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 discussion explains how to express views on ECB decisions through overnight indexed swaps (OIS) spanning meeting dates. It distinguishes a view on the size of an individual meeting’s rate change, which could be structured as an option on a spread between…
The document shows how to count ordered outcomes for three six-sided dice according to their minimum value, then use those counts to reason about the expected payoff of a call-like contract with a strike of three. The counting method starts from rolls whose…
The document discusses valuation differences between bespoke structured trades, which may be marked using consensus estimates, and listed instruments used to hedge them, which may have observable market prices. The question is whether using different marking…
The document raises whether daily historical option prices can be approximated from historical closing prices of the underlying asset. It identifies Black–Scholes as one possible pricing framework and notes that the model requires implied volatility for…
The document considers why the equivalent martingale measure is unique in the standard Black–Scholes setting. Its proof outline represents a candidate measure through a positive density process and uses the predictable representation property to express that…
The document explains how to obtain the probability that a stock price modeled by Heston will finish above a specified threshold at a future date. In options terminology, this probability is the undiscounted value of a digital call on the modeled spot…
The document examines whether Itô’s lemma can derive the risk premium of a derivative without assuming in advance that it shares the underlying asset’s Sharpe ratio. It applies Itô’s lemma to a value defined as the exponential of the risk-free rate times the…
The document explains why forward Libor rates are often modeled as lognormal in Black’s framework, while clarifying that this distribution is a modeling choice rather than a requirement of no-arbitrage. By expressing a forward rate as a ratio of zero-coupon…
The discussion examines whether the risk-neutral measure, used to price securities, should also be used to forecast real-world returns. It argues for comparing predictive performance empirically rather than relying only on theoretical objections or strong…
The discussion distinguishes listed options from over-the-counter foreign exchange options. Conventional option chains are associated with listed contracts. Interbank FX options are predominantly over the counter and are usually quoted in implied volatility,…
The document discusses how to design a cross-asset pricing library that supports multiple models and numerical methods while keeping products and payoffs immutable for serialization. Its central design principle is to keep a payoff focused on contract terms…
The document shows how to derive a par coupon from a zero-rate curve. First convert each continuously compounded zero rate into a discount factor using its maturity. Then price a hypothetical coupon bond by discounting each coupon and principal payment.…
The document considers bull and bear equity performance bonds that pay periodic coupons linked to stock returns, subject to a minimum coupon. It raises a modeling ambiguity: the coupon might be a minimum plus a positive performance component, or the maximum…
The document describes a numerical failure when calculating implied volatility for American options with RQuantLib: the solver reports that it cannot bracket a root, even though the user obtains values by entering observations manually. The suggested…
The document derives a linear state-space representation for estimating parameters in a futures price model with two latent factors. The state variables follow continuous-time stochastic processes: one mean-reverts, while the other accumulates shocks.…
The document examines whether a covered call can earn a relatively reliable profit by waiting for time decay. Its example sells calls against a large stock holding, but the response points out that the stock’s price movement dominates the small option…
The document discusses an options-text exercise comparing two quarterly interest-rate payoffs: a spread involving a five-year swap rate and compounded SOFR, and a spread between compounded SOFR and a Treasury bill rate. It reports that the solution manual…
The document raises a question about why the COS method presents a characteristic-function relation specifically for Lévy processes. It notes that if a log price is represented as an initial log-moneyness plus a random log-price change, the characteristic…
The document discusses how to construct USD yield curves from publicly available data for valuing interest rate swaps and FX forwards. It distinguishes a discount curve from a LIBOR projection curve: the response recommends bootstrapping an OIS curve for…
This note examines an apparent arbitrage in put-call parity when a stock follows a zero-drift Black-Scholes process, with no interest or dividends. For a strike equal to the current stock price, parity makes the call and put prices equal. The apparent puzzle…
The document outlines an Euler–Maruyama simulation for log asset prices under a local volatility model, using volatility that varies with time and the asset level. It asks which drift to use for option valuation versus estimating the real-world chance of an…
The document asks whether the average strike and, where relevant, average implied volatility of a set of calls can be entered into one Black-Scholes calculation to approximate the portfolio’s average delta. The scenarios hold the underlying, expiry, rates,…
The document derives lower and upper bounds for a European call using payoff dominance. A call payoff cannot exceed the underlying asset’s payoff, so its price is at most the asset price. It also dominates both zero and the payoff from holding the asset…
The discussion explains why a cash-or-nothing digital call cannot generally be replicated exactly using ordinary calls and puts at strikes spaced five dollars apart. In theory, a digital payoff can be approached by a call spread whose strike gap shrinks…