Mathematical Principles and Quantitative Finance · 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.
Stochastic Models and Processes · 12. novembre 2023
The Hull-White model is a credit derivative pricing tool that uses a stochastic hazard rate to reflect default risk and economic conditions. It calculates survival probabilities and expected losses to price Credit Default Swaps (CDS), employing a risk-neutral approach and calibration with market data for realistic valuation.
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...
15. juillet 2023
In simple terms, think of hedging like insurance. A bank sold a specific type of "insurance" (Down-and-Out European Call) that pays out only if the stock price doesn't dip below a certain level (the barrier). To safeguard itself, the bank uses a mix of buying and selling other financial "insurances" (call and put options). The magic formula ensures that if the stock dips below the barrier, the bank won't lose money. It's a balancing act, where buying one thing counteracts the selling of another