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 proposed way to handle negative variance values when simulating the Heston stochastic volatility process: discard a draw that produces a negative variance and sample again. The author argues that independent, identically distributed…
The document considers whether an option should be sold when its market quote falls below a Black–Scholes estimate. Its main guidance is to treat the discrepancy as a prompt to investigate assumptions and inputs, rather than as evidence that the option is…
The document proposes borrowing concepts from physics to describe market fluctuations. It suggests measuring price movement as velocity, with possible measures based on accumulated absolute changes, net changes, or the difference between two observations. It…
The document describes a QuantLib-Python construction error caused by passing simple cash flows to a Bond constructor that expects a leg of coupons. The proposed correction is to represent scheduled interest payments as fixed-rate coupons, with payment…
The document explains why increasing time to maturity does not have a uniformly positive effect on European option values. More time generally adds time value for an at-the-money option because the underlying has more opportunity to move favorably while the…
This document presents VBA implementations of time decay for European call and put options under Black–Scholes, with continuous dividend yield. It lays out the shared inputs and intermediate quantities, including the standard normal cumulative probabilities,…
The document explains why Girsanov’s theorem matters for geometric Brownian motion in finance. Under the original probability measure, an asset’s drift is its expected return, which generally differs from the risk-free rate. Girsanov’s change of measure…
The document clarifies how market implied volatility surfaces for caps and European swaptions relate to pricing more complex interest rate derivatives. A quoted surface represents vanilla option prices under a chosen convention or simple model, such as…
The document explains why initial margin valuation adjustment (MVA) requires simulation even though initial margin is calculated at the start of a trade. It clarifies that initial margin is recalculated over time: market conditions, portfolio positions, and…
The document asks what an unfunded total return series for the CDX North American investment-grade index represents. It cites a Bloomberg series identified as an unfunded total return index and distinguishes the question from the general difference between…
The document asks why the Heston model’s call-price boundary at zero instantaneous variance equals the discounted intrinsic value of the option. It defines the option value as a function of time, spot price, and variance, then presents the boundary condition…
The document presents Black-Scholes as a foundational model and starting point, while explaining that its simplifying assumptions do not capture several observed features of market returns. It names fat tails and skew, changing volatility over time, and…
The document distinguishes put-call gamma imbalance from a mismatch between the gamma of a put and a call at the same strike, noting that put-call parity remains intact. It discusses how dealers’ or traders’ hedging behavior may affect the underlying market…
The document introduces interest rate swap duration by describing the spot-starting calculation: compare the duration of the fixed-rate leg with that of the floating-rate leg. It frames the legs as similar to fixed-rate and floating-rate bonds, respectively,…
The document asks how to bound the price of an out-of-the-money vanilla put when the only readily observable option price is an at-the-money call. It notes two basic constraints: call-put parity and the fact that call prices decline as strike increases. The…
The document asks how to value a swap when the valuation date falls within an accrual period: use historical index fixings for the elapsed portion and project later periods from discount-factor data. The answer recommends adding available fixings to the…
The document asks which method to use for pricing American options after encountering a dismissive comment about binomial valuation. Its answer suggests that Paul Wilmott may favor a finite-difference partial differential equation approach. It presents PDE…
The document asks whether normal (Bachelier) implied volatilities can be derived directly for caps or swaptions under a Libor market model, rather than first deriving Black-76 volatility and converting it. The proposed forward-rate dynamics use a…
The document resolves a discrepancy between two derivations of geometric Brownian motion. For an Itô process with proportional drift and diffusion, taking the logarithm requires Itô’s lemma: the quadratic variation contributes a correction of negative…
The document discusses how to choose volatility inputs and calibrate a Ho-Lee style short-rate model for bond pricing. Its central point is that a model with only a small number of free parameters cannot generally reproduce prices across a large set of…
The document explains why an option’s price response to upward and downward implied-volatility shocks may be similar in magnitude without being exact opposites. A Taylor expansion expresses the price change through vega, the first derivative with respect to…
The document discusses pricing commodity swing options, which allow multiple exercise decisions subject to limits. The questioner has tried Longstaff–Schwartz Monte Carlo and asks about implementing a finite element approach for a model without jumps, using…
The document asks whether a butterfly option can be valued by pricing its component calls with Black–Scholes and combining those values. The answer explains the key principle: for European options with compatible terms, the value of a portfolio is the same…
The document derives the value of a European claim paying the logarithm of the terminal asset price relative to its strike, assuming a non-dividend-paying asset under the Black–Scholes framework. It proposes a price that is affine in the log of the current…