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 explains that a stock's log return in the Black–Scholes framework changes over time as a stochastic quantity. Starting from geometric Brownian motion for the stock price, it describes the log return as having a deterministic component tied to…
The document considers a derivative that pays at a later date the positive part of the underlying asset price observed at an earlier date minus a strike. Under risk-neutral valuation with constant rates, the supplied answer prices the claim before the…
The document asks whether an option’s vega can rise as expiration approaches, despite the usual intuition that vega declines over time. The response says the answer depends on how the option’s moneyness changes: movement of the underlying toward the strike…
The document surveys several possible ways to backtest equity options strategies online. It mentions a paid service with dedicated backtesting, a brokerage platform with some backtesting features, and a payoff calculator that can be used with manually…
The document explains a put-call symmetry relation in the Heston stochastic volatility model. A put on the underlying can be represented as a call on the reciprocal-scaled underlying, with the spot and strike exchanged and rates and dividend yield swapped.…
The document outlines a portfolio-based approach to deciding which proposed option trades to accept. For options sharing an underlying, it recommends calculating aggregate sensitivities such as delta, gamma, and vega, then comparing them with target values…
The document explains how to generate possible future prices when an asset is modeled as following geometric Brownian motion. It gives the stochastic differential equation for price dynamics and its analytical solution: the future price is the current price…
The document asks whether continuously delta hedging a long option leaves the trader flat at expiry, and how gamma profits can arise if the option is held to expiration. It frames the question with idealized assumptions: no hedge costs or slippage, no theta,…
The document asks how to compare Black–Scholes and Bachelier option prices in an energy-market setting, where the underlying can become negative. Since Black–Scholes does not accept negative underlying prices or strikes, a direct price comparison cannot…
The note describes how a local volatility surface can generate a conditional forward skew. Its suggested diagnostic is to start from a future point, simulate spot paths under the local volatility dynamics, reprice a grid of options along those paths, and…
The document asks how coupon payments should be handled when valuing a callable or puttable bond on a binomial tree: should the coupon be added before applying the call or put exercise limit, or afterward? The answer emphasizes that the result depends on the…
The document asks why QuantLib’s American put option object exposes vega and rho methods but raises runtime errors when they are called. It presents a valuation setup using a binomial Cox–Ross–Rubinstein engine and reports that price, delta, gamma, and theta…
The document examines the probability that realized volatility exceeds at-the-money implied volatility under Black–Scholes assumptions. One response treats realized volatility as the absolute value of a single log return: because a standard normal…
The document asks how a market maker can delta-hedge VIX index options when the index itself is not directly tradable like shares. One answer identifies VIX futures as the direct hedge, reasoning that the relationship is not based on a carry arbitrage. This…
The document investigates why rates inferred from a stock option chain vary with strike. It derives an implied rate from put-call parity for a non-dividend-paying stock, then reports that observed rates form a curve rather than the expected constant level.…
The document discusses negative values arising when Dupire local variance is computed from an implied total variance surface fitted with SVI. The questioner estimates the time derivative by finite differences and finds a negative numerator or denominator,…
This discussion outlines ways to model options portfolio risk when underlying price shocks also change implied volatility. It recommends identifying risk factors such as spot prices, implied volatility, rates, and credit spreads, then applying historical…
The document defines European asset-or-nothing and cash-or-nothing payoffs and presents their risk-neutral prices. A cash-or-nothing contract pays a fixed amount when the underlying finishes at or above the strike; an asset-or-nothing contract pays the…
The document asks whether the option’s theta at a future date can be calculated from only its current total price and time remaining to expiration. The accepted answer says these inputs are insufficient: an option price alone does not identify how its value…
The document explains which extrapolation settings can be changed for a QuantLib BlackVarianceSurface. Enabling extrapolation permits values outside the surface’s defined range, while selecting an interpolation method such as bicubic changes interpolation…
The document derives the risk-neutral price of a claim that pays the value of one asset when a second asset finishes below a strike. The key assumption is that the assets follow independent geometric Brownian motions. Conditional on current information,…
The document presents a numerical problem for calculating model-free implied volatility from option prices across strikes. The variance expression sums strike-weighted option-price terms and includes a forward level that itself depends on the unknown…
The document explains how to simulate discretely monitored stock paths under geometric Brownian motion to price an arithmetic Asian call. Each path contains prices at the monitoring dates, and its payoff depends on the arithmetic average of those prices.…
The document explains why a stock can have zero expected return under a risk-neutral measure while its logarithm has a negative drift. For geometric Brownian motion with zero interest and no dividends, the log-price includes a negative volatility correction.…