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.
8,116 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 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 considers whether varying the autocall level of an autocallable bond can reproduce the value of an issuer-callable bond priced with an optimal exercise policy. It explains that the issuer-callable bond is no more valuable than an autocallable…
The document explains the leverage effect by separating a company’s enterprise value from its financing. In a simple example, a business owns a gold asset and has fixed nominal debt. As the asset value changes, the debt claim stays fixed while the residual…
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 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 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 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 investigates why a SABR calibration using Bloomberg cap volatility figures produces a poor match across strikes. The question provides an example with caplet-related strikes and volatilities, estimates a forward from interest-rate curve inputs,…
This note explains why Black–Scholes vega can look large when volatility is entered as a decimal. Vega measures the option price’s sensitivity to a one-unit change in volatility, equivalent to a 100 percentage point move. The quoted S&P 500 example has vega…
The document challenges a proposed expression that would price a down-and-out call as a scaled European call with the same initial asset price, strike, volatility, rate, and expiry. The response explains that a barrier option cannot generally be represented…
The discussion explains how traders can ask for options on an unlisted stock, additional strike prices, or longer expirations. It says an exchange may accept suggestions, but a request alone does not guarantee a listing. Stocks must satisfy exchange…
The document presents a numerical attempt to apply Jamshidian’s trick to a European put on a coupon bond. It compares the bond option’s Black-76 value with the sum of Black-76 values for options on the bond’s individual cash flows. In the example, intrinsic…
The document discusses time variables used in Haug’s presentation of the Turnbull-Wakeman approximation for arithmetic-average rate options. It identifies the option’s remaining time to maturity, the original averaging-period length, the time elapsed since…