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.
10,263 documents
The document discusses potential drawbacks of using deep learning to calibrate and price a full implied-volatility surface. It notes that neural methods can produce very fast calibration at application time, while training may involve substantial…
The document addresses why an at-the-money call’s familiar delta of about one half does not match the full payoff change in a large, single-step move. Delta is a local sensitivity: in the theoretical continuous-time setting, it approximates how an option’s…
This document collects book recommendations for readers who want to understand the mathematics used in quantitative finance research. The suggestions span introductory mathematical tools, including calculus, optimization, numerical methods, and risk-neutral…
The document explains why a stochastic local volatility model can combine features of local volatility and stochastic volatility. It writes the asset’s instantaneous volatility as a stochastic factor multiplied by a state- and time-dependent local factor.…
The document presents an arbitrage argument for convexity of European call option prices as a function of strike. If the price at a middle strike were at least as high as the average prices of two equally spaced neighboring strikes, a trader could buy the…
The document asks how a risky-asset portfolio weight enters wealth dynamics and then the Hamilton-Jacobi-Bellman equation for maximizing expected log wealth. It presents a risky asset whose excess return follows a mean-reverting signal, alongside correlated…
The document addresses how to simulate the variance process in a Heston-style model when its correlated Brownian driver includes a drift adjustment linked to the wealth process. The proposed approach is to substitute the adjusted Brownian differential into…
The document explains why a floating-rate bond’s forecast coupons decline when its QuantLib curve is constructed with simple compounding. The proposed fix is to build the FlatForward curve with compounded or continuous compounding so the quoted rate is…
The document addresses how to calculate swap DV01 under shifts to both a discount curve and a three month USD LIBOR projection curve. The key issue is that the USD LIBOR index used by a vanilla swap takes a yield curve handle, so creating a separate index…
The document explains calibration as choosing a model’s parameters so its prices fit observed prices for selected liquid options. A common formulation minimizes the aggregate pricing error across instruments with specified characteristics such as strike and…
The document explains why reduced-form credit models distinguish a market filtration, containing variables such as rates and asset prices, from a default filtration that records whether and when default occurs. Their join forms the full information set used…
The document outlines the usual discrete-time Black–Scholes delta hedge for a European call on a stock. It sells the option, offsets its delta with a stock position, and places the residual value in a risk-free account. At each step, the stock price is…
The note evaluates a proposed way to choose an expiration for uncovered puts: maximize option premium divided by days to expiration. It argues that this ratio tends to mechanically favor shorter-dated contracts, because option value generally does not rise…
The note considers how an NPV function should handle cash flows when the valuation date falls during an instrument’s life. For basic instruments, the accepted answer recommends valuing only future cash flows. For products whose future payoff depends on past…
The note asks how to obtain the first, second, and fourth cumulants of the variance gamma with stochastic arrival model for use in Fourier-cosine option pricing. It defines the model through a characteristic function built from a variance gamma process with…
The note explains why multiplying an option’s current theta by the days remaining can imply more decay than its current time value. It uses a deep in-the-money call as an example: most of its price is intrinsic value, while the quoted time value is small and…
The document asks how fractional Brownian motion (fBm) might be interpreted when it replaces ordinary Brownian motion in a Black–Scholes framework. Its answer focuses less on an economic interpretation and more on a mathematical consequence: fBm is generally…
The document asks why historical volatility is commonly measured as the standard deviation of log returns. The author points out that a sequence of identical daily percentage changes would have constant log returns and thus zero standard deviation, even…
The document questions an apparent U-shaped implied-volatility pattern in SPX options, especially at far out-of-the-money strikes. A response compares the displayed pattern with a snapshot of implied volatilities for weekly options, reporting generally…
The document examines how to estimate expiration probabilities and expected value for a two-leg put credit spread. It divides outcomes into three price regions: above the short strike, between the strikes, and below the long strike. The author asks whether…
The document poses a portfolio risk question about estimating value at risk when the portfolio value is a nonlinear cubic function of one normally distributed risk factor. At the stated current factor level, both the first and second derivatives are zero, so…
The document explores how to derive a variational or weak formulation for the Black–Scholes partial differential equation. Its central issue is integration by parts in the diffusion term, where the coefficient depends on the underlying price variable.…
The document clarifies a basis swap pricing question about why a six-month forward rate can differ from the rate implied by two consecutive three-month periods. The key distinction is between the underlying reference index and the loan exposure: a…
The document addresses how to construct an implied volatility smile from US equity options when no traded option has a strike exactly equal to the underlying price. It asks how to estimate at-the-money volatility and connect out-of-the-money put and call…