Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2404.05372

The PEAL Method: a mathematical framework to streamline securitization structuring

Andrea Pinto·Antonio Scala
View original source ↗Read source document ↗Export metadata ↓

Abstract

Securitization is a financial process where the cash flows of income-generating assets are sold to institutional investors as securities, liquidating illiquid assets. This practice presents persistent challenges due to the absence of a comprehensive mathematical framework for structuring asset-backed securities. While existing literature provides technical analysis of credit risk modeling, there remains a need for a definitive framework detailing the allocation of the inbound cash flows to the outbound positions. To fill this gap, we introduce the PEAL Method: a 10-step mathematical framework to streamline the securitization structuring across all time periods. The PEAL Method offers a rigorous and versatile approach, allowing practitioners to structure various types of securitizations, including those with complex vertical positions. By employing standardized equations, it facilitates the delineation of payment priorities and enhances risk characterization for both the asset and the liability sides throughout the securitization life cycle. In addition to its technical contributions, the PEAL Method aims to elevate industry standards by addressing longstanding challenges in securitization. By providing detailed information to investors and enabling transparent risk profile comparisons, it promotes market transparency and enables stronger regulatory oversight. In summary, the PEAL Method represents a significant advancement in securitization literature, offering a standardized framework for precision and efficiency in structuring transactions. Its adoption has the potential to drive innovation and enhance risk management practices in the securitization market.

Explore related subjects

q-fin.RMq-fin.GNq-fin.PM

Keep this discovery

BibTeXRIS

Andrea Pinto, Antonio Scala. 2024-04-08. The PEAL Method: a mathematical framework to streamline securitization structuring. https://arxiv.org/abs/2404.05372

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

KEEP EXPLORING

Related papers

arXiv2026

Simplifying Cyber Cat(astrophe)s with Cyber Kittens: Power Law Plausibility for Cyber Insurance Risks

Cyber insurance requires accurate modeling of worst-case catastrophic (cat) events, but the field lacks robust quantitative approaches for estimating upper-bound losses. Building on a recent dataset of 24 cyber cat events over 30 years, this work tests whether cyber economic losses follow a power law distribution. We analyze "cyber kittens" - sub-1B USD events distinguished from cat events (1B+ USD) only by magnitude - extracted via LLM from cyber insurance claims data (2020-2024). Using victim count (weighted by claim year) as a proxy for economic loss, we link kitten-sized events to known cat events to estimate losses. The kitten distribution proved consistent with the cat dataset, and power laws were statistically plausible: each order-of-magnitude increase in event size corresponds to a 5-7x drop in probability. Extrapolating, an event 100x the largest 2020-2024 cat event is expected roughly every 206 years, translating to 100-250B USD in losses - catastrophic, but not extraordinary relative to other insurance lines.

q-fin.RM↗
arXiv2026

Pricing the DeFi Tail: Do Protocols or Depositors Price Operational Risk?

Similar to banks, DeFi protocols expose depositors to operational risk (USD 9.45 billion across 1,075 events since 2020). Unlike banks, they are not required to hold capital against it. A protocol may maintain a buffer voluntarily. Absent one, the risk falls on the depositor, who should then demand a risk premium in the supply yield. I quantify the underlying tail on one benchmark, a per-sector Basel loss-distribution approach fitted to a new operational risk event dataset, and test both margins against it. Tails in the four core sectors are no heavier than the Moscadelli banking band $[0.85, 1.39]$. Bridge, Derivatives, and the residual Other sector exhibit cyber-loss-level tails ($\hat\xi \approx 1.6$), with point estimates past the infinite-mean boundary. The Lending tail implies a $\mathrm{VaR}_{99.9}$ capital buffer of 18% of TVL and of the ten largest Lending venues, the four holding a buffer cover on average 5% of it. Under market discipline, depositors should demand a higher yield in compensation where a venue does not maintain a buffer. I find that venues without a buffer pay a higher premium than those with (a 125-bps gap in medians): evidence the market discriminates in the right direction. However, the premium falls far short of an adequately priced tail. This unpriced tail falls disproportionately on the retail depositor, who sees only the posted rate but lacks the information and skills to price it. Because these products are not bank-regulated, I recommend disclosure over capital mandates: protocols, and any service providers that front access to it, should publish standardized losses, existing capital buffers and tail coverage.

q-fin.RM↗
arXiv2026

Illiquidity at Risk

Market efficiency relies fundamentally on stable liquidity. Consequently, forecasting liquidity dynamics is a priority for both investors and regulators. We introduce a new tail-risk metric, Illiquidity-at-Risk (IlliQaR), designed to quantify the magnitude of extreme liquidity dry-ups. Relying upon the realized Amihud (a precise illiquidity measurement derived from high-frequency data as the ratio of realized volatility to trading volume) we assess the predictive power of various linear and non-linear econometric models, with a specific focus on the impact of discontinuous jump components. Accounting for these jumps is essential for achieving accurate probability coverage and better IlliQaR predictions during periods of systemic stress, where standard continuous models systematically underestimate the severity of liquidity evaporation. Our empirical analysis, encompassing the S&P 500 index and a cross-section of 25 large U.S. equities, demonstrates that incorporating jumps significantly improves forecasts of illiquidity. Our results suggest that individual stock IlliQaR violations often cluster during periods of S&P 500 liquidity stress. This indicates that Illiquidity at Risk is not just a localized concern but a systemic one, where the main index acts as a leading indicator for extreme dry-ups in individual stock liquidity.

q-fin.RM↗