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 discussion examines the value of a total return swap that either party may terminate during a performance period. It contrasts a discounted mark-to-market valuation for a non-cancellable swap with an accrual-style cancellation payoff. One answer argues…
The post asks whether linear interpolation of implied volatility can create arbitrage, distinguishing interpolation across maturities from interpolation across strikes. It notes the concern that interpolating volatility over time may violate calendar…
The document explains how a one-dimensional version of Girsanov’s theorem in Shreve’s stochastic calculus text follows from a more general formulation. The key identification is to take the Brownian motion as the local martingale and use the negative…
The document challenges a proposed rule linking an option’s time value to its delta. The claim is that when time value makes up at least a specified fraction of an option’s price, delta must be below a corresponding threshold. A Black–Scholes call example…
The document asks how to plot a one-month implied volatility smile when call and put implied volatilities and option deltas are available, but spot and strike prices are missing. It notes that volatility smiles are often displayed against delta, so the…
The document asks how to solve a three-dimensional backward Black–Scholes PDE with time- and state-dependent coefficients. Applying a Crank–Nicolson scheme across all three state variables at once creates a difficult coupled system. The response points to…
The document explains why a slightly in-the-money American option does not generally have a delta of one. Delta reflects how the option’s total value, including remaining time value, changes with the underlying price; it is not determined solely by the slope…
The document asks whether large options positions can make the underlying’s price respond to derivatives activity, especially when dealers must hedge positions with high gamma. It describes the proposed feedback: negative gamma hedgers may buy into sharp…
The document asks how to model convexity adjustments for a payoff on the spread between two constant maturity swap rates when the rates are dependent. It notes that some approaches model each rate through an annuity mapping function and then use a copula to…
The note clarifies that buying volatility is not always identical to buying an option, although vanilla options generally rise in value when implied volatility rises, all else equal. For a long option delta-hedged under a Black–Scholes model, it gives a…
The document asks whether open-source software can support commodity pricing and risk management, noting that commodity contracts may involve a wide range of specialized payoffs. The answer says the author is not aware of a dedicated open-source library for…
The document considers pricing a call-like payoff on the difference between the product of two correlated geometric Brownian motions and a scaled version of one process. It explains how to express the product process as a single geometric Brownian motion,…
The document poses a fixed-income question: how to lock in a one-year rate that begins three years from now using zero-coupon bonds with maturities from one to four years. It supplies annually compounded spot rates for each maturity and asks which bonds to…
The document presents implied volatility as a way to express option prices in familiar Black–Scholes terms. Because the model maps a vanilla option price to a volatility input, implied volatility helps compare options across strikes and maturities, track…
The document explains why adding jumps to an option pricing model represents a different risk from simply increasing diffusion volatility. In a diffusion model, variability grows with the square root of time, while a Poisson jump component contributes…
The document examines a bond yield-to-horizon calculation for a bond held until maturity. It contrasts a spreadsheet’s quoted 7.83% result with a calculation based on the ratio of horizon value to purchase price, and discusses reinvestment and compounding…
The document asks how to choose volatility and interest-rate inputs when pricing American puts with a binomial model and comparing estimates with market prices. The author proposes using the standard deviation of recent log returns for volatility and…
The document summarizes a distinction between local volatility and stochastic volatility models when representing equity option markets. It reports that local volatility can fit observed vanilla option prices but may produce unrealistic forward volatility…
The document examines whether an option’s extrinsic value, also called time value, follows a normal or lognormal shape as the underlying price changes. It describes an interpretation of the Black–Scholes call formula using a lognormal distribution of future…
The document demonstrates how to use Halton low-discrepancy sequences in Monte Carlo option pricing. Uniform sequence values are transformed through the inverse standard normal distribution, then scaled by the drift and volatility of a risk-neutral log-price…
The document explores how to interpret the Radon–Nikodym derivative that converts real-world probabilities into risk-neutral probabilities in a one-step binomial market. In the two possible states, the derivative takes the ratio of risk-neutral to real-world…
The document asks whether Black–Scholes call and put prices are convex as functions of implied volatility. The answers explain that convexity can vary with moneyness rather than holding uniformly. Vega, the derivative of option value with respect to…
The document explains why a callable bond generally has a higher yield to maturity than a comparable noncallable bond. Its price can be viewed as the value of the noncallable bond minus the value of the issuer’s embedded call option. Since that option has…
The document describes pricing a plain vanilla interest rate swap from a discount curve in QuantLib and simulating short-rate paths with the one-factor Hull–White model. It includes a detailed setup for fixed and floating legs, historical index fixings, a…