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 distinguishes the efficient market hypothesis (EMH) from the random walk hypothesis (RWH). EMH describes prices incorporating available information continuously; RWH says price changes are not predictable and follow a random walk. A random walk…
The discussion examines whether option-adjusted spread can support comparisons among bonds with embedded options, plain bonds, and floating-rate instruments, and whether a plain bond’s OAS matches its Z-spread. It also asks whether an OAS curve can help…
The post studies option pricing under a time-dependent Heston model in which mean reversion changes across time intervals while other listed parameters are held fixed. It compares prices from an Elice method and two Monte Carlo approaches, Milstein and…
The response defines delta-one products by their theoretical sensitivity to the underlying: a change in the underlying produces a corresponding change in the product’s value, giving a delta of one. It adds that the sensitivity should remain constant,…
The document outlines a proposed workflow for pricing a quanto option: estimate marginal distributions for the underlying asset and exchange rate, connect them with a copula, then calculate the expected payoff under the resulting joint distribution. Its main…
This document asks why a 15-period binomial model gives an unexpected value for an American put under specified Black–Scholes assumptions. It does not provide a corrected price or a specific diagnosis. Instead, the response offers a general debugging…
The document explains a practical way to quote a binary call by approximating its payoff with a call spread. A seller of the binary can buy a spread around the strike; the spread’s cost provides a replication-based estimate of the option’s price. The…
The question derives a replication-error expression in which the difference between assumed local volatility and realized volatility is multiplied by option gamma over time. It interprets the sign: for positive gamma, assuming volatility above realized…
This note examines a fixed-rate bond with a five-year first coupon period followed by semiannual coupons. In the described QuantLib setup, the calculated yield is below the coupon rate even though the bond is issued at par; the author reports that Bloomberg…
This note asks how to value a floating-rate note in a short-rate tree when the tree contains time steps between an IBOR fixing date and the coupon payment date. It proposes valuing backward from each fixing-date node by considering reachable payment-date…
The discussion clarifies how risk-neutral pricing connects to delta hedging and the Black–Scholes equation. In a standard setup, a self-financing hedged portfolio is locally risk-free, so its return is tied to the financing rate. The stock’s real-world…
The document examines a derivation of the change of Brownian motion between the risk-neutral measure and a bond's forward measure in a Heath-Jarrow-Morton interest-rate framework. The original argument derives a discounted bond price under the forward…
The document explains how to approximate the curvature of call prices around an at-the-money strike when option strikes are unevenly spaced. Since the risk-neutral density is related to the second derivative of call price with respect to strike, the method…
The document investigates why QuantLib’s finite-difference Black–Scholes engine produces American put prices that diverge from a reference spreadsheet when discrete cash dividends are scheduled near expiration. The question reports that call prices are close…
The document presents a slow nested-loop implementation for pricing European calls, Asian options, digital calls, and up-and-in barrier calls under the Merton jump-diffusion model. It motivates the problem as a comparison with the exponential variance-gamma…
The discussion considers how to estimate the expected termination time of an American put, counting maturity as the termination date when the holder never exercises early. One proposed approximation uses the time-zero price difference between otherwise…
The document clarifies how to apply Itô’s lemma to arithmetic Brownian motion written as a deterministic time term plus a scaled Brownian process. The key point is to define a function of two arguments, time and the current process value, then take the…
The document addresses why a futures price is modeled as a martingale under the risk-neutral measure even though its expected path under the real-world probability measure may rise. Daily settlement and the absence of a futures contract’s funding cost…
The document examines delta hedging a quanto call when the underlying is priced in a foreign currency and the portfolio is accounted for in a domestic currency. A hedge based only on the foreign share count misses the currency conversion: the domestic value…
The document explains why a simple interest-rate-differential formula may fail to match observed three-month FX forward points. It identifies cross-currency basis as the key market adjustment that emerged prominently after the global financial crisis. The…
The document derives a lower bound for a European put on a non-dividend-paying stock by comparing two portfolios. One portfolio holds the put and one share; the other holds a zero-coupon bond that pays the strike at expiration. At maturity, the put-stock…
The document asks how a delta-hedged portfolio of two options leads to a Black–Scholes pricing equation, including a term for the underlying asset’s market price of risk. It writes the portfolio as one option minus a delta-scaled position in another, then…
The document asks whether a closed-form valuation exists for an American down-and-out call whose principal amortizes linearly with elapsed time if the option is knocked out. It frames the payoff as a possible time-dependent rebate and compares the problem…
The document derives a self-financing replicating portfolio for a European put in a Black-Scholes market with a risky asset and a deterministic bank account. Applying Itô’s lemma to the option value and matching the diffusion terms identifies the risky-asset…