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 asks when an American put and a European put on the same underlying can have equal value, motivated by checking an American put binomial-tree implementation. It notes that early exercise does not benefit a call on a non-dividend-paying stock, so…
The document asks how to value a discretely sampled arithmetic Asian option at an intermediate time using Monte Carlo simulation. It gives a simplified setup with three observation dates, zero interest rate, zero strike, and a single simulated path. At the…
The document explains a change in integration order used when taking the Fourier transform of a call option price expressed as an integral over terminal log prices. The payoff contributes only when the log price exceeds the log strike, so the original nested…
The document considers a stock whose drift follows a correlated Vasicek short rate, and asks how to simulate the stock price when the integrated rate is random. It presents the exact stock-price expression in terms of the integrated short rate and stock…
The document examines an FX option whose payoff is denominated in the foreign currency. It rewrites the payoff of a call on the exchange rate as a scaled put payoff on the reciprocal exchange rate, then compares two proposed Black-Scholes-style expectation…
The document explains how a constant maturity swap (CMS) rate payoff differs from the payoff of a vanilla swap. A vanilla swap's value depends on both the rate difference and the swap's DV01, which itself varies nonlinearly with the underlying rate. A CMS…
The note outlines a way to express a Eurodollar futures rate when the short rate follows a Vasicek process. It treats the futures settlement rate as the risk-neutral expectation of the three-month LIBOR rate at its fixing date. LIBOR is written as an…
The note considers how to extend an equity local volatility model, initially calibrated to vanilla options, so it can also match liquid quanto option prices. It outlines an approach based on market smiles: use the liquid FX smile and calibrate a compo option…
The note explains why a corporate bond can show different sensitivities to Treasury-rate shifts and option-adjusted spread shifts. It distinguishes duration measured by moving the Treasury curve while holding the OAS fixed from spread duration measured by…
The question frames a best-of-seven series bet as a binary payoff and asks how to reproduce it using wagers placed on individual games. It proposes estimating the value of the position after the first game from the remaining-game win probabilities, then asks…
The document asks how to construct an FX forward curve from basic concepts such as interest rates and discounting, using EUR/USD as an example. It raises the roles of instruments such as IMM dates and overnight index swaps, but the response does not explain…
The document shows how to fit SABR model parameters to a set of observed option volatilities using Python and QuantLib. It computes model volatilities for each strike, measures the root mean squared difference from market quotes, and uses a constrained…
The document asks what implied volatility represents in vanilla option pricing and whether fitting it to market prices can reveal mispricing. It contrasts treating volatility as the adjustable input to Black–Scholes with an alternative parameterization that…
The document derives the risk-neutral drift for the one-factor Schwartz commodity model. Starting from a mean-reverting process for the logarithm of spot price, it applies a constant Brownian-motion measure change. The resulting drift retains the…
An inverted volatility surface can reflect market conditions, but sparse or unreliable option quotes may make its shape misleading. In the ONDK example, strikes are widely spaced and bid-ask spreads are broad, leaving too few useful observations to estimate…
The document describes how to estimate cross-gamma for an instrument whose value depends on multiple underlying spot prices. Cross-gamma is the mixed second derivative of value with respect to two different spot levels, and it appears off the diagonal of a…
The document asks how the discount rate used in Current Expected Credit Loss accounting differs from rates used in market pricing. It describes the CECL discount rate as an effective interest rate (EIR), represented by a single number, and contrasts this…
The document studies a linear stochastic differential equation with both additive and state-dependent drift and diffusion. It starts from an integrating-factor solution, writing the process as a product of a stochastic exponential and a second process that…
The document asks whether a forward market model (FMM), extending the classic LIBOR market model to handle backward-looking risk-free rates (RFRs) and term rates together, has been combined with stochastic volatility such as SABR. The motivation is pricing…
The exchange discusses estimating an option’s future price after a specified move in its underlying when future implied volatility is unknown. One approach is to make explicit assumptions about both the underlying price change and the change in implied…
The document raises a derivation question about two binary call options under a risk-neutral geometric Brownian motion model. It states the familiar form for an asset-or-nothing call, whose payoff is the underlying asset when its terminal price exceeds the…
The document distinguishes the drift used to price derivatives from the drift used to simulate future underlying prices. Under the risk-neutral measure, derivative valuation uses the relevant risk-free rate; for a real-world simulation of potential future…
The document sets up a payer forward contract entered at zero value and later offset by a receiver contract on the same accrual period. Subtracting the two terminal cash flows yields a payoff proportional to the change in the forward rate between the entry…
The document asks where to obtain historical overnight index swap rates across a range of maturities, motivated by pricing foreign exchange options. It distinguishes a single overnight benchmark such as the Effective Federal Funds Rate from a full OIS curve,…