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 two different rate queries for a vanilla interest-rate swap built in QuantLib. The fixed rate is the coupon already assigned to the swap when it is created. The fair rate is calculated from the swap’s market value and represents the…
The document explains how financial schedules handle a tenor addition when the target month lacks the same numbered day. Its example, adding six months to August 30, leads to February’s last day rather than carrying the excess days into March. It identifies…
The note outlines how a CDS upfront settlement value can be related to the par traded spread. It gives a simplified valuation relationship in which the difference between the contractual coupon and par spread is multiplied by the risky present value of one…
The note explains that delta 10 or delta 30 implied volatility quotes identify points on an options volatility surface, rather than a different definition of option delta. Each delta quote maps to a particular strike or moneyness under the relevant market…
This exercise asks whether a market with two assets and three states admits arbitrage, and how to bound the price of a risk-free asset. State prices assign a price to receiving a unit payoff in each state; multiplying the payoff matrix by the state-price…
This note reconciles three explanations for the inverse relationship between bond prices and yields: the return implied by paying a price for a fixed payoff, the opportunity cost of holding a bond when other interest rates rise, and the discounting of future…
The document explains how the bond price dynamics in the Vasicek short-rate model follow from the model’s closed-form bond price. That price is written as a time-dependent factor multiplied by an exponential involving the current short rate and the function…
The document discusses how to choose a risk-free rate when valuing bonds issued by Ecuador, which uses the US dollar and may not have a readily available local government yield curve in common financial databases. One answer recommends using the US dollar…
The document describes a calibration problem for a one-factor Hull–White interest rate model with constant mean reversion and volatility. The author reports that Monte Carlo prices match market prices for three swaptions in a set of four, while the first,…
The document examines whether one stock divided by another remains a martingale after changing from the money-market account to a stock numeraire. It sets out two uncorrelated stock processes under the risk-neutral measure and applies a Radon–Nikodym density…
The document asks why the characteristic function used in Heston stochastic-volatility option pricing satisfies the same partial differential equation as the probability terms in a call-price representation. It presents the governing PDE for those terms,…
The document explains the direction of a USD FRA-OIS swap position. The answer states that a trader expecting the Libor-OIS spread to widen would pay on the swap, paying OIS plus the spread and receiving Libor. This clarifies the cash-flow direction behind…
The document asks how to extend Black–Scholes pricing when the stock follows both a diffusion and a resettable Poisson jump process. One response points to the jump-diffusion version of Itô's formula and the generator-based Dynkin formula as the tools for…
The position buys two deep out-of-the-money calls and puts, while selling one nearer out-of-the-money call and put. One response describes it as a ratioed strangle switch; another views it as an iron condor combined with a long strangle. These are…
The document compares a normal model for a forward swap rate, where volatility measures absolute rate changes, with a lognormal model, where volatility measures proportional changes or log returns. It derives the relationship by considering the lognormal…
The document outlines prudential valuation adjustments (AVAs), which bridge fair value and a more conservative estimate of realizable value under orderly exit conditions. It places these adjustments in a regulatory and accounting context, noting that…
The document explains how to use QuantLib’s FixedRateBondHelper to bootstrap a discount curve from bond market data. It distinguishes the bond’s coupon, which defines its scheduled cash flows, from its quoted price, which calibrates the curve. Short-maturity…
The note explains how a proportional deterministic change in a stock price leads to continuously compounded returns. Starting from the model dx/x = a dt when the stochastic term is absent, recognize that dx/x is the differential of the natural logarithm of…
The note derives bond price sensitivity to yield for a bond with semiannual coupons and corrects a missing chain-rule factor. Differentiating the discounted cash-flow formula with respect to yield introduces a factor of one half in the first derivative and…
The note explains why a floating-rate bond is generally valued near its face value when issued and immediately after a coupon resets. For the first accrual period, the forward coupon rate is already known and matches the discount rate used for that period,…
The document presents QuantLib code that constructs a Black–Scholes process and an American-style vanilla option with specified dividend dates and amounts. The pricing function accepts a valuation date, expiry, call or put designation, strike, time-step…
The document asks how to invert an options pricing formula associated with Roll’s compound formula to investigate lead–lag effects between stocks and options. The author has daily data for the NIFTY index and is trying to understand work attributed to Roll…
The document surveys ways to express a view on how volatility itself changes. It distinguishes realized volatility of volatility from implied volatility of volatility and describes several candidate exposures: options on volatility products, variance-swap…
The document asks when prices from a Cox–Ross–Rubinstein binomial tree converge to Black–Scholes prices as the time partition becomes finer, and whether the same behavior applies to Black pricing for options on forwards or futures. The answer gives an…