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 explains why the Heston pricing framework includes a market price of volatility risk and how it relates to Monte Carlo simulation. The stock and variance processes have two Brownian drivers but only one traded risky asset, so the no-arbitrage…
The document explains how the choice of probability measure in interest-rate pricing follows from the chosen numéraire. Under the measure associated with a traded numéraire, asset prices expressed relative to it are martingales. This gives a practical way to…
The document poses a valuation problem for a forward-starting interest-rate swap in a binomial short-rate lattice. The swap begins after the valuation date, receives floating payments, pays a fixed rate, and makes payments in arrears. The questioner reports…
The document asks for a rigorous interpretation of the functional derivative terms in Bergomi’s pricing equation for a European claim. The price is viewed as depending on spot and a family of stochastic processes indexed by future times, which raises…
The document derives a zero-coupon bond price when the short rate starts at a fixed level and rises by a fixed increment at each jump of a Poisson process. The discount factor depends on the time integral of the jump count. By exchanging the order of…
The document explains why a binary call and a standard European call with matching contract inputs do not have the same delta. A vanilla call has a payoff that rises continuously with the underlying above its strike, while a cash-or-nothing binary pays a…
The document collects learning resources for someone starting with volatility modeling, especially local volatility and surface calibration. It points to a practitioner book and lectures, a thesis focused on calibrating a local volatility surface, and a…
The document explores why option-pricing ideas have not become a routine way to value risky corporate cash flows. It presents the structural analogy in which equity resembles a call option on firm assets and debt resembles a liability exposed to the firm's…
The document compares two ways to price a callable zero-coupon bond in the Ho-Lee short-rate model. One method values the bond as a straight zero-coupon bond minus a European call on that bond. The other represents the callable bond as a claim whose value…
The document poses a modeling question about pricing European options with dynamic programming. The proposed setup treats option hedging as a discrete-time, continuous-state Markov decision problem and uses a risk-sensitive action-value function: instead of…
The document gives a brief hint for a quantitative finance exercise about a European call option’s value as a function of its strike. It writes the price as an integral of the option payoff over a distribution of the underlying value, then relates…
The document is a categorized directory of online sources for finding quantitative finance research and related publications. It covers platforms that let readers search, view, or download papers; indexing services that can help locate open versions; a…
The document explains how to extend a Heston stochastic volatility option model with jumps in the underlying asset. It recommends first considering a jump diffusion such as Merton’s model, which uses lognormally distributed jump sizes, or Kou’s model, which…
The document explains why a Treasury yield-to-maturity curve cannot be used directly as a spot-rate curve. A yield to maturity summarizes the discount rate for an instrument with multiple cash flows, whereas a spot rate discounts a payment at a particular…
The document asks how to price a European-style exotic payoff equal to the square root of the stock price at the end of a one-step binomial period. Its answer uses the risk-neutral probability implied by the current stock price and the two possible future…
The document explains why a calculation of a 3M SOFR futures final settlement can differ from values in a Bloomberg historical price table. It distinguishes the daily exchange settlement, which is quoted on a futures tick grid, from final settlement, which…
The document diagnoses a mismatch between a European option’s net present value and the model value reported by a QuantLib Heston calibration helper. The example calibrates a Heston model to implied volatilities and then prices a put with what appear to be…
The document explains an arbitrage argument linking Black–Scholes option values to total variance, expressed as volatility squared times time to expiration. For otherwise comparable options, the Black–Scholes price rises with this input. If total variance…
The document explains how dividends enter vanilla index-option valuation under the Black-Scholes framework. For options written on a spot index, one response describes using a continuous dividend yield inferred from put-call parity. Another notes that actual…
The document considers how to calibrate the Heston stochastic-volatility model and narrows its response to calibration from time series. Because volatility is latent, that task can be framed as nonlinear filtering. The answer points to research methods and…
The document asks how to price a contract that gives its buyer the right to select one cashflow from a finite set in a discrete-time, arbitrage-free, complete market. The proposed approach first prices each cashflow by summing the prices of its payments,…
The document presents a Monte Carlo setup for pricing a basket option on nine currency crosses. It updates each cross over multiple time steps using lognormal dynamics, with correlated normal draws supplied in a simulation array. At each simulation’s end, it…
The document explains two relationships in a Black Scholes derivation involving implied skew. First, it shows how a no arbitrage condition links the mean and variance of log returns to the difference between domestic and foreign rates, with higher cumulants…
The document examines whether a trader can earn positive expected value from a zero-drift random walk. It presents the martingale framework: when position sizes are chosen using only past information and remain bounded, the gains process has zero expected…