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This exchange considers how the Avellaneda–Stoikov reservation price responds to a stock's price scale and an inventory measured in shares. The question compares a stock before and after a large share consolidation, where the share price and volatility per…
This discussion compares Monte Carlo simulation with analytical, partial differential equation, and numerical integration methods for option pricing. Monte Carlo is useful when the model lacks a tractable solution, payoffs depend strongly on the price path,…
The document derives the solution to a geometric Brownian motion whose drift and volatility vary with time. Applying Itô's lemma to the logarithm of the asset price produces a drift term adjusted by half the instantaneous variance, alongside a stochastic…
This discussion explains how to estimate annualized volatility from a sequence of weekly stock prices. The method is to calculate consecutive log returns, find their sample standard deviation to estimate weekly volatility, then scale it by the square root of…
The document considers whether a backtest with 50 trades and a 60% win rate reflects skill or chance. It argues that repeatedly comparing the observed result with randomly generated strategies does not, by itself, establish a false-positive probability. A…
The document addresses how to choose a threshold for volume-based sampling bars, in response to a question about setting the dollar value for dollar bars. The suggested approach uses a rolling average of recent volume to set a target sampling frequency:…
Bootstrapping a yield curve from market instruments produces discount factors or zero rates at the instruments’ maturities. These observed maturities are curve nodes; they do not by themselves specify values at every date. An interpolation method fills in…
The document outlines how extreme value theory can estimate tail risk, especially for a portfolio of long and short stock options. It recommends the peak-over-threshold approach: select sufficiently extreme losses, fit a Generalized Pareto Distribution, and…
The document asks how to implement time-shifted power-law kernels used in a path-dependent volatility model. The model forms volatility from a baseline plus weighted past returns and weighted squared returns. Separate kernels assign the lag-dependent weights…
The discussion addresses a regression intended to explain gold using the VIX, the EUR/USD exchange rate, and a US real-rate index. The model uses ridge regression because its author selected a small, theory-informed set of factors, yet reports an adjusted…
The discussion explains how a local-volatility model relates an implied-volatility surface to an instantaneous volatility function of spot and time. Its central clarification is that local volatility is calibrated from the current implied surface; if that…
The discussion considers how to make markets in assets with sparse trading, few resting orders, limited participants, high volatility, and wide spreads. Suggested price-discovery inputs include researching who holds the asset, identifying historical buyers…
The document asks how to search for predictive relationships between a target series and many candidate variables. Its example is an inverted, three-month-delayed variable that appears to lead stock prices, and the proposed application is predicting future…
The document explains the one-period binomial model’s no-arbitrage condition by comparing the stock’s up and down factors with the risk-free growth factor. If the stock’s return in both states is no better than the risk-free asset, shorting stock to buy the…
The document frames a one-month portfolio problem involving cash, a stock, and a six-month European put. Returns are evaluated under the physical measure, but the option’s future market value depends on risk-neutral pricing. The author explains why valuing…
The document asks whether hedging strategies should be compared using the absolute values of their errors or the squared errors. One response favors squared-error summability, noting that it is a weaker requirement than absolute summability and that squaring…
The document considers ways to investigate fractal behavior and harmonic patterns in stock time series, with the broader aim of building trading systems. Its concrete suggestion is to fit a Daubechies wavelet and examine coefficients across scales at a fixed…
The document explains how state prices and a stochastic discount factor express the same pricing rule in different forms. In a discrete set of possible future states, a state price is the current price of a claim paying one unit only in a particular state.…
The document compares minimizing portfolio variance for a specified expected return with maximizing expected return at a specified variance, while also requiring weights to sum to one. It derives a candidate solution for the unconstrained version of the…
The document asks how to price an Arrow security that pays one unit if a specified event occurs at a future date. It frames the question through the stochastic discount factor: the current value is expressed as the expected product of that factor and the…
The document concerns Greeks for the Bachelier model, which assumes normally distributed price changes. The author says delta, vega, and gamma are straightforward to derive, then focuses on deriving rho and theta when the interest rate is nonzero. They…
The document introduces a diffusion model that can interpolate between arithmetic Brownian motion and geometric Brownian motion. In the proposed stochastic differential equation, the diffusion term is proportional to the state raised to a power γ. Setting γ…
The document explains how the Stochastic Volatility Inspired (SVI) parameterization can represent implied total variance across option strikes. Its formula describes a smile using five parameters: a level, slope scale, skew, horizontal shift, and curvature…
The document discusses adding an explicit high- or low-volatility regime to a Fama–French regression for a stock portfolio. The proposed research question is whether a manager’s factor exposures differ by regime, such as favoring quality during high…