Short Rate & Forward Rate Models
A bond is a loan. It has future CFs: its coupons, and the loan repayment. Each future CF has a…
Market, Risk and Reference Data
The Data Science Underlying Quant Finance
When financial markets first emerged, the data they created became the basis for QF. Prices from different markets exhibited patterns…
The FRTB SA Formula
In statistics, the variance of two variables X and Y, say people’s height and weight, can be summed to get…
EWMA Volatility in Market Risk
A sales rep has a 20% chance of making a sale on a call. What is the probability that she…
Term Structure Models
The first QF models were developed for equity prices. GBM & Black-Scholes modelled equities & their options. A natural extension…
Swaption Valuation
A bank’s Rates desk has purchased a callable fixed rate bond. The embedded call means the bond’s issuer is long…
Pricing American Options with Finite Difference Methods
The BSM equation describes how an option value, V, changes over time (dV/dt). It is a PDE that describes the…
From Heat to Black Scholes
In 1789 Joseph Fourier accompanied Napoleon as scientific advisor on an expedition to Egypt. When Fourier came back, he developed…
AI vs Black Scholes
QF began in 1900 with Bachelier observing that stock price changes were random and normally distributed. The normality of price…