Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
44 documents
This article relaxes the constant volatility assumption in Black–Scholes by allowing the asset's volatility to vary over time. It models log volatility with a mean reverting Ornstein–Uhlenbeck style equation driven by a stochastic process. To represent…
The article presents LU decomposition as a way to solve linear systems that arise when implicit finite-difference methods discretize the Black–Scholes partial differential equation. Rather than directly inverting the coefficient matrix, the method factors a…
This introduction explains why ordinary differential calculus is inadequate for many random price processes: Brownian paths are continuous but generally not differentiable. In quantitative finance, Ito calculus provides a way to work with these processes…
The document explains option sensitivities—delta, gamma, vega, theta, and rho—and presents analytic formulas for European vanilla calls and puts. It then compares numerical differentiation of analytic prices with a finite difference approach applied to Monte…
The document derives a limiting asset-price distribution from a multi-step binomial model under simplifying assumptions: zero interest rates, equal up and down probabilities, and an expected expiry price equal to today’s spot. The step changes are…
The document outlines a developing Python options library that combines analytical pricing with Monte Carlo simulation. Closed-form methods use the normal probability density and cumulative distribution functions to price vanilla calls and puts, calculate…
The document presents a templated C++ array class for managing data in CUDA device memory. Its interface supports allocation at construction, resizing, querying the array length, and accessing the device pointer. Separate methods copy data from host memory…
This article proposes advanced undergraduate and early postgraduate topics for learners preparing for quantitative finance study or work. Its suggested curriculum emphasizes Brownian motion, stochastic analysis, stochastic calculus for finance and stochastic…
The article explains how to simulate standard Brownian motion and a process with constant drift and volatility using discretized time steps. It applies the recursive update to many paths at once with vectorized arrays, then plots the paths and estimates the…
This introduction presents a one-period binomial model for a vanilla call option. It starts with an asset priced at 100 today that can move to either 110 or 90 tomorrow, and a call with strike 100. With interest rates temporarily set to zero, the payoff is…
The article explains how discrete Asian options use sampled prices along an asset path to determine their payoff. It distinguishes arithmetic averaging from geometric averaging and models price paths with geometric Brownian motion. Monte Carlo pricing…
The article explains how the analytic Black–Scholes formulas for European vanilla calls and puts can be translated into a procedural C++ implementation. It defines the underlying price, strike, interest rate, volatility, and time to maturity, then uses the…
The document extends binomial-tree option pricing from a small tree to a finite N-step model. It explains backward propagation from known terminal payoffs and presents risk-neutral valuation as an alternative: calculate the probabilities of ending at each…
This note extends the one-step binomial option model from zero interest rates to a positive continuously compounded risk-free rate. It bounds the stock’s possible up and down prices around risk-free growth, then chooses a risk-neutral probability that makes…
The article derives a no-arbitrage value for a call by constructing a portfolio that combines a long position in the underlying stock with a short call. In its example, the stock starts at 100 and can finish at either 110 or 90; a call with a strike of 100…
The document compares Python threading and multiprocessing for improving simulation performance, with Monte Carlo pricing and strategy backtests as relevant examples. It explains that CPython’s Global Interpreter Lock limits CPU-bound Python threads to one…
The document explains implied volatility as the volatility input that makes a model option price match an observed market price. It motivates volatility quotes as a way to compare options whose premiums are affected by different underlying prices, especially…
The document explains Itô’s lemma as the stochastic counterpart of the ordinary chain rule. It starts from a drift-diffusion process driven by Brownian motion and describes how to find the differential of a sufficiently smooth function that depends on both…
The document explains how to approximate European vanilla option prices by solving the Black–Scholes partial differential equation with an explicit Euler finite difference scheme. It lays out the PDE domain, expiry payoff, and call boundary conditions, then…
The document explains how to estimate the price of a double digital option using Monte Carlo simulation. The option pays one unit when the underlying asset’s value at expiry lies between a lower and an upper strike, inclusive, and pays nothing otherwise. The…
The document introduces sigma algebras and probability spaces as foundations for measure theoretic probability, with the eventual aim of preparing readers for Brownian motion, Ito calculus, and options pricing. It motivates the framework through continuously…
This tutorial explains how to estimate the value of a down-and-out call using Monte Carlo simulation on a GPU. A simulated price path is invalidated if it crosses the lower barrier before expiry; absent a rebate, the payoff depends on the terminal price…
This reading guide lays out a staged path for learning mathematical finance and derivative pricing. It starts with a broad introduction to instruments and markets, then recommends a mathematically lighter bridge into calculus, arbitrage, the Black–Scholes…
This article introduces Lévy processes as alternatives to geometric Brownian motion for modelling asset prices in derivative-pricing frameworks. Under the standard Black–Scholes assumption, log returns are normally distributed; the article argues that…