Valuation of the Prepayment Option of a Perpetual Corporate Loan

Abstract and Applied Analysis ◽

10.1155/2013/960789 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Timothee Papin ◽

Gabriel Turinici

Keyword(s):

Credit Quality ◽

Default Intensity ◽

Liquidity Cost ◽

Funding Cost ◽

Liquidity Crisis ◽

Prepayment Option ◽

Cir Process ◽

Corporate Loan ◽

Cost Regime

We investigate in this paper a perpetual prepayment option related to a corporate loan. The default intensity of the firm is supposed to follow a CIR process. We assume that the contractual margin of the loan is defined by the credit quality of the borrower and the liquidity cost that reflects the funding cost of the bank. Two frameworks are discussed: firstly a loan margin without liquidity cost and secondly a multiregime framework with a liquidity cost dependent on the regime. The prepayment option needs specific attention as the payoff itself is an implicit function of the parameters of the problem and of the dynamics. In the unique regime case, we establish quasianalytic formulas for the payoff of the option; in both cases we give a verification result that allows for the computation of the price of the option. Numerical results that implement the findings are also presented and are completely consistent with the theory; it is seen that when liquidity parameters are very different (i.e., when a liquidity crisis occurs) in the high liquidity cost regime, the exercise domain may entirely disappear, meaning that it is not optimal for the borrower to prepay during such a liquidity crisis. The method allows for quantification and interpretation of these findings.

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PREPAYMENT OPTION OF A PERPETUAL CORPORATE LOAN: THE IMPACT OF THE FUNDING COSTS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024914500289 ◽

2014 ◽

Vol 17 (04) ◽

pp. 1450028 ◽

Cited By ~ 3

Author(s):

TIMOTHEE PAPIN ◽

GABRIEL TURINICI

Keyword(s):

Markov Chain ◽

Continuous Time ◽

Two Dimensional ◽

Implicit Function ◽

Discrete State ◽

Default Intensity ◽

Constrained Minimization Problem ◽

Prepayment Option ◽

Corporate Loan ◽

The Impact

We investigate in this paper a perpetual prepayment option related to a corporate loan. The short interest rate and default intensity of the firm are supposed to follow Cox–Ingersoll–Ross (CIR) processes. A liquidity term that represents the funding costs of the bank is introduced and modeled as a continuous time discrete state Markov chain. The prepayment option needs specific attention as the payoff itself is a derivative product and thus an implicit function of the parameters of the problem and of the dynamics. We prove verification results that allows to certify the geometry of the exercise region and compute the price of the option. We show moreover that the price is the solution of a constrained minimization problem and propose a numerical algorithm building on this result. The algorithm is implemented in a two-dimensional code and several examples are considered. It is found that the impact of the prepayment option on the loan value is not to be neglected and should be used to assess the risks related to client prepayment. Moreover, the Markov chain liquidity model is seen to describe more accurately clients' prepayment behavior than a model with constant liquidity.

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The Decline in Credit Quality of New-Issue Junk Bonds

Financial Analysts Journal ◽

10.2469/faj.v46.n5.53 ◽

1990 ◽

Vol 46 (5) ◽

pp. 53-62 ◽

Cited By ~ 8

Author(s):

Barrie A. Wigmore

Keyword(s):

Junk Bonds ◽

Credit Quality

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A DYNAMIC MODEL OF CENTRAL COUNTERPARTY RISK

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024918500504 ◽

2018 ◽

Vol 21 (08) ◽

pp. 1850050

Author(s):

TOMASZ R. BIELECKI ◽

IGOR CIALENCO ◽

SHIBI FENG

Keyword(s):

Dynamic Model ◽

Numerical Study ◽

Risk Measures ◽

Structure Model ◽

Counterparty Risk ◽

Dynamic Risk Measures ◽

Credit Quality ◽

Dynamic Risk ◽

Risk Sensitive

We introduce a dynamic model of the default waterfall of derivatives central counterparties and propose a risk sensitive method for sizing the initial margin, and the default fund and its allocation among clearing members. Using a Markovian structure model of joint credit migrations, our evaluation of the default fund takes into account the joint credit quality of clearing members as they evolve over time. Another important aspect of the proposed methodology is the use of the time consistent dynamic risk measures for computation of the initial margin and the default fund. We carry out a comprehensive numerical study, where, in particular, we analyze the advantages of the proposed methodology and its comparison with the currently prevailing methods used in industry.

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Macro Stress Testing of Indian Bank Groups

Margin The Journal of Applied Economic Research ◽

10.1177/0973801017722267 ◽

2017 ◽

Vol 11 (4) ◽

pp. 375-403

Author(s):

Pami Dua ◽

Hema Kapur

Keyword(s):

Exchange Rate ◽

Interest Rate ◽

Private Sector ◽

Stress Testing ◽

Inflation Rate ◽

Output Growth ◽

Foreign Banks ◽

Credit Quality ◽

The Impact

This study examines how various bank groups operating in India have fared macro stress events and conduct macro stress testing (MST) to trace the impact of certain macroeconomic stress scenarios on the credit quality of five Indian bank groups, that is, the State Bank of India (SBI) and its associates (SBGs), nationalised banks (NBs), old private sector banks (OPBs), new private sector banks (NPBs) and foreign banks (FBs), using panel data from 1997 to 2014. Credit quality is modelled as a function of both macroeconomic variables (output growth, interest rate, inflation rate and exchange rate) and idiosyncratic variables (profitability and size indicator of bank business activity). The model is estimated by employing a panel cointegration approach, and the impact of adverse scenarios on the estimated credit quality is computed. Empirical findings show that credit quality is pro-cyclical in nature and rises in the event of a slowdown in the economy. In general, the credit quality of Indian bank groups is found to be inversely and significantly related to the economy’s growth rate, inflation rate, exchange rate and profits of banks and positively and significantly related to the interest rate. Shock analysis also reveals that a downturn in the economy through certain adverse scenarios has a significant adverse impact on the credit quality. The shocks are quickly propagated across banks with substantial heterogeneities present in different bank groups. Thus, macroeconomic policy measures promoting growth with price stability are expected to impact credit quality positively. Further, measures at the bank level can improve credit quality by enhancing their profitability. JEL Classifications: C32, C58, E170, G21

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A primer on counterparty valuation adjustments in South Africa

South African Journal of Economic and Management Sciences ◽

10.4102/sajems.v17i5.648 ◽

2014 ◽

Vol 17 (5) ◽

pp. 584-600

Author(s):

Gary Wayne Van Vuuren ◽

Ja'nel Esterhuysen

Keyword(s):

South Africa ◽

Financial Crisis ◽

Credit Risk ◽

South African ◽

Credit Spreads ◽

Basel Iii ◽

Credit Quality ◽

Counterparty Credit Risk ◽

Market Variables

Counterparty valuation adjustment (CVA) risk accounts for losses due to the deterioration in credit quality of derivative counterparties with large credit spreads. Of the losses attributed to counterparty credit risk incurred during the financial crisis of 2008-9 were due to CVA risk; the remaining third were due to actual defaults. Regulatory authorities have acknowledged and included this risk in the new Basel III rules. The capital implications of CVA risk in the South African milieu are explored, as well as the sensitivity of CVA risk components to market variables. Proposed methodologies for calculating changes in CVA are found to be unstable and unreliable at high average spread levels.

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Uniform approximation of the Cox-Ingersoll-Ross process

Advances in Applied Probability ◽

10.1239/aap/1449859803 ◽

2015 ◽

Vol 47 (4) ◽

pp. 1132-1156 ◽

Cited By ~ 3

Author(s):

Grigori N. Milstein ◽

John Schoenmakers

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Wiener Process ◽

Point Of View ◽

First Passage ◽

Cir Process ◽

Quality Of Approximation ◽

Time Grid ◽

Passage Times

The Doss-Sussmann (DS) approach is used for uniform simulation of the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows us to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) depending on realizations of a Wiener process involved. By simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving the ODE, we uniformly approximate the trajectories of the CIR process. In this respect special attention is payed to simulation of trajectories near 0. From a conceptual point of view the proposed method gives a better quality of approximation (from a pathwise point of view) than standard, even exact, simulation of the stochastic differential equation at some deterministic time grid.

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