Stochastic Models and Processes · 01. novembre 2023
The Vasicek model predicts interest rates using mean reversion, volatility, and the speed of reversion. Its equation, `dr(t) = κ(θ - r(t)) dt + σ dW(t)`, models rates' return to a mean (θ) with volatility (σ) and randomness (dW(t)). It's vital for financial strategies and simulations.
12. septembre 2023
Dive into the heart of finance with the sigma-algebra concept! Think of a deck of cards. Assigning probabilities, like drawing an Ace, means defining and combining events, and understanding their opposites. This structure, crucial in finance, ensures we consistently and meaningfully talk about events, especially in complex financial markets. As we track evolving information and model future possibilities, the sigma-algebra keeps our models from descending into chaos.
Stochastic Models and Processes · 20. mai 2023
In the Black-Scholes model, N(d1) and N(d2) are like gauges measuring the likelihood of different financial events. Imagine a game where you're guessing if a stock will reach a certain price. N(d1) is your best guess, factoring in the game's rules and odds. Meanwhile, N(d2) is about how much you'd ideally pay to play based on those odds. Together, they help determine an option's value. Simply, N(d1) gives the winning chance, and N(d2) gauges the cost. #OptionsExplained #BlackScholesModel
Stochastic Models and Processes · 18. février 2023
The d₁ term in the Black-Scholes model captures key factors of option pricing like stock price, strike price, volatility, and time. N(d₁) represents the option's delta, showing how sensitive its price is to the stock price. While often mistaken for the probability of the option ending in the money, this is actually the role of N(d₂). N(d₁) primarily reflects the option's sensitivity and hedge ratio.