New model prices collateralized financial derivatives considering bankruptcy laws.
problem Inaccurate pricing of collateralized financial derivatives due to neglecting collateral and credit risk.
method Developed a new model that incorporates both collateral posting and credit risk.
result Proper accounting for collateralization is crucial for accurate pricing of financial derivatives.
Extends multi-curve framework for fully collateralized markets.
problem Lack of a complete multi-currency setup with cross-currency basis.
method Develops a new formulation of currency funding spread and a discretization of the HJM framework.
result Better formulation of currency funding spread for general dependence.
The paper presents a pricing framework for cross-currency collateralized products, addressing funding costs and market uncertainties.
problem Funding costs and market uncertainties in cross-currency collateralized products.
method General derivation of arbitrage-free pricing framework, including impact of foreign currency funding.
result Pricing framework for cross-currency swaps under different market situations.
Develops a haircut model for non-cash collateral.
problem Addressing the need for accurate non-cash collateral valuation in shadow banking and OTC derivatives markets.
method Expands haircut definitions, uses a double-exponential jump-diffusion model, and solves for credit risk measurements.
result Computational results show potential for collateral agreements and regulatory capital calculations.
New model values CDS contracts considering multiple credit risks and collateralization.
problem Valuation of CDS contracts affected by multiple credit risks and collateralization.
method Developed a new model to value CDS contracts, considering default dependency and collateralization.
result Default dependency significantly impacts asset pricing and full collateralization does not eliminate counterparty risk.
Study multi-currency markets with multiple interest rates and collateral.
problem Characterize absence of arbitrage in a multi-currency market.
method Generalize results from Bielecki and Rutkowski (2015) to a multi-currency framework, linking with Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). Characterize absence of arbitrage without collateral, then study collateralization schemes under various conventions.
result Complete study of absence of arbitrage and pricing in multi-currency markets with multiple interest rates and collateral.
Study confirms eurozone interbank market stability but finds higher collateral reuse.
problem Analyzing eurozone interbank market behavior and stability.
method Examined secured transactions data from ECB, tested stylized facts, measured network properties.
result Observed higher collateral reuse and network symmetry compared to unsecured markets.
The paper develops a new discount rate for derivatives using imperfect securities as collateral.
problem Inconsistent and non-observable collateral rates in derivatives markets.
method Synthesizes effects of imperfect collateral into a new discount rate, employs break-even repo formulae, and uses linear programming for optimization.
result Liquidity value adjustment (LVA) can be significant for long-term derivatives portfolios.
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modellin…
The paper analyzes credit valuation adjustments under collateralized interest rate derivatives, introducing a new dynamics for multiple interest rate curves.
problem The impact of multiple interest rate curves on credit valuation adjustments under collateralized models.
method Formulated a consistent dynamics for multiple interest rate curves, including the margin period of risk and stochastic basis for wrong-way risk analysis.
result Numerical results confirm the importance of stochastic basis for proper wrong-way risk analysis of sensitive products like basis swaps.
Over-the-counter derivatives have contributed significantly to the effectiveness and efficiency of the international financial system but also entail significant counterparty credit risk. Collateralization is one of the most important and widespread credit risk mitigation techniques used in derivatives transactions. Ho…
The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party c…
Abstract framework for cross-currency interest rate contracts.
problem Handling cross-currency markets with collateral and incompleteness.
method Developed a general HJM framework for abstract market indices.
result Enabled simultaneous description of multiple currency interest rate products.
Changes in collateralization have been implicated in significant default (or near-default) events during the financial crisis, most notably with AIG. We have developed a framework for quantifying this effect based on moving between Merton-type and Black-Cox-type structural default models. Our framework leads to a singl…
This study updates a model for Mexican interest rate swaps post-crisis.
problem Post-crisis divergence of interest rates and new regulatory requirements.
method Used Fujii et al. 2010b model with collateral currencies USD, EUR, MXN.
result Validated model for Mexican interest rate derivatives with collateral currencies.
Investors trade based on shifting prices, leading to market inefficiencies.
problem Market inefficiencies due to trading behavior and financial dynamics.
method Analyzes trading strategies and market dynamics.
result Arbitrage opportunities arise from concentrated ownership and low collateral requirements.
An active margin system for margin loans is proposed for Chinese margin lending market, which uses cash and randomly selected stock as collateral. The conditional probability of negative return(CPNR) after a forced sale of securities from under-margined account in a falling market is used to measure the risk faced by t…
Model explains deleveraging risks in non-custodial stablecoins.
problem Deleveraging risks in non-custodial stablecoins during market crises.
method Developed a stochastic model incorporating speculators' profit optimization and collateral liquidation costs.
result Identified deflationary deleveraging spirals and higher price variance in unstable domains.
Research proposes a decentralized invoice discounting system using Kelly criterion.
problem Persistent funding gap for SMEs and inefficiencies in traditional factoring.
method Automated Market Maker (AMM) with Kelly criterion for premium calculation.
result Resilient decentralized system with optimal profit distribution policies.
New PFL method addresses counterparty risk challenges.
problem Challenges with PFE for counterparty limits.
method Introducing PFL combining ES and LGD, and variants aPFL and paPFL.
result PFL and variants provide a better measure of counterparty risk.
This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fi…
The paper addresses how banks adjust for capital and funding costs in incomplete markets.
problem Banks adjust for capital and funding costs in derivative pricing, but this conflicts with complete markets.
method Develops a mathematical formalism for managing derivative portfolios in incomplete markets.
result Optimal strategies for retained earnings are found to ensure sustainable dividend policies.
A framework for fair derivative contract pricing and risk-sharing between parties with funding differences.
problem Price asymmetry due to funding differences in bilateral contracts.
method Defines a negotiation problem that maximizes the sum of utilities for two parties, deriving optimal prices and collateral.
result Optimal negotiation price and collateral can be used to interpret margin requirements.
Study how network structure affects collateral dynamics in banking systems.
problem Effects of network structure on collateral volume and hoarding in banking systems.
method Simple model of bank interactions via repo contracts and rehypothecation.
result Network structures with concentrated collateral flows are more exposed to large hoarding cascades.
This study examines the collateral choice option and its valuation and hedging.
problem Non-zero collateral basis spreads impact asset valuation and require complex modeling.
method Develops a stochastic valuation model for the collateral choice option and proposes hedging strategies.
result The stochastic model attributes risks to all involved collateral currencies, unlike the deterministic model.
Optimizes hedge ratio for delta-neutral liquidity positions in AMMs.
problem Balancing price exposure and liquidation risk in borrowing-funded delta-neutral positions.
method Model token prices as correlated geometric Brownian motions, derive optimal hedge ratio maximizing risk-adjusted return subject to liquidation probability constraint.
result Optimal hedge ratio h** = min(h*, h_bar(alpha)) lies between 50% and 70% for typical DeFi lending conditions.
Develops a new model for collateral choice options under stochastic rates.
problem Challenges in quantifying the value of collateral choice options under stochastic rates.
method Develops a scalable and stable stochastic model of collateral spreads under conditional independence, using a common factor approximation.
result Second order model yields accurate results for the value of the collateral choice option.
Study on nonlinear valuation equations for credit risk, collateral, and funding costs, proving existence, uniqueness, and invariance.
problem Nonlinear valuation equations for credit risk, collateral, and funding costs.
method Analyzes conditions for existence, uniqueness, and invariance of nonlinear valuation equations, including PDEs and FBSDEs.
result Existence and uniqueness of solutions for nonlinear valuation equations, with invariance of the final equations to the risk-free rate.
Study pricing derivatives in nonlinear models with market frictions.
problem No-arbitrage pricing of derivatives in nonlinear market models with funding costs, credit risk, and trading frictions.
method Extend nonlinear pricing approach by incorporating funding costs, credit risk, and trading frictions.
result Developed a comprehensive framework for pricing derivatives in nonlinear market models.
Modeling bank portfolio risk under climate transition impacts.
problem Evaluating risk measures for a bank's collateralized loans in a climate transition economy.
method Developed an end-to-end modeling framework using stochastic processes and dynamic macroeconomic variables.
result Derived expressions for risk measures as functions of climate transition parameters.
This study examines liquidation risks in DeFi lending markets.
problem Liquidity risks in decentralized finance lending protocols.
method Quantitative analysis of liquidation data from four major DeFi platforms.
result Current liquidation mechanisms incentivize liquidators but lead to excessive collateral sales.
Our previous results are extended to the case of the margin account, which may depend on the contract's value for the hedger and/or the counterparty. The present work generalizes also the papers by Bergman (1995), Mercurio (2013) and Piterbarg (2010). Using the comparison theorems for BSDEs, we derive inequalities for …
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of c…
Study on collateral currency impact in differential swaps valuation.
problem Impact of collateral currency on differential swap valuation and risk management.
method Replication using futures, explicit pricing and hedging strategies.
result Choice of collateral currency can introduce additional risk exposures.
Axient creates a blockchain protocol for managing leveraged event markets, separating roles and formalizing capital management.
problem Managing credit and losses in leveraged event markets on a blockchain.
method Develops a venue-agnostic on-chain credit architecture, formalizing roles and capital management.
result Establishes a balanced accounting system, settlement-confirmed debt priority, and loss-allocation mechanisms.
We review the main changes in the interbank market after the financial crisis started in August 2007. In particular, we focus on the fixed income market and we analyse the most relevant empirical evidences regarding the divergence of the existing basis between interbank rates with different tenor, such as Libor and OIS…
This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipović, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite dimensional Lévy process. The contribution of this work is twofold: we provide condit…
Debt-financed collateral in DeFi increases stability risks.
problem Financial stability risks in DeFi ecosystems due to debt-financed collateral.
method Categorization and classification algorithm to measure debt-financed collateral.
result Wide-spread use of stablecoins as debt-financed collateral increases financial stability risks.
In this paper we describe how to include funding and margining costs into a risk-neutral pricing framework for counterparty credit risk. We consider realistic settings and we include in our models the common market practices suggested by the ISDA documentation without assuming restrictive constraints on margining proce…
Extends pricing theory for collateralized derivatives to include jumps and dividends.
problem Pricing collateralized derivatives with jumps and dividends.
method Extends No-Arbitrage theory to semimartingales, deriving pricing, dynamics, and forward prices.
result Derives pricing, dynamics, and forward prices of collateralized derivatives.
Study examines crypto-backed stable derivatives in DeFi, focusing on DAI.
problem Stability of crypto-backed stablecoins in DeFi.
method Introduced a belief parameter to simulate DAI, proposed a mathematical model, analyzed risk factors.
result Belief parameter improves simulation of DAI price stability.
This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize…
The paper tackles dynamic collateral control for spot-perpetual basis trading in decentralized finance.
problem Dynamic control of collateral in spot-perpetual basis trading in decentralized finance.
method Solves a static control problem and derives an asymmetric dynamic extension, validated with live execution.
result The dynamic control approach provides a more robust operating benchmark and shows significant rebalancing effects.
Simple quantifier predicts financial market instability.
problem Predicting financial market instability and risk.
method Combining Information Theory and graph concepts to analyze return rate series.
result Simple quantifier highly correlated with global financial instability periods.
We explain a persistent cost-of-carry spread in EUA market and suggest ECB policy change.
problem Persistent cost-of-carry spread in EUA market.
method Cointegration analysis of EUA spread with credit spread and risk-free rate.
result Cointegration found between EUA spread, credit spread, and risk-free rate.
Margin system for margin loans using cash and stock as collateral is considered in this paper, which is the line of defence for brokers against risk associated with margin trading. The conditional probability of negative return is used as risk measure, and a recursive algorithm is proposed to realize this measure under…
The paper develops a new formula for financial pricing under multiple interest rates and collateralization.
problem Financial pricing under multiple interest rates and collateralization.
method Derives a change of measure formula for recursive conditional expectations in a jump-diffusion setting.
result Generalizes the change of numéraire technique for multiple interest rates and collateralization.
This paper designs a new on-chain option that amortizes perpetual options for blockchain environments.
problem No equivalent standard for on-chain options exists, leading to high-frequency oracles and liquidation engines failures.
method Develops an amortizing perpetual option contract tailored to blockchain constraints, introducing a decentralized market framework.
result Demonstrates that the new contract functions as a risk primitive for DeFi, enabling applications like endogenous collateralization and de-peg insurance.