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 how a swap’s discounting can change when the collateral poster may choose between eligible currencies. This choice resembles a cheapest-to-deliver option: the poster prefers the collateral class with the most favorable return, and the…
The document asks for intuition behind a forward variance stochastic differential equation used in rough volatility research. The displayed dynamics depend on the forward variance level, a volatility parameter, the Hurst parameter, the time to the forward…
The document investigates why a SABR calibration using Bloomberg cap volatility figures produces a poor match across strikes. The question provides an example with caplet-related strikes and volatilities, estimates a forward from interest-rate curve inputs,…
The document discusses what a payer of fixed interest on a swap can do when market rates move, distinguishing the original purpose of a fixed-for-floating swap from a wish to exit or offset it. One answer frames the floating leg as a hedge for floating-rate…
This note explains why Black–Scholes vega can look large when volatility is entered as a decimal. Vega measures the option price’s sensitivity to a one-unit change in volatility, equivalent to a 100 percentage point move. The quoted S&P 500 example has vega…
The document challenges a proposed expression that would price a down-and-out call as a scaled European call with the same initial asset price, strike, volatility, rate, and expiry. The response explains that a barrier option cannot generally be represented…
The document presents a numerical attempt to apply Jamshidian’s trick to a European put on a coupon bond. It compares the bond option’s Black-76 value with the sum of Black-76 values for options on the bond’s individual cash flows. In the example, intrinsic…
The document investigates why a QuantLib overnight index swap does not reproduce the quoted rate used to build a curve through DatedOISRateHelper. Its example compares a swap starting on the evaluation date and ending on a date that falls after a weekend…
The document asks how modified duration relates to observed bond price and yield changes when time passes and a bond’s remaining maturity shrinks. It defines modified duration as the negative proportional sensitivity of price to yield, using a derivative…
The document discusses time variables used in Haug’s presentation of the Turnbull-Wakeman approximation for arithmetic-average rate options. It identifies the option’s remaining time to maturity, the original averaging-period length, the time elapsed since…
The discussion recommends introductory references for learning probability, random variables, Brownian motion, Itô integration, jump processes, and stochastic calculus. Suggested books range from finance-focused texts by Steven Shreve to compact or more…
The document asks whether the fundamental pricing identity for an asset divided by a numeraire remains valid when their values are correlated. The answer explains that correlation does not invalidate the identity: under the measure associated with a strictly…
The document presents cost-of-carry relationships for pricing a forward on an asset that pays dividends or another yield. It gives equivalent expressions using a continuous yield or the present value of future cash flows, then states the value formula for a…
The document describes an attempt to reproduce a vendor price for a discrete arithmetic average price Asian call using the Haug, Haug and Margrabe approximation and Curran’s approximation. It lays out the inputs, reports the author’s calculated values and…
The document compares local volatility, stochastic volatility, and parameterized approaches for representing an implied volatility surface. Implied volatility is a transformed representation of European option prices, and interpolation in volatility space…
The document considers whether a single-factor Linear Gaussian Model calibrated to coterminal swaptions can price both payer and receiver Bermudan swaptions. The question arises because the two option types have different exercise boundaries and may respond…
The document clarifies the relationship between the drift of a price process and the drift of its logarithm under geometric Brownian motion. Starting from a stochastic differential equation for proportional price changes, Itô’s formula gives a log-price…
The document distinguishes the current VIX level from the behavior of VIX as market conditions change. VIX squared corresponds to a variance swap strike, and the answer uses an analogy with a stock whose current price does not depend on its instantaneous…
The document explains why a Black–Scholes European call with an extremely long maturity may be priced close to the current stock price. Under positive growth conditions, the stock is expected to become much larger than the strike over a sufficiently long…
The document considers a cross-currency basis swap and an offsetting hedge booked with different counterparties under different collateral agreements (CSAs). Because one trade is collateralized in euros and the other in dollars, a move in cross-currency…
The document addresses how effective and maturity dates are set for forward-starting interest rate swaps when a forward-period date falls on a non-business day. It distinguishes a swap-dealer convention, which aligns the forward swap with the date schedule…
The document explains how Eurodollar futures can provide a strip of implied forward rates and how those rates can be used to construct a fixed-for-floating interest rate swap rate. For payment dates, the forward floating rates are weighted by discount…
The document examines a Monte Carlo valuation in which a simulated American call on a non-dividend-paying stock is priced slightly below a European call with the same strike and maturity. The example fits a Student t location-scale distribution to historical…
The document derives an arbitrage-free price for a European call whose underlying is the geometric mean of several stock prices. It assumes each stock follows risk-neutral geometric Brownian motion with a common interest rate, individual volatilities, and…