN IMPERFECTLY CORRELATED INSTRUMENT

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024905003220 ◽

2005 ◽

Vol 08 (06) ◽

pp. 763-789 ◽

Cited By ~ 1

Author(s):

DAVID HOBSON ◽

JEREMY PENN

Keyword(s):

Time Horizon ◽

Fixed Time ◽

Contingent Claim ◽

Brownian Motions ◽

Quantile Hedging ◽

Terminal Wealth ◽

Hedging Problem ◽

Geometric Brownian Motions ◽

The Impact ◽

Concrete Model

Let Xϕ denote the trading wealth generated using a strategy ϕ, and let CT be a contingent claim which is not spanned by the traded assets. Consider the problem of finding the strategy which maximizes the probability of terminal wealth meeting or exceeding the claim value at some fixed time horizon, i.e., of finding [Formula: see text]. This problem is sometimes referred to as the quantile hedging problem. We consider the quantile hedging problem when the traded asset and the contingent claim are correlated geometric Brownian motions. This fits with several important examples. One of the benefits of working with such a concrete model is that although it is incomplete we can still do calculations. In particular, we can consider some detailed issues such as the impact of the timing at which information about CT is revealed.

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CREDIT DEFAULT SWAPS IN TWO-DIMENSIONAL MODELS WITH VARIOUS INFORMATIONS FLOWS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024920500107 ◽

2020 ◽

Vol 23 (02) ◽

pp. 2050010

Author(s):

PAVEL V. GAPEEV ◽

MONIQUE JEANBLANC

Keyword(s):

Financial Market ◽

Risk Model ◽

Credit Default Swaps ◽

Linear Combinations ◽

Brownian Motions ◽

No Arbitrage ◽

Default Intensity ◽

Credit Default ◽

Geometric Brownian Motions ◽

Credit Risk Model

We study a credit risk model of a financial market in which the dynamics of intensity rates of two default times are described by linear combinations of three independent geometric Brownian motions. The dynamics of two default-free risky asset prices are modeled by two geometric Brownian motions which are dependent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of both risk-free and risky credit default swaps given the reference filtration initially and progressively enlarged by the two default times. The accessible default-free reference filtration is generated by the standard Brownian motions driving the model.

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