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20,364 dokumentov
The note explains why the effective federal funds rate can trade below the Federal Reserve’s interest rate on reserve balances (IORB). The rate corridor has IORB as its lower reference point and the standing repo facility as a theoretical upper bound, but…
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 asks whether Value at Risk at probability levels α and 1−α has a general relationship when the loss distribution is asymmetric. Using a definition based on a tail probability quantile, the answer says there is no such general relationship: VaR…
The document introduces stopping times using a filtration to represent information available over time. A decision time is a stopping time when whether it has occurred by time t can be determined from information available by t. It applies this idea to…
The document considers prediction of a continuous variable when correctly ordering observations matters more than matching their values in a way that maximizes Pearson correlation. One simple approach is to transform the target into ranks and fit an ordinary…
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 asks how to infer a client’s risk-aversion parameter from an already chosen optimal portfolio of two assets under quadratic utility and a full-investment constraint. It defines portfolio utility as expected return minus a variance penalty, with…
The document describes the inventory challenge faced when quoting many option strikes and levels in a fast market. Frequent fills change the portfolio’s delta, but immediately hedging every fill with taker orders can incur substantial spread costs. Waiting…
The document explains where additional shares come from when IPO underwriters exercise a greenshoe, or overallotment, option. It says that the option is described in the prospectus and that exercising it leads the company to issue additional shares. The…
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 answer distinguishes daily returns from intraday returns when calculating historical volatility. For close-to-close volatility, it describes taking the standard deviation of daily log returns and scaling by the square root of an assumed number of trading…
The answer explains that an MA model represents a series using current and past shocks, rather than past observed values. It suggests comparing simulated AR(1) and ARMA(1,1) series with the same errors to see how the moving-average coefficient changes their…
The document asks how to set internal concentration limits for a retail credit portfolio and whether the Herfindahl-Hirschman Index (HHI) is suitable. It defines HHI as the sum of squared exposure weights and notes that its range depends on the number of…
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 explains how to represent principal repayments when constructing an amortizing fixed-rate bond in QuantLib. It first builds a semiannual schedule spanning the two stated repayment dates, then supplies a notional amount for each coupon period.…
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…
The document compares tick and minimum trade sizes for BrokerTec U.S. Treasury central limit order books. It reports that the existing venue uses different price increments across Treasury maturities, with quotes expressed per $100 of face value and a…
The document investigates why a simulated call price comes out as zero when the Black–Scholes calculation gives a positive value. Its proposed remedy is to simulate the underlying under the risk-neutral geometric Brownian motion process, using the risk-free…
The document answers whether local volatility can be estimated using only the spot price at a particular time. It explains that Dupire’s approach derives local variance as a function of option maturity and strike from a surface of call prices, rather than…
The document outlines a Monte Carlo approach for valuing performance share units whose payout depends on a company’s share-price performance relative to a peer group. It estimates daily log-return means, volatilities, and correlations from historical prices,…