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 discussion distinguishes a put diagonal spread from a put calendar spread and explains why a proposed pair of puts with different expirations but the same strike is a calendar spread. The original example uses different strikes, but the answer notes that…
The document asks why a forward price is chosen so that a newly signed contract has zero value, and whether the explanation comes from no-arbitrage or from both parties being indifferent between taking the long and short sides. It also asks why the parties…
The document sets up a structural credit model in which a firm’s asset value follows geometric Brownian motion and default occurs when it reaches an absorbing barrier. A coupon bond pays coupons while the firm survives, pays principal at maturity if it has…
The discussion asks whether a liquid interest rate swap curve can exist without a liquid government bond market, and how dealers hedge the risk they absorb. One answer describes the typical development of local currency markets: governments issue short-dated…
The document explains how to obtain a zero-coupon yield curve and distinguishes observed spot rates from a curve calibrated to traded instruments. A curve can be interpolated from spot rates when they are available, but spot rates are generally not directly…
The document asks how option Greeks, especially delta, should be interpreted under Merton and Kou jump diffusion models. Its central explanation is that a continuous hedge cannot offset a discrete price jump instantaneously. A riskless-portfolio argument…
The document asks how to understand and implement calibration of the SABR model for volatility smiles across equity, foreign exchange, and interest rate markets. Its response points readers toward several papers and practitioner resources, and mentions a…
This collection of answers challenges widely used ideas in quantitative finance, including correlation-based diversification, CAPM as an allocation rule, normally distributed independent returns, value at risk, efficient markets, copulas, and perfect delta…
The document presents a question about a paper on deciding when to sell an asset whose price trend may be increasing or decreasing. The author is trying to understand a change of measure that is intended to simplify the model: the transformed process should…
The document gives an intuitive explanation of the Merton model’s representation of risky corporate debt. A lender to a company that cannot default would receive the promised repayment, like holding a risk-free bond. With default risk, however, the lender…
The document examines the tracking error when a trader delta hedges an option using a Black–Scholes volatility that differs from the volatility the asset actually realizes. It presents an integral relating the error to the volatility difference and the…
The document examines why a QuantLib ImpliedTermStructure appears to change shape after the evaluation date is advanced. The example compares discount factors before and after moving the date by six months. The accepted explanation is that the underlying…
The document clarifies that asking whether futures follow a physical or risk-neutral distribution depends on the purpose of the analysis. The risk-neutral measure is a pricing tool: under suitable assumptions, prices of contingent claims can be represented…
The document explains that a stock’s quoted implied volatility is inferred from option prices, rather than being a direct forecast of a one-standard-deviation move. Under Black–Scholes with constant volatility, one could estimate historical volatility from…
The document derives the near-expiry approximation for the price of an at-the-money-forward European call under Black–Scholes. It rewrites the call price using the forward price and discounts the resulting payoff expression at the risk-free rate. At the…
The note examines a pricing argument for a replicable option payoff. If a trading portfolio and the derivative have equal terminal values almost surely, their discounted terminal values also agree, so their conditional expectations under a risk-neutral…
The discussion clarifies how a state price density relates to a probability density under the forward measure in a derivation involving Dupire’s formula. The forward-measure density describes the distribution of the underlying state variables at a future…
The note distinguishes a zero-coupon bond price from the pathwise discount factor used to discount cash flows. In the Vasicek model, the bond price has an analytic expression conditional on the current short rate. The discount factor along a simulated path…
The document explains how to transform a one-dimensional diffusion into a process with constant diffusion coefficient. Applying Itô’s lemma to a function of the state shows that the stochastic term is the derivative of the function multiplied by the original…
The document explains why a total return swap’s financing spread can reflect security borrow costs and how the contract relates to an index future. A TRS buyer receives the reference asset’s total return, including dividends, while paying a financing amount…
The document outlines a workflow for representing swaption volatility data in QuantLibXL and using it to price a swaption. First, construct an at-the-money volatility matrix with the QuantLibXL matrix function. Then extend the matrix into a volatility cube…
The document explains how to interpret a default probability inferred from a credit default swap spread. A quoted CDS spread is observable, while default probability, hazard rate, and recovery are not directly observable. The simple…
The document considers how to compute the differential of a positive power of a geometric Brownian motion. It applies the Itô–Doeblin formula to the process expressed as a function of time and Brownian motion, producing a stochastic differential equation for…
The document distinguishes a curve of rates across lending tenors from a forward curve for a single LIBOR tenor. A three-month LIBOR forward curve describes rates for successive future three-month periods; it is not just today’s three-month fixing. Similar…