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20,364 dokumentů
The document asks how quantitative strategies can compare derivatives with different expiries, prices, and volatility characteristics, using commodity futures as an example. It highlights a limitation of applying a single-price time-series method, such as a…
The document distinguishes adapted and predictable processes using a Brownian motion and its natural filtration. It compares the Brownian path itself, a version delayed by one time unit, and a version shifted forward by one time unit. The first is adapted;…
The document surveys strategies in which receiving market data or reaching an exchange sooner may affect execution. It describes latency arbitrage as a contest over speed, with examples including arbitrage across fragmented equity venues, triangular…
The document works through a hedge for a company planning to issue 180-day commercial paper. Because the company benefits from higher short-term rates when issuing the paper, it can short Eurodollar futures; the example scales the position by comparing the…
The document explains why a less liquid corporate bond will often have a wider bid–ask spread than a comparable, easier-to-source bond. Investors may require compensation for the risk of holding an asset that could be difficult to sell, while the bond’s…
The document considers a European payoff equal to the difference between the highest and lowest observed stock prices over a discrete period. Under its stated multi-step binomial model, the stock is assumed to be a martingale and the risk-free bond has…
The document offers a qualitative guide to who commonly trades interest rate swaps and related US Treasury instruments at different points on the curve. It associates short-dated swaps with macro traders, hedge funds, corporates hedging loans, and banks…
The document asks how to describe the distribution of the highest price reached by a cash-or-nothing digital call before expiration. It assumes the underlying follows geometric Brownian motion with constant volatility and uses the Black-style probability…
The document outlines a progression of methods for testing strategies that depend on timely execution, especially passive orders and cross-market hedging. For liquidity-taking strategies, top-of-book data may support conservative size assumptions that can…
The document examines why annualized volatility estimated from weekly or other lower-frequency returns can exceed an estimate from daily returns. The square-root-of-time scaling rule relies on returns being identically distributed and independent; serial…
A zero-mean GARCH model treats returns as conditionally centered at zero and estimates conditional variance from squared returns and past variance. If this assumption is used, the model can forecast volatility directly from the observed squared returns. When…
For European options with the same strike and expiry, put–call parity links their prices to the discounted forward price and implies consistent implied volatility when prices and market inputs are aligned. The discussion addresses why observed implied…
The document considers how to generate many Brownian bridge paths for multiple underlying assets in a Monte Carlo setting. The original routine advances through time steps and simulates one path at a time, which becomes slow when the number of simulations…
The document asks how to choose stop-loss and take-profit thresholds from trade outcomes and expected profit estimates. It points to operations research and stochastic processes, and presents differing views: one answer argues that thresholds may be…
A baker who will need wheat later can hedge the uncertain purchase price by going long futures contracts that mature when the wheat is needed. The document explains the cash flows at maturity: the futures gain is the spot price at maturity minus the initial…
The document presents a proposed backward-time finite-difference scheme for solving the Black–Scholes partial differential equation. Starting from the option payoff at expiration, it uses a Taylor approximation to step the value backward in time. It…
The note answers whether principal-only mortgage bond prices or yields rise when interest rates fall. Its conclusion is that prices rise, with two mechanisms contributing. First, the usual bond price relationship applies: lower market rates increase the…
The note explains daily variation margin by contrasting futures with assets such as stocks and options. When an investor buys a stock or an option, cash changes hands at the initial transaction; later price moves alter the account’s marked value. The…
The note explains why an American put’s value can exceed the amount available from exercising it immediately. The payoff is a lower bound: the holder can exercise and receive that amount, or keep the option alive. The right to choose later has value because…
The document asks how to split a European option’s net present value into intrinsic value and time value when pricing with QuantLib-Python’s Black–Scholes example. It explains that intrinsic value can be obtained by applying the option’s payoff function to…
The document distinguishes an option’s expected payoff from the effect of volatility on that payoff. Under risk-neutral pricing, an option value is the discounted expected payoff, so a larger expected payoff corresponds to a higher value. But raising…
The document asks how to estimate wrong-way risk for an exotic option priced by Monte Carlo under the Heston stochastic volatility model. It describes a proposed framework in which market risk factors and credit risk factors are simulated jointly. Dependence…
A Brownian motion is characterized by the distributions of its increments under a particular probability measure. The document explains that the same underlying sample space and paths can be assigned different probabilities, changing the distributions of…
The document explains how Libor fixings work when an interest rate swap pays every six months but references a three month Libor rate. Libor is typically set in advance, shortly before the start of each accrual period, and paid in arrears. In the example,…