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 clarifies the relationship between a bond position, duration, and convexity. It distinguishes a long position in a conventional coupon bond, which has positive duration and convexity, from a short position, which has negative convexity exposure.…
The document raises a practical question about calculating potential future exposure (PFE) in an XVA pricing engine. It distinguishes the valuation of a derivative at a future horizon from the market inputs used to obtain that valuation. Curves and implied…
The document explains how to value a fund arrangement in which party B receives scheduled proportional payments, party A covers a shortfall at maturity, and party C receives any surplus. Under risk-neutral valuation, the terminal claims of A and C are priced…
The document derives the cash account needed to keep a portfolio self-financing when its stock holding changes over time. Portfolio value is written as the shares held times the stock price plus the balance in an interest-bearing account. Applying the…
The document explains a QuantLib credit default swap calibration failure that occurs with a higher assumed recovery rate for the supplied market spreads. The calibration seeks risk neutral survival probabilities by solving for curve parameters. If the inputs…
This exchange clarifies how QuantLib curve constructors interpret rate inputs in a Hull–White short rate simulation setup. A FlatForward curve is built from a single forward rate quote, so passing an array of rates to its scalar quote object causes a type…
The document diagnoses an error in a currency option valuation using a six-step binomial tree. The calculation sums discounted payoffs across terminal nodes but weights each node only by the risk-neutral probability of one particular sequence of up and down…
This discussion outlines how optimal control concepts apply to quantitative finance. In dynamic portfolio construction, an investor allocates capital across instruments while accounting for expected returns, risk, and the costs of changing positions over…
This discussion separates the theoretical SABR model from formulas used to approximate its implied volatility. It examines a case with very high vol-of-vol where prices calculated by inserting Hagan implied volatilities into Black–Scholes appear to violate…
The document asks how to reduce Monte Carlo estimation error when pricing vanilla options under the Heston stochastic volatility model. The questioner reports that Black–Scholes controls using implied, average, or long-term volatility have not worked well,…
The document introduces the Black–Scholes derivative of an option’s value with respect to its strike, often called dual delta. It gives the call and put formula and asks how to interpret the measure in practice when an option’s strike is fixed during the…
The document examines how to simulate a local volatility model calibrated from European options using Dupire’s formula. It presents the Euler–Maruyama step, which evaluates volatility at the current time and state and holds it over the next interval. The…
The document examines a currency-options parity exercise and questions whether the reciprocal of a lognormal exchange rate can be priced with the same Black–Scholes setup. It derives the reciprocal rate’s log distribution, observes that the variance…
The document asks how exchanges obtain implied volatilities and Greeks for American-style stock options, where early exercise makes direct use of standard European option formulas unsuitable. It suggests that a computationally manageable tree or…
The document asks whether a stock’s dividend value under a Gordon-style discounted cash-flow model should include an additional option to sell when its market price exceeds the present value of future dividends. It frames the ability to liquidate before an…
The document explains why a trial-and-error Black–Scholes calculation can return a range of implied volatility estimates that appear to reproduce the same option price. The cause is limited numerical precision: the search stops when the difference between…
The document presents a conceptual question about risk-neutral valuation and the law of one price. It asks how equal expected cash flows could imply equal current prices, given that realized cash flows may differ and a trade intended to exploit a price…
The document asks how the transition from EONIA to the euro short-term rate (€STR, called ESTER in the text) could affect discounting for new and existing derivatives, curve construction, and the treatment of any basis between the rates. The question is…
The document raises a modeling question about representing a jump-diffusion process in discrete time. It notes that Amin (1993) presents a convergent discrete version, but describes it as computationally inefficient and non-recombining. Other proposed…
The document considers how binary options differ conceptually from casino bets. One answer distinguishes the underlying risk: financial contracts can reference economic outcomes that matter to investors and businesses even without the contract, such as…
The document derives European put-call parity by comparing a long call and short put at the same strike and maturity with a long forward contract. Their terminal payoffs match in every case: above the strike, the call pays the difference; below it, the short…
The question asks for an intuitive explanation of the Black–Scholes result that an at-the-money call's delta approaches one as volatility tends to zero when the risk-free rate is positive. The poster understands the formula but is trying to interpret its…
The document explains why a probability density evaluated at a standardized observation differs from the density on the original measurement scale. If a variable with mean and standard deviation is transformed to a unit normal variable, its density changes…
The document asks how to determine whether a market with a stock, a bond, and call options admits arbitrage when the option’s time-zero price is unknown. It proposes using the stock and bond alone to derive a range of state prices, then checking whether…