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 why a 10-year receiver and 20-year payer swap with equal and opposite DV01s may not offset under a parallel rate move. Equal DV01s cancel the positions’ first-order sensitivity at the starting curve, but they do not ensure equal…
The document addresses which date to enter when calculating a Treasury bond’s yield from its clean price, and whether auction prices use the same approach. The answer recommends using the settlement date rather than the trade date or the most recent coupon…
The document describes how to align a QuantLib fixed-rate bond valuation with a Bloomberg clean price. The example concerns a Polish government bond valued on a specified date at a given yield. The initial QuantLib calculation differs from Bloomberg by a…
The document answers a question about how far an asset price might move over a three-month horizon given its annualized volatility. The response treats the estimate as a static one-standard-deviation range, scaling volatility by the square root of time and…
The document explains how to obtain a forward discount factor and forward reference rate from discount factors observed from today to two future dates. For dates t1 and t2, it uses the multiplicative relationship between discount factors: the factor from t1…
The document asks how to value a one-year at-the-money European call when volatility is specified as 20% for the first half-year and 90% for the second half-year. The proposed answer combines the two periods’ variances, weighted by their durations, and takes…
The document sets up an arbitrage check for calls on the same underlying with strikes 100, 120, and 130 and prices 8, 5, and 3. It represents a portfolio with signed quantities, requires a negative initial cost, and writes its maturity payoff across regions…
The document studies the stochastic behavior of marginal default density when default intensity follows a lognormal diffusion. It writes default density as intensity multiplied by survival probability, then applies Itô’s product rule to derive a stochastic…
The document corrects a digital-call valuation under the stated risk-neutral dynamics, where the price has drift proportional to its current level and constant diffusion. The original calculation omitted the conditional mean of the terminal price, leading to…
The document distinguishes zero rates, used to derive discount factors for valuing cash flows today, from forward rates, which are implied by zero rates and no-arbitrage relationships to describe rates over future periods. It frames curve selection as…
The document asks what information a binomial tree must retain when valuing an up-and-in barrier option. The response assumes a European-style contract and proposes using knock-in/knock-out parity: the value of the corresponding vanilla European option…
The document presents a question about implementing Tilley’s algorithm for pricing American options through simulated asset paths. The shown R approach generates risk-neutral paths, works backward through exercise dates, sorts paths by asset value, estimates…
The document explores whether implied volatility in a diffusion model must be bounded by the model’s instantaneous volatility. It assumes the asset follows a stochastic-volatility diffusion under the pricing measure and considers a setting where…
The discussion explains how negative risk free rates affect equity and index option valuation. It says the Black Scholes framework can accommodate negative rates, and an answer suggests setting very small negative CHF rates to zero as a practical…
The document asks whether a Heston stochastic volatility model and a local volatility model derived from it produce identical option prices. It points to a comparison in Gatheral’s book and asks whether the equivalence depends on spot and variance having…
For puts with the same underlying and expiry, the displayed bid and ask quotes generally increase as strike prices rise. The question arose because some last-traded prices appeared to violate that pattern, leading the answers to distinguish current quotes…
In investment banking, a curve is a set of values indexed by date, such as discount factors across maturities. A practical curve stores values at selected dates and uses interpolation to estimate values between them, since a value for every possible date is…
The document asks how to interpret the ratio of a standard normal upper-tail probability to its density when evaluated at Black–Scholes d₁ for a put option. It identifies this as the Mills ratio and relates its reciprocal to the normal hazard rate, a concept…
The document distinguishes three option price references. The last-traded price records the most recent execution and can remain unchanged when no further trades occur, even as current quotes move. A closing price may reflect the market around the exchange’s…
The document discusses the practical standing of the Linear Gauss–Markov model for interest rates and its relationship to other short-rate frameworks. It reports that one reference treats LGM under the name “Hagan and Woodward Parameterization,” and that two…
The document asks why a bond pricing system switches discount factors during the final year before maturity. It contrasts annual compounding, using a factor based on yield raised over the time to payment, with simple-interest discounting, using yield…
The document values a perpetual claim that pays one unit when a stock first reaches an upper barrier and pays nothing if it reaches zero. Under geometric Brownian motion, zero interest rates make the claim worth one, assuming the upper barrier is eventually…
The document distinguishes current coupon spread duration from option-adjusted spread (OAS) duration for mortgage-backed securities. Current coupon spread is the excess yield on the current coupon mortgage over a reference yield curve. Its duration is…
The note discusses how a short stock position can affect the carry embedded in an option strategy. In a short sale, the trader receives proceeds that may earn interest, while also paying a stock borrow fee. The net financing effect can reduce the effective…