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 asks how unexpected loss is treated under Basel II and presents the advanced internal ratings-based framework’s expected-loss expression, correlation and maturity adjustments, capital requirement, and risk-weighted asset calculation. Its…
The discussion compares at-the-money payer swaptions with different expiry and underlying swap terms: one-year expiry on a ten-year swap and ten-year expiry on a one-year swap. It explains that expiry affects option value through volatility accumulated over…
The document frames a valuation question about the equity component of a convertible bond under the Tsiveriotis–Fernandes approach. It distinguishes the cash component, which represents coupons and principal and is discounted at a risky rate, from the equity…
The document explains why an American call or put, with the other contract and market assumptions held fixed, is worth at least as much when its maturity is extended. The central argument is based on exercise flexibility: any stopping time available before…
The document discusses the two-dimensional term structure of lognormal implied volatility for European swaptions, varying by option expiration and underlying swap tenor. It describes a typical pattern in which volatility may rise over the shortest…
The document explains why a common Bloomberg approximation for the five-year inflation rate beginning five years ahead uses twice the 10-year zero-coupon inflation swap rate minus the 5-year rate. It contrasts that linear calculation with a compounded…
The note discusses how to represent recovery for a bond whose promised solvent-state cash flows have fallen far below its original notional. It cautions against assuming that recovery should simply be a standard fraction of face value: distressed creditors…
The note explains how to translate option sensitivities into approximate dollar gains or losses for specified changes in the underlying price and implied volatility. It defines delta and vega as changes in option value for unit changes in their respective…
The document distinguishes constant-volatility geometric Brownian motion from a model in which returns have time-varying conditional volatility. It explains that a GARCH model is fitted to historical returns, typically by estimating its parameters, and then…
This note explains a negative-time pricing error when using a QuantLib zero curve to value a credit default swap. The cause is the curve’s first date: the example builds the curve from rates beginning one month after the evaluation date, so discounting or…
The note explains the theoretical replication of a variance swap using out-of-the-money options across strikes. Its fair variance is expressed as an integral of put prices below the forward and call prices above it, weighted inversely by squared strike.…
The document distinguishes a process value, its increments, an ordinary time integral, and an integral with respect to process increments. It presents dX as notation for small changes in a process and cautions against treating it as an ordinary derivative…
The document examines a three-strike call position: buying calls at the lower and higher strikes while selling two calls at the middle strike, all with the same expiration. It asks why the position can have a negative value at inception. The replies point to…
The document asks how to choose bond positions that replicate the issuer exposures of an equally weighted CDS index. Its two-issuer example contrasts investing equal bond notionals, which produces unequal market-value weights when the bonds trade at…
The document clarifies why finite-difference descriptions for option pricing may appear to reverse the usual pairing of explicit schemes with forward time differences and implicit schemes with backward differences. It explains that explicit and implicit…
The document asks how to simulate a stochastic differential equation whose diffusion term depends on the current state as a power of the asset price. The question compares this process with geometric Brownian motion and attempts to derive a closed-form…
The document describes how a swaption trader can move from an at-the-money implied volatility surface to prices for options struck away from the money. The answer says that desk models commonly add parameters for the volatility smile and skew: these capture…
The discussion explains why discount factors are often expected to fall as payment dates move further into the future. It frames discounting as valuing later cash flows through successive periods: if each period has a discount factor below one, multiplying…
The document shows how to translate a terminal-value partial differential equation into a stochastic expectation using the Feynman–Kac formula. For the operator with diffusion coefficient proportional to the state, it identifies a geometric Brownian motion…
The document asks whether a LIBOR rate can be modeled like a stock price with geometric Brownian motion, then outlines concerns with that choice. One response argues that interest rates tend to exhibit stationarity, whereas Brownian motion does not, so the…
The document explains why two familiar closed-form geometric Brownian motion equations appear to differ. One subtracts half the variance from the exponent’s drift term; the other does not. They correspond to stochastic differential equations with different…
The document describes a numerical problem in recovering probability densities with the COS method. The author compares truncation intervals built from cumulants through orders two, four, and six, and reports that the resulting densities shift substantially…
The note gives the Black–Scholes put-call parity relation for asset-or-nothing options. It expresses the asset-or-nothing put price as the prepaid underlying value less the corresponding call price, then substitutes the call pricing formula to obtain the put…
The document derives the sensitivity of European option prices to the risk-free interest rate in the Black–Scholes model. Differentiating the call price and simplifying with the relationship between the normal density values at d1 and d2 produces call rho as…