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.
12,303 documents
The document explains why a local volatility model can be useful after fitting an implied volatility surface to vanilla option prices. Under Dupire’s approach, the surface is converted into a local volatility function that can be used to model the underlying…
The document addresses the expectation of an Itô integral whose integrand combines a deterministic volatility function with the complex exponential of a Brownian-driven process. Its central principle is that an Itô integral with an adapted, square-integrable…
The document explains how to retrieve Bloomberg historical volatility and reproduce a 90-day estimate from price history. It identifies a volatility field that can be requested through the API and reports that, for two Hong Kong stocks in the example, its…
The document derives the distribution of the integral of time multiplied by Brownian motion over a fixed interval. Although the integral can be expressed as a difference of Gaussian terms, those terms are correlated, so their distributions cannot be combined…
The document considers pricing options on an illiquid currency pair when only one bank provides option quotes. It asks whether historical realized volatility can support implied volatility estimates, how a market maker might account for a risk premium, and…
The document examines a proposed estimator for Expected Shortfall (ES) from simulated losses. It assigns extra weight to the worst observed loss and adjusts the weight on the loss at the Value-at-Risk threshold, while other tail observations use a basic…
The discussion explains why calibrating a Bermudan swaption model only to coterminal European swaptions may miss important market drivers. A Bermudan’s exercise value can depend on swap rates and swaption prices across many expiries and tenors, including…
The document discusses pricing single- and double-window barrier options, whose barriers are monitored only during a specified interval within the option’s life. It cautions that closed-form formulas are generally limited to Black–Scholes settings with…
The document derives the expected number of observation dates on which an asset price falls between two bounds. It treats the count as a sum of indicator variables and uses linearity of expectation, so the calculation needs the probability of being inside…
The document explains how option Greeks can help attribute changes in a delta-hedged position. Gamma captures the effect of underlying price movement and realized variance relative to the volatility assumption; vega measures sensitivity to changes in the…
The document explains how to infer a later-dated option’s implied volatility from a calendar put spread when the earlier straddle’s fair value is known. It first compares the trade price with model values to estimate the spread’s edge, then uses put-call…
The document clarifies the meaning of the Poisson rate in Merton’s jump-diffusion model. The rate λ is an intensity measured as expected jumps per unit of time. Over a short interval of length dt, the expected number of jumps is λdt, which corresponds to the…
The document asks how implied volatility across strikes should behave for electricity options. It describes differing possibilities, including a convex smile and a skew with higher volatility at elevated strikes. The replies discuss German electricity market…
The document presents a VBA routine that estimates European call and put prices with a Black–Scholes formula, then attempts to solve for implied volatility by iterating on volatility. A reply identifies the very small volatility step used to approximate…
The document compares finite-difference PDE methods with Monte Carlo simulation for pricing options under complex models. In a relatively simple setting such as Black–Scholes with a payoff that does not require modeling volatility convexity, a PDE can be…
The document explains how to translate intraday volatility into a daily or annualized estimate when volatility changes across the trading session. It points out that dividing annual volatility evenly across all intraday bars assumes identical variance in…
This post describes an implementation problem in a bivariate tree used to price American options under the Heston stochastic-volatility model. The author reports getting a negative probability for the middle stock-price move while following a published tree…
The document discusses implementation options for smoothing an implied volatility surface while enforcing arbitrage-free conditions. One response characterizes this as a difficult task and suggests that ready-made implementations may be uncommon outside…
The document works through an algebraic attempt to derive equation 8 in Derman and Kani’s implied binomial tree for local volatility. Starting from an earlier call-price relation, the answer substitutes the risk-neutral probability, rearranges terms to…
The document explains why a pricing partial differential equation can be useful for deriving the relationship between option vega and gamma even when volatility is constant. In the Black–Scholes setting, volatility is a parameter of the differential…
This document collects suggested online lectures, conference talks, courses, and notes related to quantitative finance. The topics range from financial mathematics, risk-neutral pricing, delta hedging, and option strategies to volatility, interest rate and…
The document asks whether forward-looking volatility estimates can improve an estimate of an asset’s CAPM beta for the coming month. The proposed approach replaces historical market variance with VIX-implied volatility and historical asset volatility with…
The document asks how to use a Python-defined local volatility function with QuantLib’s Black–Scholes process. It clarifies that a local volatility term structure handle cannot simply be constructed from an arbitrary Python function in the shown way; the…
The document explains how to translate annualized implied volatility into a one-period price move. Under the Black–Scholes interpretation, volatility is the standard deviation of log returns, so a sigma-scaled move is expressed by multiplying the current…