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 that an FX swap carries interest rate exposure because its cash flows can be viewed as borrowing in one currency and lending in another. Changes in rates in the two currencies can alter the value of the locked-in funding terms, so the…
The document explains how to describe and assess a roll between Treasury futures delivery months. The quoted market roll is the front contract price minus the back contract price, expressed in thirty-seconds. A theoretical comparison starts with the fair…
The document asks for a detailed introduction to stochastic calculus for Poisson and other jump processes, including random intensities and jump sizes. It notes that standard derivative-pricing texts tend to emphasize Brownian motion, with jump-diffusion…
The document describes an attempt to calibrate the two-factor G2++ interest-rate model to cap volatility quotes using QuantLib's Python interface. The example builds a yield curve, creates cap helpers from maturities and volatility inputs, sets an…
The document explains why swap valuation may require separate discounting and forward curves, and why the appropriate forward curve depends on the floating rate index in a swap. For a vanilla swap, the curve built from the most liquid swap quotes and futures…
The document explains the source of a one-half term in a Fourier-based option-pricing derivation. It gives the Gil-Pelaez inversion formula, which relates an integral involving the real part of a characteristic function to the probability that the terminal…
The document examines why an option’s expected payoff cannot simply be discounted at the risk-free rate under the real-world probability distribution. The underlying asset is risky too, and its expected growth rate is uncertain and potentially dependent on…
The document considers whether antithetic variates must produce a positive Monte Carlo estimate for a European call when every payoff from the original simulated draws is zero. The answer is no: pairing each draw with its antithetic counterpart does not…
The document distinguishes the real-world probability measure P from the risk-neutral measure Q and explains their roles in research and pricing. P is used to describe outcome probabilities and expected returns, while Q offers a convenient way to price cash…
The document describes a market quotation for a one-year at-the-money straddle on the difference between the ten-year and two-year constant maturity swap rates. The quoted bid and offer are given as prices in percentage terms, rather than as an implied…
The document explains how to obtain the dynamics of a zero-coupon bond price from a stochastic model for the short rate. Under the risk-neutral measure, the bond price is expressed as the expected discount factor from the current time to maturity. Assuming…
The document raises a fixed income question about callable perpetual bonds. It observes that Bloomberg’s calculated yield uses the first call date as the workout date, and that for a fixed price this date appears to produce the lowest yield among the…
The document explains why overnight indexed swap rates became a common discount curve for collateralized derivatives. In the US example, OIS reflects expectations for the Fed Funds rate, which monetary policy influences, while private interbank funding rates…
This note compares approaches for fitting European call prices across strike and recovering the risk-neutral distribution implied by options. One method fits call prices directly with arbitrage-constrained cubic smoothing splines; the second derivative of…
This note explains two assumptions desks use to update an implied volatility surface between full calibrations. Under sticky strike, implied volatility stays fixed for each strike as the underlying price changes. An option at a given strike is therefore…
The document asks why a swap’s annuity factor should be proportional to its coupon value change for a one basis point move, called CV01. It starts from the par swap pricing equation, expressing the fixed coupon and discount-factor sum alongside the maturity…
The document explains how to select curves for valuing interest rate swaps and swaptions when floating indices have different tenors, such as three or six months. The curve associated with the floating index is used to forecast its cash flows: a swap…
This introductory explanation clarifies the meaning and timing of an option premium and distinguishes exercise rules by option style. In the example, the quoted trading price of a call is its premium: the buyer pays that amount when entering the option…
The document asks why stochastic-volatility modeling often introduces a market price of risk when option pricing can begin directly under a risk-neutral measure. It describes a traditional setup in which variance has historical dynamics, its drift changes…
The document presents a question about a European call priced below its put-call parity lower bound. In the example, an arbitrageur shorts stock, buys the underpriced call, and invests the cash proceeds. At expiry, if the stock is above the strike,…
The document offers two practical ways to build intuition about whether an option’s volatility skew is unusually cheap or expensive. One approach is to consider how realized volatility might differ when the underlying is near a particular strike. If…
The document explains why making a discounted dividend-paying stock price a martingale under a chosen probability measure does not, by itself, justify risk-neutral pricing. The key condition concerns discounted values of self-financing portfolios. Holding a…
A hedge curve template (HCT) specifies the market instruments and curve-building method used to create scenarios for measuring an instrument’s risk. Its design determines which rate changes the risk report can show and how closely those scenarios resemble…
The document discusses constructing a model-free implied-volatility measure from a range of traded call and put prices. The described procedure first builds an implied-volatility skew by interpolating and extrapolating market observations with a cubic…