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 clarifies that a partial differential equation’s linearity depends on how it involves the unknown function and its derivatives, not simply on whether volatility is constant. In the heat-equation form presented, the unknown and its time and…
The question outlines a Monte Carlo approach to option-adjusted spread (OAS) for a mortgage-backed security: simulate interest rates, derive mortgage rates along each path, project cash flows, discount them, average the resulting values, and find the spread…
The discussion asks how to build a static hedge for an up-and-out call on the S&P 500. Its central point is that European options alone generally cannot provide an exact static hedge for a barrier option. A barrier’s payoff depends on whether and when the…
The document explores extending the Heston stochastic volatility model to represent mean reversion in the asset price or returns as well as in variance. The answer proposes a price-level adjustment in which the drift of log price pulls it toward a long-run…
The document examines how volatility affects the risk-neutral probability that an option finishes in the money under Black-Scholes. For a call, that probability is represented by the cumulative normal value at d2, so its response to volatility depends on…
The document explains risk-neutral pricing through a one-period binomial model with a stock and a risk-free account. When the risk-free growth factor lies between the stock's down and up factors, the model rules out simple arbitrage and defines risk-neutral…
The discussion asks where to find practice problems for market risk, with particular interest in vanilla and exotic options. Responses suggest using free FRM-style exercises and an exam with explanations, consulting Carol Alexander's Market Risk Analysis,…
The document raises a question about how to express an FX option’s delta when the trading book uses an accounting currency different from either currency in the option. Its example is a one-year at-the-money EUR call and USD put, with option and rate inputs…
This note explains why a Bloomberg VCUB option matrix may show different values for strike and straddle views. The distinction is the displayed measure: the strike view presents volatility, while the straddle view presents a premium. A premium-based straddle…
The note shows how to use the Gaussian shift theorem to evaluate an expectation involving two correlated standard normal variables. It first states the theorem: an exponential tilt inside an expectation can be converted into a shifted argument of the…
The document explains that implied volatility is the Black–Scholes volatility that matches an observed option price; it is a way to express market prices through that model, not proof of a uniquely correct price. It also cautions that the strike pattern…
The document compares pricing an at-the-money European call on a two-stock basket with a multivariate local volatility model using constant correlation and a Gaussian copula using the same correlation. It reports a result for models calibrated to each…
The document concerns a numerical issue in the Longstaff–Schwartz least-squares Monte Carlo method for valuing early-exercise options. At each exercise date, the continuation value is estimated by regressing future cash flows on basis functions using only…
The document poses a relative valuation problem: comparing callable bonds from the same issuer when their call schedules differ. It asks whether option-adjusted spread can be compared directly across those bonds, given that OAS accounts for embedded option…
The document describes an observed inverse relationship between strike and Black–Scholes implied volatility for Ibex 35 options. The author says the option prices and strikes came from daily exchange data, plots spot alongside the volatility curve, and…
The document explains how to create an implied-volatility curve from option prices generated by a Heston model. For each strike, first evaluate the Heston call price using the chosen model parameters and maturity. Then find the Black-Scholes implied…
The document explains why an RQuantLib valuation of an American option can return a price while showing missing values for delta, gamma, vega, theta, rho, and dividend rho. The accepted answer attributes this to the selected pricing engine: the simplified…
The document examines why Monte Carlo estimates of a European call option vary when the random-number seed changes. A seed determines a reproducible pseudorandom sequence, so changing it changes the simulated terminal prices and the resulting sample-average…
The document explores an analogy between the short side of a zero-investment momentum portfolio and selling a call on the broad equity market. It references research describing how momentum can suffer sharp losses when markets rebound rapidly after declines:…
The document describes problems backing out implied volatility from 30-minute options bars, especially for in-the-money contracts near expiration. The question uses a numerical root-finding approach with a short-term Treasury yield as the risk-free rate…
The document explains why a currency call option payoff can be calculated by subtracting a strike exchange rate from the market exchange rate. In the example, both values are quoted in euros per dollar, so their difference is also an exchange-rate amount,…
The question concerns pricing an American put when the underlying follows a square-root diffusion, and asks whether QuantLib-Python can use its SquareRootProcess class. The author proposes parameter values for mapping the stated process to that class, but…
The document explains the sign of convexity for payer and receiver swaptions by starting with the underlying interest rate swap. A payer swap pays fixed and receives floating, so it benefits when rates rise. However, the gains from higher rates are…
The document explains how traders summarize the shape of an implied volatility smile or skew. It defines the risk reversal as the difference between 25 delta call and put volatilities, and the butterfly as their average relative to at-the-money volatility.…