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.
8,116 documents
The document raises a risk-management problem for a vanilla option that terminates if realized volatility over the option’s life exceeds a preset barrier. Such a condition could reduce the option’s price, but it also makes the payoff depend on the path of…
The document asks whether a two-factor Hull–White short-rate model, also called G2++, can represent swaption volatility smiles or skews, and whether fitting it to out-of-the-money swaptions would help. The answer points to local- and stochastic-volatility…
The document addresses unstable numerical integration in Heston option pricing, where an oscillatory or slowly decaying integrand can produce negative computed prices, especially for deep out-of-the-money options. A recommended first remedy is the Little…
The document explains how a Lévy process such as variance gamma, NIG, or CGMY can be time-changed by the integrated rate of a mean-reverting CIR process. This produces a stochastic volatility Lévy process: the clock remains nonnegative and increasing, but…
In swaption quoting conventions, a volatility surface is often arranged with option expiry increasing down the first column and the maturity of the underlying swap increasing across the top row. Under that layout, the upper-left region represents options…
The document considers an Asian-style payoff equal to the square of the time average of an asset following geometric Brownian motion under risk-neutral dynamics. It asks whether the discounted conditional expectation has a closed-form value, noting that the…
The document explains how to price a European claim that depends on the asset price at maturity in a recombining binomial model. Starting from the terminal payoff, it works backward through the tree, taking conditional expectations under risk-neutral…
The document derives the hedging error that arises when a call is priced with Black–Scholes implied volatility but the underlying stock realizes a different volatility. The option price satisfies the Black–Scholes partial differential equation using the…
The document explains why a callable bond’s Z-spread may not map cleanly to a unique price. The call option makes the bond’s value depend on whether and when the issuer exercises, and that decision is affected by both risk-free rates and credit spreads.…
The document resolves a portfolio valuation question by clarifying the option position’s direction. A portfolio holding shares plus a long call includes the call’s positive value; a portfolio that has sold the call must subtract the liability represented by…
The document considers whether counterparty risk invalidates the Black–Scholes hedging argument. It distinguishes listed options, where central clearing and collateral arrangements are intended to mutualize or mitigate default exposure, from over-the-counter…
The document explains why forward prices can matter to option valuation even when a Black–Scholes formulation is written using spot and an interest rate. For equities, no-arbitrage cash-and-carry reasoning connects spot, funding, dividends, and the forward…
When calibrating an option pricing model across several maturities, the risk-free input should come from securities whose prices primarily reflect interest rates, rather than being chosen to fit the options themselves. The answer recommends building a…
The document considers how to quantify liquidity in listed equity, index, and ETF options for scanning or analysis. It recommends looking beyond contract volume to bid–offer spreads, option notional traded, changes in quotes relative to movements in the…
The document defines IMM dates as the third Wednesday of March, June, September, and December, then gives an Excel date formula for generating the next quarterly date from a starting date. The formula advances three months, finds the first Wednesday in the…
The document explains the phrase “no shorts left” in a market commentary passage describing an increasingly bullish market. In this context, shorts are investors holding positions that benefit from falling prices, reflecting a negative market outlook. The…
The document values an option to reroll a fair six-sided die when the player may keep the first result or replace it with a second roll. The decision rule is to reroll when the first outcome is below the expected value of a fresh roll, and otherwise stop.…
The document clarifies a misconception about path dependence in binomial option pricing. Backward induction through time does not itself mean the model represents the full sequence of market states along a path. A tree compresses information into states that…
The document considers a seller of a swaption who delta-hedges once per day and asks what share of daily theta decay remains as profit when the underlying rate move is smaller than a stated breakeven move. The proposed fraction is one minus the squared ratio…
The document asks whether an at-the-money SPX put spread has an edge over a same-width call spread because the put spread's stated reward-to-premium ratio is higher. It frames the comparison as a roulette game with different payouts but supposedly equal…
The document asks whether spot price can be calculated directly from a target option delta when strike, expiry, volatility, rates, and other inputs are known. It discusses Black–Scholes and Bjerksund–Stensland models, which provide option prices and Greeks…
The document presents a failed calibration of the raw SVI total-variance parametrization for a single options maturity. The example converts market implied volatilities to total variance, computes forward log-moneyness, and minimizes squared fitting error…
The document explains why a simple unilateral credit valuation adjustment for an option must combine the option’s future value with the counterparty’s probability of default. The suggested discretized calculation averages discounted expected exposure at…
The document clarifies how a volatility surface indexed by moneyness can remain consistent with put-call parity. Although the question assumes calls and puts use opposite moneyness ratios, the answer explains that moneyness is generally defined the same way…