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 addresses which implied volatility to use in a convexity adjustment when valuing a Libor-in-arrears swap cash flow. The relevant volatility comes from an option whose expiry matches the rate reset date and whose underlying rate covers the…
Defaulted loans can retain value through collateral, restructuring, or eventual repayment. Buyers estimate potential recovery and pay less than that expected value, accepting uncertainty and the possibility that actual recoveries will be lower. Specialists…
The document addresses why a standard perpetual-option PDE solution for an American put does not transfer directly to a call. In the no-dividend setting, the continuation-region solution for the call has a linear form, and the question is how to determine…
The document explains why querying a QuantLib discount curve at a time of two years may not return the discount factor supplied for a date two calendar years after the curve’s reference date. The curve is constructed from dates and discount factors using the…
Option pricing models can support trading in several ways. A market maker can use a model to estimate option sensitivities, hedge exposures, and seek returns from the bid–ask spread. A risk taker can compare model values with market prices and trade options…
The discussion distinguishes two quantities often called forward implied volatility. One is calculated from the change in implied variance between two maturities for vanilla options at a fixed strike. It represents a forward measure inferred from today’s…
The document discusses implementing Carr–Madan Fourier pricing for European calls under Black–Scholes. It outlines a characteristic function, a damped transform, and a fast Fourier transform approximation using Simpson weights. The author reports that an…
The document examines an approximation used in deriving a convexity adjustment for a bond forward. It expands the bond price as a function of yield around today’s forward yield, then asks why the expected squared yield change can be approximated by the…
The document derives the no-arbitrage forward price for a coupon-bearing bond delivered at a future date. It starts from the condition that a newly entered forward has zero value, so the discounted expected delivery value minus the forward price must have…
The document explains how to price a commodity forward under a mean-reverting log-price model, then compare Monte Carlo estimates with an analytical forward price. It emphasizes simulating terminal prices under the risk-neutral measure, calculating the…
The document addresses how to interpret the yield of a forward bond price when the available input is a zero curve quoted with continuous compounding. The example concerns a European put on a coupon bond and a relation that uses duration to translate forward…
The document explains why a claim paying an index value multiplied by one numéraire can have a different value when priced in units of another. It defines an adjusted initial index value as its expectation under the measure associated with the second…
The document examines how to combine the delta, vega, and theta of a long at-the-money SPX put and a short at-the-money VIX call. It gives example option Greeks and a historical VIX-to-SPX beta, then applies that beta to estimate a combined delta. The author…
The discussion separates a forward price from a forecast of the asset’s future spot price. A forward contract sets a price today for an exchange at a later date; financing costs and the value of holding or using the asset can make that price differ from an…
The document explains how to hedge an interest rate swap portfolio using the risk buckets in a delta ladder. When each bucket records the market value change from a one basis point shift in a par instrument, the hedge should offset the portfolio’s DV01 in…
The document discusses two fundamental asset pricing claims: the law of one price is equivalent to the existence of a state price vector, and, when the law holds, uniqueness of that vector is equivalent to market completeness. The response focuses on the…
The answer explains how to bootstrap a forecasting curve separately from an overnight-indexed discount curve in QuantLib. In the example, an OIS curve is built first for discounting, while a LIBOR curve is bootstrapped for forecasting. Swap-rate helpers for…
The document responds to a student seeking manageable machine-learning project ideas with two research directions from quantitative finance. The first is deep hedging for risk management, along with data-driven estimates of option Greeks such as delta.…
The document raises a question about the relationship between the familiar gamma contribution to the P&L of a delta-hedged position and a proposed calculation based on the change in delta during an underlying price move. It presents the gamma-and-theta…
The document asks whether familiar models for an underlying asset can be derived from assumptions about the discounted profit and loss of a delta-hedged European option. It writes the hedged portfolio P&L in terms of the option payoff, initial premium,…
The document frames European call pricing on a finite binomial stock tree as a superhedging problem. With zero interest, the goal is to find the least initial wealth that can fund a bond-and-stock portfolio, adjusted at the tree’s nodes without later cash…
The document addresses how to represent correlated Brownian shocks for a payoff depending on three underlying assets. The answer recommends applying a Cholesky decomposition to the assets’ covariance matrix. For a symmetric covariance matrix, the lower…
The document discusses an approximation that relates implied volatility for a spot and strike pair to the average of local volatility across the price interval between them. The motivating explanation is that paths ending in the money may spend much of their…
The document explains how to retrieve the next cash flow date and amount from a plain vanilla interest rate swap in QuantLib’s Python interface. One approach subclasses the swap class, converts the fixed leg entries to coupons, and selects the first cash…