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.
8,116 documents
The document frames the construction of an FX volatility surface for pricing vanilla European options and testing systematic option strategies. It focuses on risk reversals, strangles, and butterflies quoted at 10-delta and 25-delta, and on tracking premiums…
The document considers pricing a European option with a payoff that depends nonlinearly on the underlying asset, under a Black–Scholes model with a continuous dividend yield. The response derives the pricing partial differential equation from the…
The note explains the value of an American option in a binomial model as the larger of its immediate exercise payoff and its discounted expected value from holding the option. The continuation value uses risk-neutral probabilities for the next-period option…
The document examines whether an option’s delta can be used to infer its expected positive or negative exposure profile. Delta measures sensitivity to changes in the underlying, and a regulatory exposure formula cited in one answer links exposure to delta,…
The document discusses converting market normal volatilities into shifted Black volatilities for SABR calibration in a negative-rate setting. Its stated approach is to treat each implied volatility as a way to represent an option price: calculate a price…
The document addresses a possible numerical or formula issue in implementations of the Bjerksund–Stensland 2002 American option approximation, focusing on its early-exercise boundaries. The response identifies the lower boundary, B0, as potentially…
The document discusses boundary conditions in finite-difference option pricing, contrasting Dirichlet conditions, which prescribe the value at the boundary, with Neumann conditions, which prescribe a spatial derivative. It notes that Neumann conditions can…
The document asks how to compute Dupire local volatility from an implied variance surface, focusing on the required derivatives with respect to maturity and log strike. The questioner reports that finite differences at small step sizes produce very large…
The document clarifies that an option pricing model and a method for solving or evaluating it are separate concepts. Black–Scholes is a model with a closed-form solution under its assumptions, but the same model can also be evaluated using numerical…
The document addresses how implied probabilities relate to option prices when Black–Scholes implied volatility varies with strike and maturity. Its central result is that the second derivative of a call price with respect to strike, scaled by the discount…
The document explains why geometric Brownian motion (GBM), a stochastic differential equation with drift and volatility, should not be treated as a reliable point forecast for a particular stock. Simulated paths vary randomly, and fitting model parameters to…
The document explains a cancellable interest rate swap from the perspective of a dealer that pays fixed and has the right to terminate. It represents the cancellable structure as a vanilla swap combined with an option to enter an offsetting swap. This option…
The document explains how to price a European call with a recombining binomial model. After fixing the asset's up and down factors and the per-step interest rate, it derives the terminal price distribution and its risk-neutral probabilities. The option value…
The document describes ways to construct an implied volatility smile from standard FX quotes, including at-the-money volatility, risk reversals, and strangles at specified deltas. One approach fits a quadratic curve in delta space, using the at-the-money…
The document explains why an option’s implied volatility can fall even when the underlying stock price barely moves. Since implied volatility is inferred from option prices, it can change with option supply and demand and with shifts in expectations,…
The document distinguishes joining an established options market from creating a new or illiquid one. In a functioning market, a new participant mainly provides liquidity, with the pricing model chosen to suit the product. When developing a market, the…
The document considers how to represent clients’ non-optimal exercise of Bermudan swaptions, with the observation that decisions may respond to past rate movements as well as current rates. One proposed route is supervised learning: build observations…
The document asks how logarithmic price and time-to-maturity substitutions change derivatives in the Black–Scholes partial differential equation, and how a further change of variables removes its first-order spatial term. The chain rule gives \(V_S=V_y/S\)…
The document sets up a call option whose payoff depends on the lower of two underlying asset values under a Bachelier model. Both assets are modeled as arithmetic Brownian motions with no drift, constant volatilities, and constant correlation. It writes a…
The document discusses calibration of a Heston local stochastic volatility model, which combines a stochastic variance process with a state- and time-dependent leverage function. The leverage function is chosen so the model reproduces a target local…
The document asks what daily return a market-making algorithm should target. Its answer suggests framing the estimate through net profit per completed round trip rather than choosing a daily ROI figure in isolation. The cited practitioner account gives an…
The document examines a proposed trade involving American and European put options on the same asset, strike, and expiry. The idea is to sell the American put and buy a cheaper European put, potentially collecting cash if the European contract is priced…
The document raises a question about interpreting implied volatility when prices are generated under a model with normally distributed returns and then inverted through the Black–Scholes formula. It asks whether the resulting Black–Scholes implied volatility…
The document considers whether to reuse the same random numbers for each objective-function evaluation when calibrating a stochastic model to option prices by Monte Carlo. Keeping the seed fixed makes successive evaluations comparable by reducing simulation…