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 market curve calibration and trade valuation can use different collateral assumptions. Its example is a EUR/USD cross-currency swap with basis: the collateral currency affects which discount curves apply to each currency’s cash…
The document describes a least squares approach to infer discount factors from a set of benchmark bond prices. It represents each bond price as the sum of its cash flows multiplied by discount factors, then models each discount factor as a polynomial in time…
The document describes a proposed tree-based approach for valuing an American call with two possible exercise references: a fixed strike and a floating strike tied to a 10-day moving average. The proposed model tracks both the underlying price and the moving…
The problem considers a European payoff that pays a fixed amount below a strike and declines as the inverse square of the asset price above it. Under geometric Brownian motion with continuous dividends, the proposed value splits into two discounted…
The document collects suggested reading for someone implementing option pricing with Markov chain Monte Carlo methods. One cited paper applies MCMC to continuous-time option models, including constant-volatility, stochastic-volatility, price jump-diffusion,…
The discussion distinguishes risk-neutral preferences from risk-neutral pricing. A risk-neutral investor values uncertain payoffs by their expected value, while a risk-neutral world is a hypothetical setting in which such preferences imply risky assets earn…
The discussion explains why Gatheral's SVI smile is parameterized in implied variance rather than volatility or total variance. Variance is a natural scale because the model is linear in variance in the far strike wings. This makes the asymptotic slopes,…
The discussion asks whether the Feller condition, expressed through the Heston variance parameters, should be enforced when calibrating option prices. The motivating examples reportedly place the condition close to its boundary, with some parameter sets…
The document asks how to obtain discount factors for payment dates that do not align with standard swap payment schedules, using a forward starting long-dated interest rate swap as an example. Such cash flows may fall between dates supported by a…
The document asks how to recover the SABR parameters for the lognormal case, where beta equals one, from the local Taylor expansion of implied volatility around the forward. It labels the constant term as at-the-forward volatility, the linear coefficient as…
The note explains why EURIBOR remains widely used in European swaps and floating-rate notes despite the shift toward overnight risk-free rates such as €STR. It distinguishes EURIBOR from Euro LIBOR: Euro LIBOR was little used and ceased following regulatory…
The document asks how the floating leg of an interest rate swap referencing a risk-free rate is determined over a multi-month accrual period. It contrasts using a forward-looking rate known at the start of the period with compounding daily observed overnight…
The document explains why vega is less straightforward in stochastic volatility models than in Black–Scholes, where volatility is a direct input. It describes two common bump-and-reprice interpretations: a model Greek, formed by perturbing model parameters,…
The document describes a question about pricing instruments by simulating share prices with geometric Brownian motion, calculating a payoff on each path, and averaging many simulated payoffs. The author reports that estimates can have very different…
The note derives the Black–Scholes call delta by differentiating the call-price formula with respect to the current stock price. Applying the chain rule produces terms involving the normal density and the sensitivities of the two standardized variables. An…
The note introduces the Heston stochastic volatility model, in which the stock price and its variance evolve together, with correlated shocks. It gives the risk-neutral characteristic function for log stock price and defines its component expressions. These…
This explanation motivates common boundary conditions for pricing a European call under the Heston stochastic-volatility model. At maturity, the option equals its payoff; when the underlying price is zero, the call is worthless. As the underlying price…
The document frames a Greeks estimation problem for a derivative paying the square root of the positive part of the difference between the terminal stock price and the strike. It assumes geometric Brownian motion and writes the terminal price distribution…
The document sets up a comparison between two ways to price European calls under the Merton jump-diffusion model: the analytical Poisson-weighted Black–Scholes series and a numerical Carr–Madan Fourier inversion. It outlines the characteristic function, the…
The document explains intuitive bounds on VIX futures using forward-starting volatility and variance swaps. A volatility swap reflects expected future volatility, while a variance swap reflects expected squared volatility. Because the square-root function is…
The document poses a pricing question for an American put on a non-dividend-paying stock. Its strike declines over time at the risk-free rate, and the stock is assumed to have constant volatility. This setup makes the contract different from a standard…
The document introduces binomial trees as discrete-time, lattice-based models for option valuation. At each step, the underlying instrument is assumed to have two possible price moves, producing a branching set of possible paths through time. This structure…
The document explores whether probability distributions can be derived as solutions to differential equations, motivated by the Black–Scholes–Merton model. It questions whether dynamic hedging is best understood as a modeling assumption that leads to an…
The document outlines single-curve construction from market quotes for instruments such as deposits, forward rate agreements, futures, and swaps. A parameterized discount curve is fitted by repricing those instruments, typically through optimization over…