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20,364 dokumenter
The document examines interest-rate sensitivity for an option on a futures contract when the option and futures use futures-style settlement. It uses the Black 76 call-pricing expression, in which the option value is discounted by the risk-free rate while…
The document examines how to interpret variance vega in a stochastic volatility model. It considers changing the variance at the valuation time by a small amount and asks whether that change should be added to the variance path at every later time, or…
The document explains why the meaning of delta depends on whether someone is discussing a model Greek, an individual trade, or portfolio exposure. A single option’s pure delta is a sensitivity to the underlying price and is dimensionless; multiplying it by…
The document compares Brigo and Mercurio’s interest rate modeling text with Andersen and Piterbarg’s multi-volume treatment. It presents contrasting reader assessments: one favors Brigo and Mercurio for clear explanations, practical techniques, and a direct…
The document explains how to reproduce a plot illustrating the False Strategy theorem: as more independent strategies are backtested, the best observed Sharpe ratio can rise even when the strategies have no genuine edge. The example computes the 25th, 50th,…
The note explains a futures-based method for separating an unexpected policy-rate change from the expected component. The cited approach uses the change in the rate implied by a current-month federal funds futures contract around the policy event, scaled to…
The note addresses which interest rate to use when evaluating stock index futures arbitrage. It recommends matching the financing rate to the expected life of the trade, typically the time remaining until futures expiry at the outset, because the…
Dupire local volatility calibrates a deterministic function of time and spot to reproduce observed European option prices across strikes and maturities. This makes it convenient for matching the initial vanilla option surface, but the model ties volatility…
The note explains how the risk-free rate enters the standard CAPM as the intercept and as the benchmark subtracted from expected market return. In the standard setup, these roles use one rate; lending and borrowing at different rates can appear in a capital…
The response offers a large-sample variance expression as a starting point for estimating uncertainty in an empirical Expected Shortfall measure. The formula expresses the estimator’s asymptotic variance through a double integral over the distribution’s…
The response derives the price of a contract paying the squared log return at expiry. It first expresses the payoff as a function of the terminal asset price and values it as a discounted expectation under the risk-neutral measure. It then applies the…
The discussion explains a possible meaning of the phrase “variance swap volatility.” It interprets the quantity as the volatility level associated with a variance-swap strike that makes the contract have zero value at the relevant time. This is a concise…
The discussion addresses whether log-periodic power law (LPPL) models used in crash prediction should be treated as continuous- or discrete-time processes. Its main answer is that the model is defined continuously in time, while discrete price observations…
The document reviews a Python implementation of the Parkinson volatility estimator, which uses high and low prices rather than close-to-close returns. Its central calculation squares the log ratio of each period’s high to low, sums those values over a…
The document considers whether Yahoo Finance adjusted closing prices can be used to calculate mutual fund total returns. It distinguishes returns based on unadjusted closing prices, which track changes in quoted prices, from total returns that account for…
The document distinguishes arithmetic average returns from cumulative, compounded performance. A portfolio can have a higher average periodic return yet finish with a lower cumulative value, because cumulative performance depends on the sequence and…
The document explains why a bond’s best quoted bid can equal its clean price. Clean prices exclude accrued interest, while dirty prices include it; most bonds are quoted using the clean-price convention. This makes equality between a quoted bid and a clean…
The document presents an exercise involving prices of calls across strikes and asks how to derive prices for two other terminal-payoff claims: a digital that pays when the underlying exceeds a strike, and a squared call payoff. It defines the call value as…
The document considers whether a holder of bitcoin can mimic put-option protection by shorting CME bitcoin futures above a chosen price and returning to a neutral position when the price crosses that threshold. The motivation is concern that a rising market…
The document asks whether a low-frequency US equity statistical arbitrage strategy can assume that liquid stocks are available to borrow. The strategy holds roughly equal-sized long and short stock baskets, trades at the open, and replaces much of its…
The note clarifies how to interpret year labels and short-rate nodes in a Black-Derman-Toy bond tree. It explains that the initial rate, r₀, discounts the bond over the period from now to one year, while the up and down rates at the next tree level apply…
The document distinguishes forward variance swap volatility from the future implied volatility smile used to value forward-start options. Under idealized assumptions of a pure diffusion and continuously measured variance, the forward variance swap rate can…
The document raises whether the volatility and correlation statistics for USD/JPY and GBP/USD are enough to calculate the correlation of the derived GBP/JPY cross rate, given that GBP/JPY equals GBP/USD multiplied by USD/JPY. It also asks whether a…
The document explains how to search academic work on strategies that exploit knowledge of clustered orders. It distinguishes stop orders, which are not publicly displayed, from visible limit orders in the order book. For visible liquidity and imbalances, it…