II. Mathematical Tools and Principles · 13. November 2023
The Black-Scholes model is key in options trading, calculating European option prices with assumptions like log-normal stock prices and constant volatility. It excludes dividends and leverages stochastic calculus, impacting theoretical and practical finance. The model's formula involves stock and strike prices, time to expiration, and risk-free interest rates, integrating volatility into option pricing. This framework is crucial for understanding option pricing and risk management in finance.
II. Mathematical Tools and Principles · 09. November 2023
Richardson extrapolation refines the accuracy of exotic option pricing in financial modeling. It adjusts for errors from numerical methods by using varied step sizes, leveraging the principle that error decreases quadratically with smaller steps, yielding more precise pricing estimates.
II. Mathematical Tools and Principles · 10. October 2023
The Fourier Transform is a tool that transforms complex stock price movements into simpler, frequency-based components. In a mathematical context, this transformation is executed through a specified formula that facilitates a detailed analysis of the stock price movements at various frequency levels. The mathematical foundation of this process lies in the formula F(w) = ∫_(-∞)^(∞) f(x) * e^(-jwx) dx. Here, f(x) represents the time-domain data of a stock’s price, and F(w) gives its...
II. Mathematical Tools and Principles · 09. October 2023
Quantitative finance relies on rules from stochastic calculus, like dW^2=dt, highlighting Brownian motion's unpredictability, and Zero Rules, underscoring infinitesimal term behaviors, crucial in financial modeling and risk management.
#Finance #RiskManagement
II. Mathematical Tools and Principles · 08. September 2023
Unravel the simplicity of Copula in pair trading & Taylor expansion in quantitative finance. Copula simplifies understanding correlated assets for optimized trading. Taylor’s expansion breaks down complex financial models, akin to predicting a mountain's terrain with each step. Discover, learn, and apply these concepts with ease. #Copula #PairsTrading #TaylorExpansion #QuantFinance
II. Mathematical Tools and Principles · 08. July 2023
The Black-Scholes partial differential equation in layman’s terms…
#OptionPricing, #BlackScholes, #FinancialModeling, #QuantitativeFinance, #RiskNeutralMeasure
II. Mathematical Tools and Principles · 01. July 2023
The Moment Generating Function (MGF) in layman’s terms… The Moment Generating Function (MGF) is designed to provide insights into the entire range of possible values of a random variable. It's a mathematical tool that captures information about the distribution of a random variable, including its moments (like mean, variance, skewness, kurtosis, etc.). Discrete Time: In discrete time, the random variable takes on distinct values at specific points or intervals. When calculating the expected...
II. Mathematical Tools and Principles · 18. March 2023
Navigating options is like hiking. To gauge a trail's steepness, you take small steps and check the height difference. This is the "slope" in hiking or the "delta" in options. But trails can vary in steepness, akin to the "gamma" in options. The finite difference method is our way of taking these small steps, offering insights into options without needing a full formula. Simply put, it's understanding changes step-by-step, just as in hiking. 🌄💹🚶♂️📊 #FiniteDifferenceMethod #OptionsInsight