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 clarifies how carrying costs and dividends enter equivalent forms of put-call parity. Its central explanation is that parity equates a stock-minus-bond position with a call-minus-put position. A stockholder bears financing or other carry costs,…
The document poses a derivatives-pricing problem: valuing a European payoff based on the square of an underlying stock price when the stock follows a geometric Brownian motion. It applies Itô's lemma to the squared price and observes that the resulting…
The document gives a brief rule of thumb for choosing an option-pricing model by underlying: Black–76 is suggested for options on index futures, while Black–Scholes is suggested for options written directly on an index, such as SPX options. It points readers…
The discussion compares two ways to express the profit and loss of a long delta-hedged option when realized volatility exceeds implied volatility: marking the option using realized volatility, or retaining the implied-volatility mark and allowing…
The document derives the expectation of the product of two correlated geometric Brownian motion processes, such as a foreign asset price and an exchange rate. It reduces the weighted sum of their Brownian shocks to a single Gaussian shock whose variance…
The document asks how to obtain Black-Scholes implied volatility from a model’s characteristic function using an integral relation attributed to Gatheral’s treatment of Lewis inversion. It focuses on the contour used to value a covered call, why the payoff…
The document asks whether a basic Black–Scholes spreadsheet for European options can be adapted to price American options. It suggests Whaley’s approximation as a possible spreadsheet method when limited accuracy is acceptable. The approach requires…
The document raises a question about redundancy when three securities each have two possible future payoffs. It describes a common exercise setup: represent each asset by its payoff in the two states, then solve two equations to find holdings in two…
The document explains why binomial option pricing models often set the up and down factors as reciprocals. That condition makes the price tree recombine: an up move followed by a down move reaches the same node as a down move followed by an up move, keeping…
The note explains why a short position’s compounded return can differ in magnitude from a long position’s return, even though the profit and loss on a matched long and short exposure are equal and opposite. It distinguishes a simple short in a future from a…
The document addresses how to compare equity option implied volatilities across the transition from LIBOR to SOFR discount curves. Its answer points to contractual benchmark fallback conventions: a replacement risk-free rate can be paired with a spread…
The document considers a claim whose terminal payoff is the ratio of two stock prices. It outlines a delta-hedging framework for a derivative on two correlated geometric Brownian motion assets, then applies risk-neutral valuation to the ratio payoff. Under…
The document clarifies three terms used in forward markets. The forward price is the current price for entering a new forward with a given maturity, and it changes as market conditions change. The delivery price is the amount fixed in an existing contract…
This note compares sensitivity methods for discrete Asian options when the underlying follows geometric Brownian motion. A geometric-average Asian option has an analytic price under Black–Scholes assumptions, allowing Greeks to be obtained from the…
This short exchange clarifies the payoff notation for a forward contract on a zero-coupon bond. Although the forward price quoted before delivery can vary over time as market conditions and remaining time change, the delivery price agreed when the contract…
This discussion asks how to estimate the exercise probability of the embedded American call in a convertible bond using QuantLib, and distinguishes that probability from delta. It describes approximating the option’s sensitivity to strike, also called dual…
The document concerns technical and practical pricing of insurance-linked securities, especially catastrophe bonds. Its answer characterizes many underlying contracts as excess-of-loss insurance covers, suggesting that actuarial literature on those contracts…
The document compares linear interpolation of quoted rates with constant-forward-rate interpolation when constructing a rate curve for pricing American and European options. It highlights that linear interpolation can create discontinuities in instantaneous…
The document considers how to estimate an implied volatility surface for an asset that has spot data but no options market. It outlines several practical approaches: estimate realized volatility with a model such as GARCH and add a chosen risk premium; scale…
The document addresses why a bank would sell an option when a favorable move in the underlying could make the payout larger than the premium collected. The example assumes a call premium of five dollars and a later stock price of one hundred ten dollars, but…
The question seeks an integral-based route to barrier option prices, motivated by the reflection principle and a guessed reflected probability density. The answer points to a derivation for Black–Scholes barrier options that uses reflection together with…
The document clarifies that negative variance values can arise from numerical discretization even though the continuous-time Heston variance process does not become negative. Flooring values, taking absolute values, or otherwise altering simulated variance…
The document compares local-volatility and stochastic-volatility valuations for a double no-touch option that pays a fixed amount if spot remains between two barriers until maturity. It assumes both models are calibrated to the same implied volatility…
The document explains why a floating-rate swap leg can be valued from the next payment and the discount curve without forecasting every future rate. Under a single curve where discounting uses the same benchmark as the floating coupons, a sequence of bond…