Modeling liquidation risk with occupation times

2016 ◽  
Vol 03 (04) ◽  
pp. 1650028 ◽  
Author(s):  
Roman N. Makarov
Keyword(s):  
Brownian Motion ◽  
Structural Model ◽  
Cox Model ◽  
Analytical Formula ◽  
Diffusion Models ◽  
Geometric Brownian Motion ◽  
Occupation Times ◽  
Proposed Model ◽  
Asset Value ◽  
Limiting Case

In this paper, we develop a new structural model that allows for a distinction between default and liquidation to be made. Default occurs when firm’s asset value process crosses a bankruptcy barrier. Here, we do not assume that default immediately triggers liquidation. Instead, the firm is allowed to continue operating even if it is in default. Liquidation is triggered as soon as the firm’s asset value has cumulatively spent a prespecified amount of time below the default barrier or has dropped below the liquidation barrier. The proposed model includes the Black–Cox model as a limiting case. A semi-analytical formula of the liquidation probability is derived for the case where firm’s asset value follows a geometric Brownian motion. Nonlinear volatility diffusion models are discussed as well.

scholarly journals Research on Systemic Risk of the Turkish Banking Industry Based on a Systemic Risk Measurement Framework of the Fractional Brownian Motion

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hong Fan ◽  
Lingli Feng ◽  
Ruoyu Zhou
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Financial Market ◽  
Systemic Risk ◽  
Banking System ◽  
Risk Measurement ◽  
Geometric Brownian Motion ◽  
Hurst Index ◽  
Measurement Framework ◽  
Asset Value

Since the 2008 financial crisis, it is an important issue to assess the systemic risk of banks, but there is a lack of research on the assessment of the systemic risk of Turkey’s financial system. In addition, geometric Brownian motion is used in most of the assessment frameworks of systemic risk under the normal financial market state, while the Turkish financial market has the situation of spike and thick tail. Therefore, this paper proposes a fractional Brownian motion measurement framework of systemic risk to study the systemic risk of the Turkish financial system. Firstly, this paper uses the data of 11 Turkish listed banks from 2014 to 2019 to conduct a normality test and demonstrate that its market has the characteristics of a fractal market; that is, there is a spike and thick tail distribution phenomenon in the stock price trend. Then, this paper proposes a fractional Brownian motion systemic risk measurement framework (fBSM). Based on the proposed theoretical framework and the actual data of Turkish listed banks from 2014 to 2019, a dynamically evolving Turkish banking network system is constructed to measure the systemic risk in the Turkish banking system. The research results find that the systemic risk is the highest in 2017, which then improved and gradually recovered. In addition, when analyzing the sensitivity of the Hurst index, it shows that with the increase in Hurst index, the Hurst index elasticity of Turkish banks’ asset value increases gradually and the asset value also increases continuously. Hence, the Hurst index has a greater impact on asset value. Therefore, the measurement framework of systemic risk based on the fBSM can better monitor the systemic risk than the traditional geometric Brownian motion in the Turkish banking system.

scholarly journals Valuasi One Period Coupon Bond dengan Aset Mengikuti Model Geometric Brownian Motion with Jump Diffusion

2021 ◽  
Vol 3 (2) ◽  
pp. 94
Author(s):  
Meiliawati Aniska ◽  
Di Asih I Maruddani ◽  
Suparti Suparti
Keyword(s):  
Brownian Motion ◽  
Extreme Values ◽  
Jump Diffusion ◽  
Geometric Brownian Motion ◽  
Default Probability ◽  
Corporate Bond ◽  
Extreme Condition ◽  
Asset Value ◽  
Maturity Date ◽  
Coupon Bond

<p>One period coupon bond gives coupon once a bond life together with the principal debt. If the firm’s asset value on maturity date is insufficient to meet the debtholder’s claim, then the firm is stated as default. The well-known model for predicting default probability is KMV-Merton model. Under this model, it is assumed that the return on the firm’s assets is distributed normally and their behaviour can be described with the Geometric Brownian Motion (GBM) formula. In practice, most of the financial data tend to have heavy-tailed distribution. It indicates that the data contain some extreme values. GBM with Jump is a popular model to capture the extreme values. In this paper, we evaluate a corporate bond which has some extreme condition in their asset value and predicts the default probability in the maturity date. Empirical studies were carried out on bond that is issued by CIMB Niaga Bank that has a payment due in November 2020. The result shows that modelling the asset value is more appropriate by using GBM with Jump rather than GBM modelling. Estimation to CIMB Niaga Bank equity in November 2020 is IDR 246,533,573,844,229.00. The liability of this company is IDR 4,205,751,155,771.00. The prediction of CIMB Niaga Bank default probability is 1.065812 ´ 10<sup>-8</sup> at the bond maturity. It indicates that the company is considered capable of fulfilling the obligations at the maturity date.</p><p><strong>Keywords: </strong>jump diffusion, extreme value, probability default, equity, liability</p>

scholarly journals Geometric Brownian motion with affine drift and its time-integral

2021 ◽  
Vol 395 ◽  
pp. 125874
Author(s):  
Runhuan Feng ◽  
Pingping Jiang ◽  
Hans Volkmer
Keyword(s):  
Brownian Motion ◽  
Geometric Brownian Motion ◽  
Time Integral

THE FEYNMAN–KAC FORMULA AND PRICING OCCUPATION TIME DERIVATIVES

1999 ◽  
Vol 02 (02) ◽  
pp. 153-178 ◽  
Author(s):  
JULIEN-N. HUGONNIER
Keyword(s):  
Brownian Motion ◽  
Time Derivative ◽  
Occupation Time ◽  
Barrier Options ◽  
Occupation Times

In this paper, we undertake a study of occupation time derivatives that is derivatives for which the pay-off is contingent on both the terminal asset's price and one of its occupation times. To this end we use a formula of M. Kac to compute the joint law of Brownian motion and one of its occupation times. General pricing formulas for occupation time derivatives are established and it is shown that any occupation time derivative can be continuously hedged by a controlled portfolio of the basic securities. We further study some examples of interest including cumulative barrier options and discuss some numerical implementations.

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