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 how to translate a USD Libor curve into an equivalent EUR funding curve. Its central method is to convert EUR into USD at spot, accrue the USD cash at the relevant Libor rate, and convert it back to EUR at a forward FX rate. Comparing…
The document considers which volatility input to use when pricing options on futures with the Black model or a binomial tree. Its central point is that the appropriate volatility depends on the asset class and on which instrument provides the most relevant…
The document explains why variance swaps can serve as vega hedges and distinguishes several meanings of vega. A variance swap has sensitivity to its variance strike; option vega may instead refer to sensitivity to a parallel volatility shift or to changes in…
The document shows how a Taylor approximation connects a variance swap expression to the correction term in the VIX variance formula. It begins with the logarithmic forward-to-reference-level ratio in the continuous-strike expression and rewrites the ratio…
The document shows how a pair of European calls on the same underlying, with the same maturity, can imply an upper bound on the risk-free rate. The example uses a lower-strike call priced at 12 and a higher-strike call priced at 3, with strikes of 40 and 50…
The document asks how to build a USD multi-curve setup for trading Fed Funds and Eurodollar futures, with Fed Funds and three-month LIBOR forecast curves. It compares discounting from an OIS curve based on effective Fed Funds with using the Interest on…
The document derives a futures rate from the expected value of a money-market rate in a one-factor Heath–Jarrow–Morton framework. Using the bond-price dynamics, it obtains a convexity term expressed as an integral involving bond volatilities. The adjustment…
The post asks how to solve the Black–Scholes heat-equation formulation for an up-and-out call. It contrasts the option's absorbing barrier condition with the vanilla call problem and the down-and-out case, where a reflection construction is suggested. The…
The answer explains why the at-the-money caplet formula contains the forward rate for the accrual period. It assumes that this rate follows a lognormal process under the forward measure associated with the bond maturing at delivery. Discounting the expected…
The discussion separates the computational cost of option pricing from the difficulty of modeling market values. Under Black–Scholes–Merton assumptions, a European option has a closed-form price with little computational work. American options require…
The document asks how to assign an overall buy or sell direction to a complex order containing several options and a stock leg, and how to recognize an identical order versus one with every leg reversed. Its central lesson is that a structure’s direction…
The document describes a practical problem in calibrating a SABR volatility model: the fitted volatility smile differs substantially from implied volatilities observed for S&P index calls. The question identifies the market inputs needed for the calibration,…
The note addresses how to value an uncollateralized swap when the bank must fund its exposure. It describes two equivalent framing choices: discount cash flows using a curve that reflects the bank’s unsecured funding rate, or use OIS discounting as the base…
The document sets up an equity log-price as a function of firm asset value and time, plus a mean-reverting market-noise component. It gives real-world dynamics for the asset value and noise, then applies Itô’s lemma to obtain the drift and two diffusion…
The document explains how a change from the real-world measure to a risk-neutral measure can alter diffusion drifts while preserving instantaneous volatility and correlation. In a geometric Brownian motion example, the market price of risk shifts the…
The document asks whether a payoff equal to the square of the terminal stock price is worth the initial stock price squared grown at the risk-free rate. The response explains that taking a power does not commute with taking an expectation: convexity makes…
The document examines how the Heston stochastic volatility model changes when moving from the historical probability measure to the risk-neutral measure used for derivative pricing. It describes how the variance risk premium shifts the variance process…
The document explains how to value an American call on a non-dividend-paying stock with a risk-neutral binomial tree. At each node, the option value is the greater of its immediate exercise value and its discounted expected value at the next step, using…
The document sets up a short-rate model with mean reversion, square-root diffusion volatility, and independent positive jumps whose sizes follow an exponential distribution. It presents the pricing PIDE for a security paying a function of the terminal rate…
The document discusses a one-period, two-state replication of a forward using stock and cash. The stock holding is chosen to match the difference between the forward payoffs across the two future states, and the cash position makes the combined portfolio…
The document asks whether an option buyer who initially delta hedges using the option’s implied volatility should keep using that original volatility or update the hedge as implied volatility changes. The response says accurate dynamic hedging requires…
The document discusses Fourier-based pricing of European calls using a model’s characteristic function. It presents an integral representation that expresses the call price through two probability terms and asks how the formula is derived, when it applies,…
The document explains how to estimate simulation error when pricing an option with Monte Carlo. It identifies the relevant quantity as the standard error of the estimated price, calculated by dividing the estimated standard deviation of simulated outcomes by…
The document asks how to adjust discounting and projected forward rates when valuing collateralized derivatives under a CSA currency with no directly quoted swap or OIS curves. Its response says that FX forwards, local-currency rates, and collateral discount…