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 the link between an option’s Black–Scholes value and the cost of replicating its payoff. It asks whether continuous rebalancing creates a loss from buying the underlying after it rises and selling after it falls, even when trading is…
The document explains how to interpret an FX forward quote and calculate the implied funding yield and FX basis. Under covered interest rate parity, the forward exchange rate relates spot, the two currency interest rates, and the accrual period. Rearranging…
The document distinguishes tranche implied correlation from base correlation in collateralized debt obligation pricing. Implied correlation is the correlation input in a chosen copula model that reproduces the market price of one tranche. Depending on the…
The discussion concerns calibrating a Dupire local volatility model and asks whether the Andreasen and Huge interpolation method is robust and widely used. The response frames the choice of method around the source of concern, especially how implied…
The document considers how to price and hedge an option on EUR/CAD when EUR/USD and USD/CAD markets are available. It constructs the cross rate by multiplying the two quoted rates, with the quote convention needing careful attention. It then treats that…
The document explains why, under an equivalent martingale measure, traded asset prices have drift equal to the short rate when expressed relative to a risk-free money-market account. The key definition is that each discounted asset price must be a martingale…
The document asks how to define a shock to a system driven by credit default swap spreads. It offers one possible measure: an increase in spreads, with a threshold chosen to mark when that increase qualifies as a shock. It does not provide additional…
The discussion distinguishes two related questions: whether short-maturity options have higher implied volatility levels, and whether their implied volatilities fluctuate more. It attributes greater short-term movement partly to recent realized volatility…
The document presents a numerical attempt to recover a local volatility surface from market implied volatilities using the Dupire equation. The author interpolates a grid of strike and expiry observations, estimates the required first and second derivatives…
This document raises questions about applying Itô calculus to geometric Brownian motion, including why the squared Brownian increment contributes a variance term and whether it is reasonable to remove the random component from the stochastic differential…
This note asks how to price a three-month European put when a single cash dividend is expected before expiry. For the no-dividend case, the question supplies Black–Scholes inputs and a computed put value. The answer suggests approximating the dividend’s…
This note explains why a QuantLib SABR swaption volatility cube does not take a separate shift input. The shift is obtained from the supplied at-the-money volatility surface and applied across the smile, including out-of-the-money strikes. Consequently, the…
The document examines the relationship between a state-dependent expectation for a diffusion and the conditional expectation given the process’s history. For a Markov process, the function of time and current state defined by the expected terminal payoff…
The document asks how to derive the dynamics of a forward price formed as the ratio of two zero-coupon bond prices in the Vasicek interest-rate model. Its proposed calculation applies Itô’s product rule to the numerator bond price and the reciprocal of the…
The document presents a two-period binomial option-pricing exercise with a specified initial asset value, up and down factors, interest rate, and strike. It asks for prices of an American put, an American call, and an American claim whose payoff is the…
The document raises practical questions about valuing put protection on a fund with a strong historical record and relatively stable volatility. It asks whether the fund price can serve as the underlying in a Black–Scholes framework, how to account for…
The document sets up a claim replication problem in a Markovian stochastic volatility model. An asset price and its variance evolve with correlated Brownian shocks, and two additional traded assets are represented as smooth functions of price and variance.…
The document explains how swap rates can be used to infer zero-coupon rates under a single-curve framework. Each swap rate gives a valuation equation involving the floating rates paid over its schedule. With swaps of progressively longer tenors, these…
The document explores why a positive future cash flow from an uncollateralized derivative is sometimes described as economically similar to lending to the counterparty. The question challenges the idea that the recipient must literally borrow to realize a…
The document sets out the valuation equation for a perpetual coupon-paying defaultable bond in a structural credit model. It gives the differential equation and a general solution containing unknown constants, then specifies boundary conditions: bond value…
The note diagnoses why a manually calculated one-year forward rate does not match a displayed Treasury forward quote. The key issue is that the initial one- and two-year rates are coupon bond yields, rather than zero rates. Coupon yields cannot be…
The note explains a separation argument used when deriving an option pricing PDE under stochastic volatility. If an expression involving the option price and its derivatives equals another expression involving a traded volatility-related instrument and its…
The document considers Monte Carlo estimates of a vanilla European call compared with the Black–Scholes value, asking why the estimates diverge as volatility rises. Each simulated path depends on volatility and random draws; greater volatility spreads…
The discussion asks whether a stock forward priced using the risk-free rate creates an expected profit for a long investor when the stock’s physical-measure expected growth rate is higher. The responses distinguish expected return from arbitrage: holding the…