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 · 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 · 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 · 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
I. Stochastic Models and Processes · 12. novembre 2023
The Merton model, essential in credit risk analysis, views a company's equity as a call option on its assets, crucial for default probability assessment. Using the Black-Scholes formula, it combines equity with zero-coupon debt for valuation. Despite its innovativeness, the model's reliance on market data and idealistic market assumptions limit its applicability. This has spurred alternative approaches like reduced form models, addressing these shortcomings in credit risk evaluation.
III. Quantitative Finance Applications · 10. novembre 2023
Convertible bonds blend debt and equity, featuring an option to convert into a set number of shares. Key factors include conversion ratio and price. Valuation hinges on stock dynamics, credit risk, and hazard rate. At maturity, value is the higher of face value or conversion outcome. Monte Carlo simulations help in pricing, considering callability and putability options. #ConvertibleBonds #CreditRisk #FinancialModeling #InvestmentStrategies
II. Mathematical Tools and Principles · 06. novembre 2023
Chaos theory is a field of study in mathematics that deals with systems that appear to be disordered, but are actually following deterministic rules that are highly sensitive to initial conditions. This sensitivity causes the system to appear random and unpredictable. One of the simplest mathematical models to demonstrate chaos is the logistic map. This is a recurrence relation which is used to model population growth and is given by: x(n+1) = r * x(n) * (1 - x(n)) Here, x(n) is the proportion...