MODELING LIFETIME EXPECTED CREDIT LOSSES ON BANK LOANS

The guidelines of various Accounting Standards require every financial institution to measure lifetime expected credit losses (LECLs) on every instrument, and to determine at each reporting date if there has been a significant increase in credit risk since its inception. This paper models LECLs on bank loans given to a firm that has promised to repay debt at multiple points over the lifetime of the contract. The LECL can be written as a sum of ECLs (estimated at reporting date) incurred at debt repayment times. The ECL at any debt repayment time can be written as a product of the probability of default (PD), the expected value of loss given default and the exposure at default. We derive a stochastic dynamical equation for the value of the firm’s asset by incorporating the dynamics of the factors. Also, we show how the LECL and the term structure of the PD can be estimated by solving a Black–Scholes–Merton like partial differential equation. As an illustration, we present the numerical results for the various credit loss indicators of a fictitious firm when the dynamics of the short-term interest rate is characterized by a Cox–Ingersoll–Ross mean-reverting process.

PORTFOLIO INSURANCE UNDER ROUGH VOLATILITY AND VOLTERRA PROCESSES

Affine Volterra processes have gained more and more interest in recent years. In particular, this class of processes generalizes the classical Heston model and the more recent rough Heston model. The aim of this work is hence to revisit and generalize the constant proportion portfolio insurance (CPPI) under affine Volterra processes. Indeed, existing simulation-based methods for CPPI do not apply easily to this class of processes. We instead propose an approach based on the characteristic function of the log-cushion which appears to be more consistent, stable and particularly efficient in the case of saffine Volterra processes compared with the existing simulation techniques. Using such approach, we describe in this paper several properties of CPPI which naturally result from the form of the log-cushion’s characteristic function under affine Volterra processes. This allows to consider more realistic dynamics for the underlying risky asset in the context of CPPI and hence build portfolio strategies that are more consistent with financial data. In particular, we address the case of the rough Heston model, known to be extremely consistent with past data of volatility. By providing a new estimation procedure for its parameters based on the PMCMC algorithm, we manage to study more accurately the true properties of such CPPI strategy and to better handle the risk associated with it.

DYNAMIC PROBABILISTIC FORECASTING WITH UNCERTAINTY

In this paper, we introduce a dynamical model for the time evolution of probability density functions incorporating uncertainty in the parameters. The uncertainty follows stochastic processes, thereby defining a new class of stochastic processes with values in the space of probability densities. The purpose is to quantify uncertainty that can be used for probabilistic forecasting. Starting from a set of traded prices of equity indices, we do some empirical studies. We apply our dynamic probabilistic forecasting to option pricing, where our proposed notion of model uncertainty reduces to uncertainty on future volatility. A distribution of option prices follows, reflecting the uncertainty on the distribution of the underlying prices. We associate measures of model uncertainty of prices in the sense of Cont.

DEFAULTABLE TERM STRUCTURES DRIVEN BY SEMIMARTINGALES

In this paper, we consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general semimartingale. Second, the Heath–Jarrow–Morton (HJM) approach is extended with an additional component capturing those future jumps in the term structure which are visible from the current time. Third, the associated recovery scheme is as general as possible, it is only assumed to be nonincreasing. In this general setting, we derive generalized drift conditions which characterize when a given measure is a local martingale measure, thus yielding no asymptotic free lunch with vanishing risk (NAFLVR), the right notion for this large financial market to be free of arbitrage.

THE AFFINE RATIONAL POTENTIAL MODEL

We develop a class of rational term structure models in the framework of the potential approach based upon a family of positive supermartingales that are driven by an affine Markov process. These models generally feature nonnegative interest rates and analytic pricing formulae for zero bonds, caps, swaptions, and European currency options, even in the presence of multiple factors. Moreover, in a model specification, the short rate stays near the zero lower bound for an extended period.