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 derives a conditional expectation of cumulative inflation when nominal and real short rates follow correlated mean-reverting Gaussian diffusions. It first writes each rate as its initial value, an integrated drift contribution, and a stochastic…
The document considers an OTC swap intended to offset deviations of stochastic contract cashflows from their expected values. It frames the central pricing question as determining the premium for taking on that residual variability, which may arise from…
The document proposes a way to construct model inputs for year-on-year and zero-coupon inflation options when example quotes are unavailable. Comparing yields on Treasury Inflation-Protected Securities with yields on nominal Treasury securities of similar…
The document outlines a first-order and second-order method for assigning daily option profit and loss to delta and gamma. Delta contribution is estimated from delta times the underlying price change, while gamma contribution uses one half of gamma times the…
The document asks how to build a non-USD discount curve for EUR/USD and GBP/USD mark-to-market basis swaps collateralized in USD. The proposed construction uses forward rates for the short end and cross-currency basis swaps at longer maturities. The central…
The document clarifies how to identify the cheapest-to-deliver bond in a futures contract. The seller’s relevant comparison is each eligible bond’s market price relative to its futures invoice price, which incorporates the conversion factor. The CTD is the…
The document asks whether European options can be priced in closed form when the variance gamma model’s drift, volatility, and variance rate are random. It explains that unrestricted random coefficients generally do not yield a closed-form price:…
The document shows how to replicate a payoff that is zero below a lower strike, rises linearly between two strikes, and is capped above the higher strike. The call construction is a bull call spread: buy a call at the lower strike and sell a call at the…
The document explains why a high correlation between a call option’s price and its underlying stock does not conflict with a much smaller option delta. Correlation describes how consistently the two prices move together, while delta estimates the option’s…
The document discusses what traders mean by spot volatility and how it can be expressed through traded instruments. It presents several interpretations: volatility swaps can provide exposure linked to realized volatility; options can express implied…
The document asks whether negative state prices, which may appear when extracting risk-neutral distributions from option prices, can have an economic interpretation. It describes a state price as the current value of a claim paying one unit in a particular…
The document describes a QuantLib issue encountered while bootstrapping a futures-based yield curve. A FuturesRateHelper constructed with explicit start and end dates, an ASX futures type, and numeric price and convexity inputs returns a null maturity date;…
The document distinguishes the market exposure of an equity CFD from the additional risks created by the contract structure. It argues that, for the same underlying equity, market risk should be similar, while leveraged CFD trading adds liquidation risk and…
The document asks why the stated theta of an Apple put appears large when compared with its midpoint and the time remaining before expiration. The question treats the option’s value divided by theta as if it directly represented the number of days until the…
The document compares discounted cash flow intuition for stocks and bonds with derivative pricing. For an option, the future payoff is uncertain and depends on an underlying asset, so a discounted-cash-flow approach would first require a probability…
The document raises a statistical inference problem for a time series of variance risk premia derived from options and realized variance, following Carr and Wu. The author wants to assess whether the series has a statistically significant mean and considers…
The document explains how to construct curves for valuing cross-currency swaps in a multicurve framework. It starts with overnight-indexed swap discount curves and single-currency forward curves, then uses cross-currency swap quotes, spot FX, and the…
The document outlines how to price American options when the underlying pays discrete dividends. Because exercise may be optimal before expiration, the problem is treated as an optimal-stopping problem. A numerical grid method, such as a recombining tree or…
The discussion corrects a misunderstanding about the Heath–Jarrow–Morton framework. The familiar expression that determines the forward-rate drift from its volatility applies under the risk-neutral measure, where it is part of the no-arbitrage restriction.…
The document addresses how to interpret a convertible bond whose yield is negative and how to estimate its implied credit spread. The response attributes the negative yield primarily to the embedded conversion option, which has both conversion value and time…
The document compares two objective types for calibrating a one-factor Hull–White interest-rate model to caplet or similar market data. A price-based calibration minimizes differences between quoted instrument prices and prices produced by the model. A…
The document addresses an apparent conflict between the Black–Scholes relationship linking spot and forward prices and models that assign different volatility processes to forwards with different maturities. With a constant interest rate and a deterministic,…
The document explains why a payer swap’s key rate sensitivities can appear unintuitive when the swap is decomposed into a long floating-rate bond and a short fixed-rate bond. The discussion recommends measuring exposure against standard market curve pillars,…
The document considers pricing a discounted payoff that depends jointly on two equity prices at a future date. Its central point is that pricing requires a joint risk-neutral distribution; a copula is one way to construct one, but it is not the only possible…