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 examines why a bisection-style search for Black–Scholes implied volatility can fail for a put even when it works for a call. The key diagnosis is that the put price in the example is above the greatest value a European put can reach under the…
This document asks why a leveraged WTI exchange-traded note and its inverse counterpart appear to trace different slopes during large price moves. One note is described as providing leveraged long exposure and the other as leveraged inverse exposure. The…
The document explains how ATR-based position sizing estimates a share count from account capital, a chosen risk fraction, and a stop distance expressed as a multiple of average true range. The resulting count represents shares sized to a target loss if the…
The document addresses how to summarize implied volatility across an option chain rather than relying only on the at-the-money option. It describes a model-free variance-swap approximation built from option prices over a range of strikes: calls above the…
The document discusses how to evaluate residuals when comparing time-series forecasts, including volatility forecasts from models such as GARCH. It recommends examining autocorrelation: if errors contain predictable structure, the model may be missing a…
The document outlines several ways to think about pricing options on a volatility index such as VIX. One approach starts from the option portfolio used to replicate variance and adds a convexity adjustment that accounts for the square root linking variance…
The document considers how to recover FX option strikes from broker volatility quotes, forward points, deposit rates, and delta conventions. It explains that the ATM strike formula depends on the convention: a delta-neutral strike with premium-adjusted delta…
The document examines limitations of variance as a portfolio risk measure, especially when return distributions are not well described by a stable normal model. One example compares two hypothetical single-stock portfolios with the same variance: one has…
The document explains why investors may hold VXX despite the ongoing value decay commonly associated with contango in VIX futures. It presents two uses: a short-term directional view on volatility, or a hedge for portfolios and trading strategies that are…
The discussion considers how to infer implied volatility from option bid and ask quotes across strikes, expiries, calls, and puts. It covers estimating forwards through put-call parity, choosing representative option prices, and fitting a consistent…
The question asks how to obtain the volatility input needed to calculate an option’s Black–Scholes delta. The replies explain that this input is commonly implied volatility: the volatility value consistent with the observed market price of the option and the…
The document discusses pricing a European exchange option that pays the positive difference between two stock prices at expiry. The assets follow correlated geometric Brownian motions. One answer changes to a measure using one asset as numeraire; under that…
The document asks how to obtain implied volatility for a specific overnight period in foreign exchange, such as the night before a particular trading day. It then asks how to translate an overnight volatility quote into an implied breakeven exchange-rate…
The document asks how option Greeks, especially delta, should be interpreted under Merton and Kou jump diffusion models. Its central explanation is that a continuous hedge cannot offset a discrete price jump instantaneously. A riskless-portfolio argument…
The document distinguishes an asset’s expected arithmetic return from its compounded growth rate. Under the return model described in the question, the expected return over a short interval is given by the drift, while the continuously compounded rate…
The document asks how to understand and implement calibration of the SABR model for volatility smiles across equity, foreign exchange, and interest rate markets. Its response points readers toward several papers and practitioner resources, and mentions a…
The document examines the tracking error when a trader delta hedges an option using a Black–Scholes volatility that differs from the volatility the asset actually realizes. It presents an integral relating the error to the volatility difference and the…
The document explains that a stock’s quoted implied volatility is inferred from option prices, rather than being a direct forecast of a one-standard-deviation move. Under Black–Scholes with constant volatility, one could estimate historical volatility from…
The document derives the near-expiry approximation for the price of an at-the-money-forward European call under Black–Scholes. It rewrites the call price using the forward price and discounts the resulting payoff expression at the risk-free rate. At the…
The document asks whether an individual stock’s historical monthly return frequencies can provide a valid expected return estimate. The proposed method groups observed log returns, treats each frequency as an estimated probability, multiplies returns by…
The document outlines a workflow for representing swaption volatility data in QuantLibXL and using it to price a swaption. First, construct an at-the-money volatility matrix with the QuantLibXL matrix function. Then extend the matrix into a volatility cube…
The discussion considers a foreign-exchange volatility market maker who is long a EURUSD straddle and short a USDJPY straddle, then must quote a EURJPY straddle. It asks whether the existing positions imply an appropriate trading bias for the cross-currency…
The explanation shows how to approximate the change in an option’s value as the underlying price and time change. Expand the option price around the current underlying price: the first-order term is delta times the price move, and the second-order term…
The document clarifies that moneyness in the illustrated option pricing context is the ratio of the underlying stock price to the strike price. It addresses confusion about a paper’s graph by reproducing a related set of curves using European call prices…