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 raises a question about how to express a zero-coupon bond’s price at a future time when only earlier information is available. It gives the affine Vasicek pricing form, in which the bond price at a given time depends on the short rate at that…
The document explains how to interpret Eurodollar futures prices as implied forward rates and use them to build a sequence of zero-coupon rates and discount factors. Its central step is to convert each quoted futures price into a rate by subtracting the…
The document raises a derivatives-pricing question about VXTY futures, whose contract specification references options on ten-year Treasury futures. The author distinguishes option selling, which involves receiving an option premium, from entering a futures…
The document examines how changing the shift in a SABR model affects recalibrated parameters and swaption sensitivities. It describes experiments that fit shifted SABR to a constructed volatility set, first freeing correlation and volatility of volatility,…
The document outlines a proposed backtest of a receiver swaption under a one-factor Hull–White or Gaussian Markov HJM framework. It describes forward rates in Musiela form, relates continuously compounded yields to average forward rates, and gives an…
The document gives a concise reason quadratic variation matters in quantitative finance: Brownian motion has nonzero quadratic variation, whereas a continuously differentiable path has zero quadratic variation. Because Brownian motion is a central model for…
The document clarifies the difference between a portfolio’s payoff at maturity and its price when established. A proposed structure combines European puts at two strikes with a European call at a higher strike. Evaluating the payoff formula at a particular…
The document explains how exercise of a call option on a futures contract creates a futures position whose mark-to-market depends on its entry price. Because futures settle daily, the delivered position is treated as entered at the most recent settlement…
The response clarifies that a forward rate agreement, a caplet or floorlet, and an option on an FRA are different instruments. A caplet and a floorlet on the same future LIBOR fixing have complementary single-period option payoffs and can approximately…
The document outlines a QuantLibXL workflow for valuing a floating-rate bond whose cap and floor strikes vary by coupon. It recommends supplying a strike for each coupon to the floating-rate bond, then pricing the bond with a bond engine. An Ibor coupon…
The document presents an attempted trinomial-tree implementation of an uncertain volatility model for pricing European calls between minimum and maximum volatility bounds. It lays out a backward-induction scheme, defines a discrete second-difference term…
The document asks how to model changes in implied volatility when approximating an option portfolio’s profit and loss with delta, gamma, and vega terms. It distinguishes historical VaR, which can reprice a portfolio across observed market scenarios without…
The document asks whether the volatility smile and the volatility-of-volatility smile can both arise from dependence between spot and volatility. It proposes viewing the relationship in two directions: volatility moves affecting spot may help explain the…
The document explains how to express a view that policy rates will stay higher for longer than the market expects. In a fixed-for-floating swap, paying fixed and receiving floating benefits if the floating rate over the relevant period is higher than the…
The document clarifies an example about a forward-start variance swap and whether a statement about implied volatility contains a typo. It explains that the relevant forward-start swap strike represents today’s expectation of the variance-swap strike for a…
The document explains how Dupire’s formula relates local volatility to the time and strike derivatives of call prices, assuming no dividends. It walks through a small strike-and-maturity table to estimate those derivatives with finite differences and obtain…
The document introduces an approach for inferring a liquidity parameter from market bid and ask prices for a European call. The parameter, denoted by λ, represents a symmetric distortion around the option’s mid price. Rather than deriving liquidity from the…
The document examines why an American call on a stock with one known dividend can be worth more than a European call with the same strike and expiry. It first proposes estimating the difference through European calls around the ex-dividend date, adjusting…
The document clarifies that geometric Brownian motion can be simulated by multiplying lognormal price relatives across time steps. In the direct approach, each step’s gross price ratio should itself be lognormally distributed, with log-mean and…
The document explains why digital options can be difficult to hedge near expiry: their payoff changes abruptly at the strike, creating steep or concentrated sensitivities. One practical approach is to approximate a digital with a call spread. A tighter…
The document discusses three probability and option-pricing questions: when to stop drawing from a balanced deck while betting on card color, how to value a call whose underlying payoff is the number of heads in a fixed sequence of flips, and whether equal…
The note presents a way to obtain the probability density of a basket formed by summing two correlated geometric Brownian motion assets. Although each asset is lognormally distributed, their sum is generally not lognormal. The proposed density follows from…
The note derives a forward price when an asset pays a deterministic proportional dividend before contract expiry. Its main method compares the forward payoff with a cash-and-carry position: borrow funds to buy the stock, account for the dividend cash flow,…
The note explains why an at-the-money short-dated straddle can be approximated using implied volatility. In a Black–Scholes setting, put-call parity reduces the value of an ATM-forward straddle to twice the call value. The ATM call value is approximated as a…