III. Quantitative Finance Applications
III. Quantitative Finance Applications · 10. juin 2024
L'évaluation des risques dans les CDO repose sur deux concepts pivots : la théorie des probabilités et la corrélation entre les actifs sous-jacents. Alors que la théorie des probabilités offre des informations sur la probabilité d'événements de défaut individuels, la corrélation fournit une mesure de la manière dont ces défauts sont liés. Les CDO, structurés en tranches seniors (*), mezzanines et equity, supportent chacune des degrés de risque variables en fonction de leur...
III. Quantitative Finance Applications · 02. juin 2024
A Total Return Swap in the fixed income context is a derivative contract where one party, the total return receiver, gains the total return (interest, principal repayments, and any capital gains or losses) of a specified credit asset, such as a bond or loan portfolio. In return, the total return payer receives a regular payment based on a predetermined fixed or floating interest rate, often linked to a benchmark like EURIBOR. For instance, suppose Party A (total return receiver) and Party B...
III. Quantitative Finance Applications · 19. avril 2024
Understanding the probability of events like bond defaults requires recognizing that individual likelihoods, or marginal distributions, don't inherently reveal the likelihood of multiple bonds defaulting simultaneously. Even if two sets of bonds have identical marginal probabilities, their joint probabilities can differ significantly based on default correlations.
Marginal distributions describe individual behavior without considering other variables.
III. Quantitative Finance Applications · 28. février 2024
Risk assessment in CDOs involves probability theory for individual defaults and correlation analysis for linked defaults. CDOs have senior, mezzanine, and equity tranches with varying risks. High correlation suggests simultaneous defaults and larger losses, while low correlation indicates independent defaults, impacting different tranches.
#CDOsExplained #RiskAssessment #DefaultFrequency #ProbabilityTheory
III. Quantitative Finance Applications · 09. février 2024
Sklar's Theorem, a pivotal concept since 1959, separates the modeling of individual behaviors and dependencies in multivariate analysis, reshaping risk management and probabilistic modeling. It states that any multivariate distribution can be expressed via a copula linking its univariate marginal distributions. This theorem allows the copula to remain constant despite changes in individual distributions, enabling flexible and accurate modeling of complex dependencies.
III. Quantitative Finance Applications · 07. février 2024
Explore the hypercube's critical role in CDO risk modeling within quantitative finance. A hypercube extends a 2D square or 3D cube into an N-dimensional space, each axis representing a financial asset's cumulative distribution in copula functions. It's pivotal for visualizing complex dependencies in a CDO, where each axis indicates the default probability of different assets.
III. Quantitative Finance Applications · 05. janvier 2024
Discover the role of copulas in statistics, crucial for analyzing relationships between multiple variables in multivariate analysis. Copulas uniquely capture dependence structures, distinct from individual distributions. Focusing on the Gumbel copula, known for modeling tail dependencies in finance, we explore its effectiveness in assessing risks, like joint defaults in CDOs.
III. Quantitative Finance Applications · 14. novembre 2023
A swaption is a derivative allowing the choice to enter a swap, key for banks managing interest rate risks. It enables receiving a fixed rate while paying a floating rate, beneficial when hedging against rate decreases. Banks use long receiver swaptions and short payer swaptions to simulate swap payoffs in different rate scenarios. This strategy converts floating rate loans to fixed, aligning with their hedging objectives.
III. Quantitative Finance Applications · 14. novembre 2023
In the Black-Scholes model, N(d2) calculates the probability of a call option being in the money at expiration, balancing its potential profitability and expected exercising cost. This risk-neutral measure assumes investments grow at a risk-free rate, crucial for arbitrage-free option pricing. #BlackScholesModel #RiskNeutralValuation #OptionPricing #N(d2)Explained
III. Quantitative Finance Applications · 13. novembre 2023
In the Black-Scholes formula, Δ is the option delta, showing the price change of a call option for a $1 change in the stock price. Δ equals N(d1), where N is the cumulative normal distribution function, and d1 factors in the stock price, strike price, time to expiration, risk-free rate, and volatility.
#OptionsTrading #Delta #BlackScholesModel