คลังความรู้

The example considers a portfolio value defined as Brownian motion squared minus time. Applying Itô’s lemma to this function produces a drift term from the time derivative and the second derivative with respect to the Brownian state, alongside a stochastic…

A question reports unstable or negative option values when the step count in an FFT-based binomial calculation becomes large. The accepted response suspects numerical precision loss in the terminal stock-price calculation, which raises up and down factors to…

The thread addresses implementation questions for two-step estimation of a dynamic conditional correlation GARCH model. In the second-stage likelihood, the log of the determinant of the conditional correlation matrix is a scalar, as is the quadratic form…

The discussion distinguishes two research questions that can look similar but require different outcomes. To compare volatility estimators as forecasting inputs, regress a later realized-volatility measure on each estimator available at the forecast date. A…

The document explains that derivative counterparty-risk models must specify how a defaulted transaction is valued for settlement. It distinguishes risk-free close-out, which values the contract without counterparty-related risk factors, from substitution or…

The document asks how to apply antithetic sampling when simulating the Heston stochastic volatility model with a discretized process. The central issue is whether to reverse the random draws only for the stock price or for both the price and variance…

The discussion compares evaluating a strategy through trade or portfolio returns with simulating a starting capital amount and measuring ending equity or annualized return. It argues that the appropriate view depends on the strategy and how closely the…

The document presents a QuantLib Python calibration attempt for a time dependent Heston model that fails with a Boost assertion. The code builds a volatility surface, creates a piecewise time dependent model, attaches an analytic pricing engine, and…

The document discusses why an online broker may cap the number of legs in a single options spread order. Its main explanation is that brokers submit orders using structures recognized by options exchanges, and the permitted order formats and applicable rules…

Liquidity depends on the asset class and on how participants access each market. The document compares spot, futures, options, and swaps across currencies, single stocks, equity indices, commodities, and fixed income. It offers a practical framework: there…

The document explains why counting losses beyond Value at Risk on the same sample used to estimate the quantile cannot validate a VaR model. For a historical VaR estimate based on past profit and loss observations, the proposed approach is to use a rolling…

The document considers whether an equity option’s implied volatility should be adjusted when the underlying price moves. It describes alternative ways to hold the volatility surface fixed: sticky strike keeps implied volatility tied to each strike, while…

The document estimates the chance that a stock reaches a buy limit price at least once during a waiting period. It models log prices as Brownian motion with constant volatility, uses the distribution of the running minimum to relate a price threshold to a…

The document explains how the Cox–Ross–Rubinstein binomial option-pricing recursion approaches the Black–Scholes model as the time step shrinks. It corrects the risk-neutral pricing equation, then uses first-order expansions of the up and down moves and the…

The document examines implausible risk-free rates inferred by regressing option collars on SPX options close to expiration. It explains that put-call parity calculations can become distorted when options and their underlying continue trading on different…

The discussion offers several explanations for why stock prices may hold up even when current corporate earnings fall sharply during an economic shock. Lower interest rates can support higher valuation multiples because future cash flows are discounted less…

The note explains why portfolio theory commonly plots expected return against standard deviation rather than variance. Its example combines a risk-free asset with a risky asset: scaling the risky position by one half scales standard deviation by one half,…

The document examines a reported average duration of roughly 25 minutes for continuous ETH price rises or falls, measured in five-minute intervals over three months. The response recommends defining what would count as unusual and comparing the observation…

The document addresses a numerical implementation issue in the CGMY model’s characteristic function. The questioner encounters an error because the expression includes gamma functions evaluated at negative values and asks whether the formula is incorrect.…

The document discusses autoquotes in the context of research on locked and crossed markets. It distinguishes the paper’s reference to small displayed limit orders that other market participants might trade through from an explanation of the exchange’s…

The document compares two ways to generate paired Brownian increments with a specified negative correlation and time-step variance. One approach draws independent standard normal samples and transforms one using the target correlation; the other draws…

The discussion explains how the cheapest-to-deliver bond can make a Treasury futures curve trade differ from the yield spread suggested by the contract names. A 10-year Treasury note future may be priced around a deliverable bond with a maturity closer to…

This beginner discussion distinguishes an option’s payoff at expiration from its value before expiration. Changing volatility does not alter the European option’s terminal payoff diagram; it changes the premium beforehand by changing the range of possible…

The responses survey reinforcement learning (RL) applications in quantitative finance, with portfolio allocation as the main example. They describe critic-only methods, which choose actions using learned value estimates; actor-only methods, which optimize…