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.
10,263 documents
The document considers how to turn over-the-counter FX option quotes, reported at different strikes and maturities, into a usable volatility surface. One proposed workflow starts from standard delta quotes, converts each maturity’s deltas to strikes using…
The document investigates a negative value appearing in a plotted down-and-out call price when the underlying starts below the barrier. It presents a Black–Scholes barrier pricing expression, defines its parameters, and compares that expression with an…
The document examines how credit risk and contract terms affect the Black-76 valuation of options on corporate bonds. It highlights that the forward bond price must reflect the bond’s risky market value and financing or discounting assumptions; treating a…
The question seeks a way to estimate the risk-neutral variance of an underlying stock’s gross return and considers option-implied distributions alongside estimates made from data under the physical measure. One reply assumes geometric Brownian motion under…
The note explains the convexity adjustment between forward rate agreements and interest-rate futures. It rejects the common explanation that daily futures margining alone creates the difference: collateralized FRA cash flows have a comparable reinvestment…
The note addresses why implied volatilities calculated from option prices differ across strikes. It explains that Black–Scholes implied volatility is the volatility input that reproduces a given market price under the model; when the model assumes a single…
The note explains why a CDS premium leg includes an accrual-on-default term alongside scheduled spread payments. Because default can occur between coupon dates, the protection seller is owed premium for the portion of the period elapsed since the last…
The document asks why a strongly path-dependent option’s value is written as a function of the asset price, time, and an accumulated quantity. The payoff depends on a path summary defined as the time integral of a function of the asset price and time. Since…
The question describes using QuantLib to price options from a dataset containing contract start dates, expirations, and strikes. The proposed workflow groups contracts by expiration, supplies implied volatilities and market inputs to Heston model helpers,…
The document outlines a first-order way to estimate the mark-to-market PnL of a CDS as its maturity shortens and its market spread changes. From the protection buyer’s perspective, it expresses value using the difference between the market spread and the…
The document explains why an outright FX forward can have theta even though it has no option-style time value. It frames theta more broadly as the change in a position’s value when time advances while market inputs are held fixed. In an FX forward, this…
The document asks whether a forward price under the risk-neutral measure follows the same drift as a spot price, and examines pricing a payoff tied to a forward maturing after the payoff date. It sets out a geometric Brownian motion model for spot and…
The document derives the differential of a time integral whose integrand is a function of an Itô process. It first considers the integral of the process itself, substitutes its drift and stochastic-integral representation, and applies stochastic Fubini to…
The document addresses why option implied volatility may show a smile or a directional skew, and whether turbulent markets necessarily make one pattern more likely. Its central distinction is that a smile reflects a premium across the wings associated with…
The document derives the Black–Scholes price of a claim paying the terminal stock price multiplied by its logarithm. It changes from the risk neutral measure associated with the bank account to the stock measure, applying Girsanov’s theorem to adjust the…
The answer considers whether option positions can combine long gamma with short volatility, or short gamma with long volatility. It argues that a short-dated long straddle against a longer-dated short straddle does not provide the proposed combination, and…
The question asks how to adapt Black’s approximation, commonly used for American calls on dividend-paying stocks, to price puts when dividends are discrete. The response does not derive a put-specific version of Black’s approximation. Instead, it points to…
The discussion explains two identities used in variance swap analysis. Applying Itô’s lemma to the log of an asset price shows that its quadratic variation can be written as twice the integral of the asset’s proportional price change minus twice the change…
The document distinguishes valuing a floating-rate note from estimating its expected coupon cash flows. For valuation under a single-curve framework, one can derive forward rates from the yield curve, use them to estimate future coupons, and discount those…
The document describes a research need for reliable Heston option prices, especially for options far out of the money. The author reports that numerical instability in a current implementation produces slightly negative or oscillating prices, which then…
The document introduces a reduced-form credit bond model in which default is represented as the first jump of a Poisson process and the hazard rate is stochastic. It writes a differential expansion for bond price as a function of time, hazard rate, and the…
The document contrasts local volatility models, where price diffusion is driven by a volatility function of price and time, with stochastic volatility models that add a random volatility state coupled to the price process. It asks whether a local volatility…
The document explains how implied volatility affects option value across moneyness in the Black–Scholes framework. Put–call parity links a deep in-the-money call to an out-of-the-money put, so their volatility sensitivities are qualitatively symmetric. This…
The document investigates why two R packages produce different values for an American call using the Barone-Adesi–Whaley approximation. The answers identify two interface issues: one function takes spot before strike while another expects strike before spot…