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20,364 dokumenter
The document answers a data-timing question about Bloomberg Open Symbology’s precanned files. It reports that the files are updated twice daily, at 8 a.m. and 2 p.m. Eastern time. For someone planning a single daily refresh at 9 a.m. Eastern, the reported…
The document considers a game that pays a fixed amount only if five coin flips all land heads, then asks how much a player should pay for one round versus many repeated rounds. It starts from the expected payoff, but notes that this value does not capture…
The document raises a notation issue in Fourier option pricing with the Heston model: some characteristic functions include a term for the current log-price, while others show only terms involving the model’s variance state. The distinction is whether the…
The document examines two Black–Scholes sensitivities for an at-the-money European option: how Vega changes as time to expiry grows, and how option price changes as implied volatility rises. For the expiry question, it considers the derivative of Vega with…
The document explains why a vanilla bond’s duration and DV01 can move in opposite directions as its coupon changes. Duration describes price sensitivity relative to the bond’s value, while DV01 measures the approximate dollar price change for a one basis…
The document proposes estimating equilibrium exchange rates across three traded asset pairs without simulating arbitrage trades through every order book. It formulates a constrained optimization that minimizes the volume-weighted squared deviations between…
The document considers a cash-or-nothing claim that pays when one of two risky assets exceeds the other at maturity. Both assets are modeled with geometric Brownian motion driven by the same Wiener process, alongside a risk-free asset. The proposed pricing…
The document shows how to solve for the continuously compounded yield of a two-year coupon bond when its price is expressed as the discounted value of the coupon payments and principal. The suggested substitution sets the exponential discount factor equal to…
The document proposes estimating a Treasury bond futures price from a selected Treasury bond’s cash price and the conversion factor for the cheapest-to-deliver bond. It suggests dividing the bond price by that factor, then comparing the estimate with the…
The document explains why a forward contract with zero value at inception generally has a delivery price different from today’s spot price. It uses replication: hold the underlying asset and finance the delivery payment with a riskless bond position.…
The document explains how to express gold’s price against a basket of currencies to reduce dependence on any single currency’s movements. Its example basket combines fixed amounts of US dollars, euros, and Japanese yen, then converts the basket value into…
The discussion asks whether an unhedgeable option should be valued using real-world probabilities rather than risk-neutral pricing. Its central point is that risk-neutral valuation relies on relationships supported by trading and hedging in the underlying.…
The document considers selecting a subset of currency pairs to form a basket subject to correlation, a second property, and a minimum basket size. Rather than enumerate every subset, the answers recommend defining a clear score or treating one target as an…
The document examines a mismatch between two calculations of a one-day stock-price move under a lognormal model. The questioner starts from annualized return and volatility, scales them to a daily horizon, and solves for the annual parameters using two…
Lévy processes do not necessarily have probability densities, and even when a density exists it may not have a closed-form expression. The document contrasts this with familiar exponential Lévy examples, including geometric Brownian motion and a…
The explanation distinguishes the volatility parameter in a geometric Brownian motion model from the standard deviation of the asset price itself. For an Ito process with proportional diffusion, the price is lognormally distributed, so its variance is shaped…
This discussion addresses whether SABR should be calibrated directly to cap quotes or to the individual caplets that compose those caps. Its proposed workflow is to first strip market cap quotes into a caplet volatility surface, then calibrate SABR…
This exchange explains how to represent an FRA whose start date does not fall an integer number of months after the valuation date when constructing a yield curve with QuantLib. The suggested approach is to calculate the interval from the valuation date to…
The document gives simple bounds for American calls and puts on an underlying with continuous dividend yield. Because an American option can be exercised at maturity, its value is at least that of the corresponding European option, so the European lower…
The document distinguishes real-world probability estimates from risk-neutral derivative pricing. It explains that using expected returns in place of the risk-free rate changes the underlying dynamics, while option prices also depend on the market price of…
The document asks how to infer the mean-reversion rate in a deterministic process that moves toward a known long-run level. Its stated dynamics contain only a drift term proportional to the distance from that level, with no random component. The terminal…
The document describes a simulation question for a SABR-LMM model under a selected numeraire. Forward LIBOR rates have shifted SABR dynamics, stochastic lognormal volatilities, and correlated Brownian drivers. The author already uses Euler discretization…
The document defines rolling returns from stock prices using a chosen observation window and shift, then notes that the resulting return distribution may have multiple peaks. It asks how volatility should represent risk when returns are multimodal. The…
The document considers whether assets with extreme estimated betas should be excluded when using CAPM to predict expected returns and calculate residual, or idiosyncratic, returns. The proposed model estimates monthly total returns against a global equity…