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 describes Markov-functional interest rate models as low-dimensional representations of the term structure built from functions of a Markov process. It notes their ability to calibrate to market prices and capture volatility smiles, while raising…
The document examines how a short three-month SOFR futures position compares with a short single-period swap (SPS) over the same accrual period. Its answer emphasizes that the IMM dates and exact number of days matter when matching the instruments’ rate…
The discussion clarifies that a probability calculated from option implied volatility is not automatically a real-world forecast. Under Black–Scholes assumptions, the probability of finishing below a strike differs depending on the chosen pricing measure:…
The question asks whether the normal or shifted log-normal model is the industry standard for pricing swaptions during negative-rate conditions, with the stated purpose of supporting credit valuation adjustment work. The response does not choose between…
The discussion explains why a risk-free rate appears in asset pricing and why its sign is not fixed. One account treats the rate as compensation for lending money and giving up access to it until repayment. Other explanations emphasize time preference,…
The discussion addresses why discount factors inferred from put-call parity across strikes may appear nonconstant. The key missing input is dividends: the basic parity equation without dividend treatment does not describe the relationship correctly when the…
The note shows how to establish that a call and put have the same vega when they share the same forward underlying, strike, maturity, and volatility inputs. It starts from put-call parity, which expresses the call-minus-put price difference as the forward…
The note asks for the risk-neutral dynamics of a zero-coupon bond whose price is exponential-affine in a short rate following a linear diffusion. It gives the time equations for the affine coefficients and compares applying Itô’s lemma to the bond price with…
This thesis-related question asks how to choose bounds for the Heston model parameters kappa, theta, sigma, and rho when generating synthetic data to train a neural network for calibration. It compares one published set of ranges, described as excluding…
This discussion considers a European call with an early-exercise feature that lets the holder exercise a portion and receive that portion’s current Black–Scholes value. The proposed replication is to hold the call and sell the corresponding fraction whenever…
This short discussion addresses how to calculate the maturity amount for an overnight index swap over a short accrual period. It distinguishes a simple interest calculation over the full period from compounding a sequence of overnight rates. The answer says…
This discussion explains why a bond’s coupon is not a reliable stand-in for its credit spread when assessing a CDS–bond basis trade. A coupon includes compensation tied to the bond’s cash flows and market interest rates, while the z-spread measures the…
The document poses a valuation question about floating-floating cross-currency basis swaps whose coupons reference overnight risk-free rates and whose discounting uses the same rate. It cites a par-value expression for a basis swap and notes that its…
The document describes a calibration problem for a Libor market model used to value a Bermudan swaption. The proposed volatility structure has a parametric time-to-maturity shape and period-specific scaling factors, while correlations follow an exponential…
The document explains how a 30/360 day-count convention affects discounting dated bond cash flows. Under this convention, elapsed time is computed by treating months as 30 days and years as 360 days, with details depending on the specific convention used.…
The document introduces a lookback option whose value depends on the underlying asset price and its running maximum. It defines the underlying as a diffusion process and presents the running maximum as the limit of an integral-based approximation using…
The document examines whether a futures contract’s price relative to its underlying asset predicts the underlying’s later direction. It proposes a historical check: compare the contract’s position above or below the underlying with the underlying’s eventual…
The document addresses why option pricing under the risk-neutral measure uses the risk-free rate rather than a stock’s real-world expected return. It begins with a discrete-time replication argument: a call payoff can be matched by a portfolio of stock and…
The document asks how to compute an option-value expectation expressed as a path integral. The central practical answer is to use Monte Carlo simulation: generate many possible realizations of the stochastic process and estimate the expectation with a…
The document explains how to estimate a variance risk premium when the available inputs are probability densities rather than volatility estimates. It defines the premium, loosely, as the difference between objective and risk-neutral variance of future…
The document considers insurance payoffs that combine a financial asset with survival or death, such as an endowment paying a stock-linked amount if the policyholder survives. Its answer explains a simplifying approach: assume financial and mortality risks…
The document explains how to value the EUR leg of a EUR-GBP cross-currency swap when GBP collateral is specified. The EUR leg needs both a three-month EURIBOR forward curve and a EUR discount curve that are consistent with GBP collateral. In theory, these…
Implied volatility is the volatility input that makes an option pricing model, such as Black–Scholes, match an option’s market price. Because each strike, maturity, and option type is a distinct contract, each can trade at a different price and therefore…
The document describes difficulty obtaining stable parameters when calibrating a two-factor Hull–White interest-rate model to cap prices. The five parameters are two mean-reversion rates, two volatility parameters, and the correlation between factors.…