Risk

This post outlines a platform architecture designed to model the impact of a hybrid risk registry (qualitative and quantitative risks) on an oil company’s key financial KPIs like EBITDA and Cash Flow on a monthly basis. The design emphasizes modularity, auditability, and the integration of expert judgment with stochastic simulation. 1. Core Principles & Objectives Single Source of Truth: Establish a centralized, versioned Risk Registry for all identified risks. Hybrid Modeling: Natively support both quantitative risks (modeled with probability distributions) and qualitative risks (modeled with structured expert judgment). Financial Integration: Directly link risk events to a baseline financial plan (P&L, Cash Flow statement) to quantify impact. Probabilistic Output: Move beyond single-point estimates to deliver a distribution of potential outcomes (e.g., P10/P50/P90 EBITDA). Auditability & Reproducibility: Ensure every simulation run is traceable to a specific version of the risk registry, assumptions, and financial baseline. User-Centric Workflow: Provide intuitive interfaces for risk owners to provide input without needing to be simulation experts. 2. High-Level Architecture The platform is designed as a set of modular services that interact through well-defined APIs and a shared data layer. ...

Market Risk Simulation for Multi‑Currency Revenue Linked to Brent (EUR Book) This guide shows how to simulate monthly revenue risk when commodity prices are linked to Brent (in USD), the book currency is EUR, and you have revenue streams across EUR, USD, INR, and AUD markets. We model Brent with a mean‑reverting process and preserve correlation with FX using a Monte Carlo method. Assumptions: Prices are monthly and linked to Brent in USD. Brent follows a mean‑reverting (Ornstein–Uhlenbeck) process in log‑space. FX pairs are modeled in log‑space (e.g., GBM for simplicity) and jointly simulated with Brent via a correlation matrix. Book currency is EUR; portfolio revenue is aggregated in EUR. Why this setup works: ...

Numerical SDE Methods for Interest Rate Dynamics This post shows how to simulate short-rate models for interest rates and use them in Monte Carlo pricing/valuation. We cover discretization choices (Euler–Maruyama, Milstein, exact), correlation handling, and practical tips for stability and accuracy. Scenarios: Path‑dependent discounting for cashflows: $DF = \exp\big(-\int r_t dt\big)$. Pricing/valuation under short‑rate models: Vasicek/OU, CIR, and a note on Hull–White. Monthly or finer time steps with correlated factors. Models Vasicek (Ornstein–Uhlenbeck on $r$): $\mathrm{d}r = \kappa(\theta - r)\mathrm{d}t + \sigma \mathrm{d}W_t$. Mean‑reverting, Gaussian; can be negative; has exact discretization in discrete time. CIR (Cox–Ingersoll–Ross): $\mathrm{d}r = \kappa(\theta - r) \mathrm{d}t + \sigma\sqrt{r} \mathrm{d}W_t$. Mean‑reverting, strictly positive if Feller: $2\kappa\theta \ge \sigma^2$; has exact transition via noncentral $\chi^2$. Hull–White (time‑dependent Vasicek): $\mathrm{d}r = a(t)\big(b(t) - r\big) \mathrm{d}t + \sigma(t) \mathrm{d}W_t$. Matches an initial yield curve; can simulate with Euler or semi‑exact integrator. Discretization methods Euler–Maruyama (EM): strong order 0.5; simple and widely used. Milstein: strong order 1.0 for scalar SDEs; adds a diffusion derivative term (useful for √r in CIR). Exact schemes (when available): Vasicek/OU in discrete time has a closed form. CIR has an exact transition: $r_{t+\Delta} = c \cdot \chi^2_{\nu}(\lambda)$ for appropriate $(\nu, \lambda, c)$. Guidance: ...