知識圖書館

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 examines a past-return reversal strategy that buys prior losers and sells prior winners, referring to a paper's rule for constructing portfolio weights. The questioner understands the use of a half-gross-exposure scaling term but is unsure why…

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 explains the distinction between US M1, which covers balances readily used for transactions, and broader M2, which also includes savings balances, time deposits, and retail money funds that can be converted to spendable funds. It describes how…

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 document presents a QuantLib setup for building a USD OIS discount curve and a SOFR projection curve from deposit, futures, and swap quotes, then pricing swaps at matching quoted tenors. The author reports small differences between the calculated fair…

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 explains how to aggregate daily security-level contributions to return (CTR) across a multi-day period while preserving the portfolio total. It first sums security contributions for each day to obtain the portfolio’s daily return, then compounds…

The document examines whether a short run of profitable manual trades in equity-index futures can support expectations of unusually high annual returns. The responses caution that a small number of recent trades is weak evidence for persistent skill, and…

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 describes a thesis design for testing cross-sectional momentum in cryptocurrencies. Each week, coins are ranked by their past value-weighted log returns over several lookback windows, then divided into five equal-weighted portfolios. The…

The document clarifies the meaning of price overshooting in the context of predatory trading. A distressed investor’s need to sell can prompt other traders to sell as well, intensifying downward price pressure; they may later buy back the asset. Such…

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 outlines several ways to think about future short-term interest rates. It emphasizes the role of central bank decisions, since short-maturity government yields tend to track policy rates such as the Effective Federal Funds Rate or the midpoint of…

The note addresses one part of the Gibbons, Ross, and Shanken test used to evaluate asset-pricing factor models. The test statistic combines estimated pricing errors with a scaling adjustment based on the factor returns. The specific question is how to…

The note shows how to choose the 5-year and 10-year weights in a 5s/7s/10s interest-rate butterfly so its exposure to the first two principal components is zero. It represents the portfolio’s key-rate sensitivities in PV01 terms, sets the 7-year position as…

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 derives the relationship between a real estate asset's cap rate, its discount rate, and income growth using a perpetuity model. With constant income, value is income divided by the discount rate; with income growing at a constant rate, value is…

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…