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 investigates why a EUR/USD discount curve bootstrapped from a single cross-currency basis swap helper does not make a constructed EUR leg’s net present value zero. The example builds SOFR and €STR curves, creates a three-month basis quote,…
The document asks how to query an implied volatility surface when simulating an option under a local volatility model. The surface is described in terms of log forward moneyness and expiry. For vanilla implied volatility, the questioner uses the expiry…
The question seeks binomial-model parameters that would make early exercise possible for an American call. The answer gives a general condition instead of a numerical example: a positive dividend rate or a negative interest rate is needed. Under the standard…
The discussion compares approaches to simulating the Heston stochastic volatility model, prompted by a moment-matching method that can fail when volatility of volatility is large and the Feller condition is strongly violated. In that method, equations for…
The document shows how to price a claim that pays only when a stock finishes at one specified discrete price. For an interior state, a tight butterfly made from calls at the target strike and the adjacent strikes reproduces the one-state payoff. Its…
The document explains how the time-varying drift in the Ho-Lee short-rate model can be recovered from zero-coupon bond prices implied by an initial yield curve. It presents the bond-pricing relationship and shows that the drift function depends on the second…
This note addresses apparent asymmetry between out-of-the-money put and call implied volatilities near at-the-money. It attributes the discontinuity in the displayed data to an implied-volatility calculation that uses the spot index in place of a…
This discussion explains why daily delta rebalancing can leave substantial losses when an underlying makes a large discontinuous move. In a continuous price model, frequent rebalancing can offset local price exposure, but a jump creates a move that the hedge…
The document outlines a theoretical way one country could fund another country’s borrowing at a lower apparent rate. An intermediary country could borrow in its own currency at a low rate, lend to the borrower at a somewhat higher rate, and use a…
The document asks how to derive the stochastic process for an accumulated quantity defined as the time integral of a function of a price process. The price is modeled with a stochastic differential equation whose drift is proportional to price and whose…
The document asks whether Heston model calibration requires first constructing a smoothed, arbitrage-free implied volatility surface, as is commonly needed in local volatility work. The accepted response describes Heston calibration as fitting model…
The question asks how the intensity, or hazard rate, follows from a survival function defined as one minus the cumulative distribution. For an exponential distribution with rate parameter λ, the cumulative distribution is one minus the exponential survival…
The question considers a contract that transfers ownership of an existing forward at a later date, and asks whether pricing it creates arbitrage or reduces it to a direct forward on the asset. In the example, one forward promises delivery of a…
The discussion distinguishes the mechanical calculation of yield to maturity from the risks reflected in a risky bond’s market price. Yield to maturity is derived from price and promised cash flows; it does not explicitly insert a default probability into…
The note describes a volatility surface calibrated with singular value decomposition, comparing current implied volatilities with a previous surface. For maturities without market quotes, the author extrapolates at-the-money volatility using forward…
This document asks why yield curve construction may interpolate the logarithm of discount factors and what robustness means in that context. It relays a documentation claim that linear interpolation of log discount factors keeps instantaneous forward rates…
The document asks whether theta should be combined with delta when estimating an option’s leverage and expected price change. Its example considers a call option whose delta estimates the effect of a one-unit increase in the underlying, while theta…
The document discusses the result that an American call on a non-dividend-paying stock has the same value as a European call under the model considered. The quoted explanation relates this to the discounted immediate-exercise payoff behaving as a…
The document asks how a call writer’s risk-free asset position changes over time in a Black–Scholes delta hedge. It states the stock position as the call’s delta, given as the cumulative normal distribution evaluated at d1, and proposes an initial risk-free…
The document asks how modified duration translates a yield change into a bond price change when the quoted price is expressed as a percentage of face value. Its example uses a bond quoted at 103 with modified duration of 4.62 years and a one percentage point…
The document describes fitting a one-factor Vasicek short-rate model to at-the-money cap volatilities across several maturities. It reports the input volatility term structure and the fitted mean-reversion speed, long-run rate, volatility, and starting rate,…
The document asks for the probability distribution of a European call option's price at an intermediate time under the risk-neutral measure. The response starts from the Black–Scholes pricing function, which maps the underlying asset price and time to…
The document explains how a firm can hedge counterparty credit risk embedded in a derivative portfolio and how CVA relates to the hedge. In a simplified example with zero recovery, a nonnegative derivative value is paired with a credit default swap on the…
The document asks why a volatility model should calibrate the S&P 500 index and VIX together, and whether an underlying asset’s model should use implied or realized volatility. Its answer links the indices through VIX’s construction: VIX is derived from a…