Credit risk with asymmetric information and a switching default threshold

Imke Redeker; Ralf Wunderlich

Home/Archive/arXiv

arXiv · 1910.14413

Credit risk with asymmetric information and a switching default threshold

Imke Redeker·Ralf Wunderlich

View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the impact of available information on the estimation of the default probability within a generalized structural model for credit risk. The traditional structural model where default is triggered when the value of the firm's asset falls below a constant threshold is extended by relaxing the assumption of a constant default threshold. The default threshold at which the firm is liquidated is modeled as a random variable whose value is chosen by the management of the firm and dynamically adjusted to account for changes in the economy or the appointment of a new firm management. Investors on the market have no access to the value of the threshold and only anticipate the distribution of the threshold. We distinguish different information levels on the firm's assets and derive explicit formulas for the conditional default probability given these information levels. Numerical results indicate that the information level has a considerable impact on the estimation of the default probability and the associated credit yield spread.

Explore related subjects

q-fin.PR

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Imke Redeker, Ralf Wunderlich. 2019-11-17. Credit risk with asymmetric information and a switching default threshold. https://arxiv.org/abs/1910.14413

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Yet another asymptotic formula for implied volatility

We derive a first-order representation of Black-Scholes implied variance in a continuous local martingale model. Total implied variance is the conditional expectation of the quadratic variation of the log price given its terminal value, up to a smaller-order term, for bounded standardized log-strikes. The framework incorporates small volatility-of-volatility, fast mean-reverting, and short-maturity asymptotics.

q-fin.PR↗

arXiv2026

(Early) AI Compute Asset Pricing

Compute (computing power) is a scarce, capital-intensive input at the center of the AI economy. Compute capital expenditure and service flow already exceed 1% of U.S. GDP and are growing rapidly. The price of compute reflects uncertainty over AI adoption. The announced launch of compute futures turns this uncertainty into a tradable risk, raising questions on the pricing of a new asset class. We provide an early asset-pricing framework for compute. We begin by discussing the underlying compute rental market and its indexation. We then turn to pricing: 1) direct no-arbitrage links between futures prices and current spot prices fail due to the non-storable nature of compute, 2) synthetic futures prices from existing term rental contracts are likely upper bounds on true futures prices and, 3) upon financialization, futures prices will be investors' expectations of spot prices at expiration net of a risk premium. Using synthetic futures as stand-ins before the compute futures market launches, we construct the first compute futures return panel sorted by GPU generation and maturity. Our preliminary evidence is consistent with a positive compute risk premium, suggesting hedging pressure on the part of compute providers.

q-fin.PR↗

arXiv2026

The existence of optimal bang-bang controls for GMxB contracts

A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the admissible set. Often, such contracts specify that the holder exert control at a finite number of deterministic times. The existence of an optimal bang-bang control, an optimal control taking on only a finite subset of values from the admissible set, is a common assumption in the literature. In this case, the numerical complexity of searching for an optimal control is considerably reduced. However, no rigorous treatment as to when an optimal bang-bang control exists is present in the literature. We provide the reader with a bang-bang principle from which the existence of such a control can be established for contracts satisfying some simple conditions. The bang-bang principle relies on the convexity and monotonicity of the solution and is developed using basic results in convex analysis and parabolic partial differential equations. We show that a guaranteed lifelong withdrawal benefit (GLWB) contract admits an optimal bang-bang control. In particular, we find that the holder of a GLWB can maximize a writer's losses by only ever performing nonwithdrawal, withdrawal at exactly the contract rate, or full surrender. We demonstrate that the related guaranteed minimum withdrawal benefit contract is not convexity preserving, and hence does not satisfy the bang-bang principle other than in certain degenerate cases.

q-fin.PR↗