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 explains why the usual present-value sum of known cash flows and discount factors cannot be applied directly when the cash flows depend on future interest rates. In that case, the cash flows are random variables, so their discounted sum is…
The document interprets the stock return term in the Black–Scholes setting as a proportional, rather than dollar, rate of price change. Dividing the instantaneous price change by the current price expresses movement as a percentage change. The discrete-time…
The document explains that implied volatility is inferred by applying an option-pricing model in reverse to quoted option prices. In the Black–Scholes framework, a higher quoted option price corresponds to a higher implied volatility, so the displayed…
The document asks whether historical implied volatility can be downloaded from Interactive Brokers. The responses indicate that a dedicated utility may not be available and describe a possible workaround: retrieve historical option prices through the API,…
The document considers a three-day, 95% value-at-risk estimate for a long European call when the underlying follows geometric Brownian motion. It describes valuing the option with Black–Scholes, deriving a lower-tail stock-price quantile from the lognormal…
The document discusses how to build mathematical foundations for quantitative finance and statistics. The questioner seeks rigorous, proof-based study of relevant tools such as linear algebra, probability, set theory, stochastic calculus, and measure theory,…
The discussion asks how to infer a stock price probability distribution from option prices and track changes in that distribution over time. One response identifies implied probability densities, also called state price densities, as the relevant framework.…
The discussion surveys possible ways to obtain historical daily quotes across VIX option strikes and expirations. One response says reliable public data may be unavailable and cautions that analysis may also require the corresponding VIX futures history,…
The answer explains how to move from a Bachelier underlying with an unspecified physical drift to a risk-neutral process for pricing a European call. It starts with the discounted asset price and uses the martingale condition to identify the required drift…
The document reviews a Heston option-pricing implementation that produces negative probabilities or prices under extreme inputs, despite giving plausible at-the-money results for other parameter choices. The implementation applies a characteristic-function…
The note resolves how to obtain a short-maturity yield expansion from a Taylor expansion of a zero-coupon bond price. Starting with the price written as one plus successive powers of time to maturity, it applies the logarithm series and then negates and…
The note explains why the profit and loss of a portfolio hedged with stock must include dividends received or owed on the stock position. It writes the portfolio value with a money market account, stock, and short derivative, then tracks those holdings over…
The note rewrites the payoff of a power option, defined as the underlying raised to a power times a call payoff, as a difference of two asset-or-nothing binary call payoffs. It first expands the payoff into two terms, each gated by the condition that the…
The document frames a model-design problem for estimating the concentrated positions component of an additional valuation adjustment for derivatives. It proposes relating price or volatility impact to the volatility of valuation inputs, bid–ask spread…
The note asks whether the expected product of increasing functions of two correlated stochastic processes rises as their instantaneous correlation rises. The response sketches an Itô-calculus argument in a simplified setting: it assumes zero drift and unit,…
The document discusses how to validate an implementation of Dupire’s equation when deriving local volatility from an implied volatility surface. The question proposes starting with a flat implied-volatility surface, then testing a surface with term structure…
The document examines whether an option and its underlying stock require risk premiums in a binomial pricing model when their payoffs can be replicated using other instruments. The central issue is a confusion between replication and hedging: constructing a…
The document considers whether an FRA rate or an interest rate futures rate is the better proxy for an expected future fixing. The two instruments can imply different values because their settlement structures create a convexity difference. The answers…
The document explains when an FX volatility smile quote for a put can be matched to a call quote with the complementary delta. Under the forward delta convention, put and call deltas at the same strike sum to one, so a 95-delta put and a 5-delta call…
The document presents a Delphi implementation of the Black-Scholes formula for European call and put options. It calculates the standard d1 and d2 terms from spot price, strike, time to expiration, interest rate, and volatility, then applies the cumulative…
The answers explain that FX outright delivery dates are convention driven and can vary with the currency pair, market, and trade details. Relevant inputs include spot settlement timing, holidays in each currency, weekends, whether USD holidays are included,…
The document examines how correlation can affect best-of and worst-of options and discusses confusion arising from the payoff definition. The questioner's Monte Carlo example simulates correlated terminal prices for two assets and reports that the price of a…
The document distinguishes two conventions for compounded overnight-rate swap coupons. In a lookback without an observation period shift, each daily rate observation is moved earlier by a set number of business days, while the accrual weights remain tied to…
The document explains that the right bond comparison measure depends on the task. For an indicative price on an illiquid bond, it describes interpolating between observable bonds that mature earlier and later. For amortizing bonds, weighted average life may…