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.
5,701 documents
The document addresses why a drift adjustment may appear unnecessary when changing from the money-market account numeraire to a zero-coupon bond maturing at the payoff date. It defines the money-market account and bond price, then shows that with…
The note explains that a mandatory break in an interest rate swap generally does not change the swap’s ordinary valuation or hedge. It can, however, reduce counterparty valuation adjustment and funding valuation adjustment charges because the contract is…
The document explains how to obtain raw moments of a future short rate in the Cox–Ingersoll–Ross model by differentiating a conditional transform. It defines a function as the conditional expectation of the exponential of minus λ times the future rate. This…
The document addresses unequal coupon amounts generated by QuantLib’s amortizing fixed-rate bond constructor when monthly payments start on the last day of a month. The example shows February’s short length shifting interest between adjacent payments, even…
The document considers adding vanilla interest rate swaps to an existing Monte Carlo VaR process for foreign exchange and commodities. The proposed simplified method estimates volatility and correlation from daily changes in par swap rates, simulates rate…
The document derives the value of a perpetual bond, or consol, that pays a fixed annual coupon. Under discrete annual compounding, the bond’s price is the sum of each future coupon discounted by the corresponding power of one plus the required rate. Treating…
The document considers how to assess a proposed interest-rate cap volatility surface for arbitrage. A cap consists of caplets, and the response recommends stripping caplet values from cap prices across maturities. In a simplified setting with a flat yield…
The document asks how to estimate future values for a portfolio containing a stock, a long-term coupon bond, and a European call option. It provides example daily inputs for the stock price, required yield, volatility, and short-term interest rate, and asks…
The document works through a derivation of the price dynamics of a zero-coupon bond in the Ho–Lee short-rate model. The question starts from the model's short-rate process and a conditional expectation representation of the bond price, then applies Itô's…
The document explains how to convert a bootstrapped Ibor discount-factor curve into zero rates. It contrasts simple interest conversion, where the discount factor uses a linear accrual term, with annual compounding, where the rate is exponentiated by the…
This document explains the convention used by QuantLib's zero-yield structure when it converts a zero rate into a discount factor. The implementation applies the exponential discount formula, which corresponds to continuous compounding. The question is…
The document interprets a formula that extracts an annual longevity risk premium by comparing discounted risk-neutral and physical expectations of a longevity index across payment dates. The risk-neutral expectation is described as inferred from traded…
The document asks how to build a zero or spot curve from two observations: one-year and three-year zero-coupon swap rates. It explains that interpolation is underdetermined because the observed rates do not reveal the path of intermediate forward rates. Two…
The discussion asks whether U.S. Treasury cash flows should be discounted using SOFR or a security-specific repo curve. One answer emphasizes that Treasuries are liquid and trade at observable market prices, so practitioners generally do not need to infer…
A default indicator for one borrower can be modeled as a Bernoulli trial. For a portfolio of loans, the default count is binomial when defaults are treated as independent trials with a common probability. This gives a straightforward way to describe…
The document compares buying a one-year S&P 500 index future with buying a six-month future and replacing it with another six-month contract at expiry. The question assumes the six-month funding rate stays static and that profit earned during the first…
The document clarifies what to do when a requested maturity falls outside the known terms used by a raw yield-curve interpolation formula. Such a case is extrapolation rather than interpolation, because the desired point lies beyond the range of observed…
The question describes a two-factor Hull–White short-rate model in which the short rate combines a deterministic shift, calibrated to the initial forward curve, with two mean-reverting Gaussian factors. It asks how to update the entire forward curve through…
The discussion distinguishes modeling returns under the real-world probability measure for risk analysis or portfolio construction from modeling under the risk-neutral measure for derivatives pricing. For observed log returns, estimate the mean and variance…
The discussion explains why swap desks may maintain several interest rate curves. In a multicurve framework, an overnight indexed curve is used to discount future cash flows, while separate curves estimate the future fixings that determine floating-leg…
The document explains why a credit recovery rate may be reported on a discounted basis. A recovery rate measures the share of an obligation ultimately repaid after default. Because insolvency proceedings can delay payments and recoveries may arrive in…
The note frames a catastrophe bond from the insurer or sponsor’s perspective as a way to transfer catastrophe risk and reduce the need to hold capital against adverse events. The economic comparison is between the cost of issuing the bond and the cost of…
The document outlines a proposed approach to building a central bank meeting-date curve from overnight indexed swap quotes. It starts with overnight and monthly OIS rates, adjusts them using the spread between the policy target and the effective overnight…
The document addresses a one-factor Hull–White calibration that fits mean reversion and a single volatility parameter to market normal-volatility quotes for at-the-money swaptions. The reported fit is poor across quotes, raising the question of how to…