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20,364 dokumentov
The document poses a problem about finding a high quantile for the sum of two dependent random variables. Each variable is modeled with an extreme value distribution, and their dependence is represented by a Gumbel copula. The question highlights a common…
The document outlines a multi-curve approach to building the euro three-month forward curve alongside the OIS discount curve. It identifies short-dated futures, swaps at longer maturities, and LIBOR–OIS basis swaps as market instruments used in the process.…
The document addresses whether the time integral of squared Brownian motion is a random variable and how to find its first two moments. It computes the expectation by interchanging expectation and integration, then using the fact that standard Brownian…
The document shows how to calculate a cohort-level single monthly mortality rate (SMM) from loan-level data. The cohort SMM is the total prepaid monthly balance divided by the total scheduled balance across the loans in that cohort. Equivalently, it is a…
The document explains the difference between credit default swaps and recovery swaps in the context of loan default risk. A CDS provides protection when a defined credit event occurs, such as a borrower’s failure to make a coupon payment. The protection…
The document distinguishes returns from cumulative returns and explains how the definition of the cumulative window affects stationarity. A cumulative return measured from a fixed starting date accumulates variation over time, so even when the underlying…
Fast stochastic %K and Williams %R both measure a closing price’s position within the high-low range over a chosen lookback window. The document defines %K as the close’s distance above the low, scaled to a 0–100 range, and %R as the distance below the high,…
The document frames numerical solution of a nonlinear pricing PDE for a derivative under the uncertain volatility model. Volatility is selected from a lower or upper bound according to the sign of the solution’s second spatial derivative, so the PDE is…
The discussion explains why estimating returns and covariances from historical prices for Modern Portfolio Theory (MPT) does not, by itself, contradict the weak Efficient Market Hypothesis (EMH). MPT prescribes how to allocate assets given expectations about…
The discussion presents stochastic portfolio theory (SPT) as a framework for portfolio growth that accounts for asset variances and co-movements. It contrasts arithmetic expected returns with long-run logarithmic growth, explaining that volatility can reduce…
The discussion distinguishes a derivative’s contractual cash flows from the funding burden a dealer may face while holding and hedging an uncollateralized position. A forward entered at zero value can later become an asset or liability without requiring the…
The note examines whether Rebonato’s swaption volatility approximation works only near the money. The questioner compares Black prices using the approximation with Monte Carlo prices, reporting larger discrepancies for strikes farther from at-the-money in…
The document connects the elliptic form of the Heston stochastic volatility operator to a boundary value problem with Dirichlet conditions. It explains that solutions to obstacle problems for this operator can represent value functions for perpetual…
The discussion considers software requirements for currency arbitrage, including fast market-data updates, processing many combinations, exchange connectivity, account support, and algorithm scripting. The replies caution that FX markets are not generally…
The note derives a Monte Carlo estimator for a European log-contract whose terminal payoff is the logarithm of the asset price relative to its initial price. Under risk-neutral Black–Scholes dynamics, Itô’s lemma gives a lognormal terminal asset price, which…
The document considers why the Black–Scholes stock-price expression includes volatility while its expected price growth appears independent of volatility. It asks whether this means investors should accept a risky asset whose expected return equals the…
The document raises a measurement concern for historical tests of covered interest rate parity (CIP). It notes that interbank forward quotes are commonly expressed against the US dollar, with a stated exception, and asks whether inconsistencies between…
The document asks whether the Poisson-mixture formula used to price European options under Merton’s jump-diffusion model can also price American options. For European contracts, the cited formula weights Black–Scholes prices adjusted for the number of jumps…
The document explains how to interpret a table reporting the risk of a dynamically delta-hedged option position. It describes simulating stock-price paths at the stated weekly frequency, computing the option delta at each step, and adjusting the share…
The document considers whether historical VaR for a single instrument can be extended to a one-year horizon. The main answer warns that long-horizon estimates are highly sensitive to the assumed or estimated mean return. Since drift is difficult to estimate…
The document collects suggested reading for an internship in model risk management focused on counterparty credit risk, especially exposure from derivatives. Its references cover modeling, pricing, and hedging counterparty exposure; credit valuation…
The document asks which unsupervised learning methods can help discover patterns in manually selected financial time-series features, with the aim of making broad predictions about future price behavior. It gives examples ranging from predicting the next…
The document discusses how to compare the VIX with realized volatility calculated from daily S&P 500 index prices. The questioner computes rolling volatility from log returns, annualizes it using the square root of 252, and asks whether a 30-day or roughly…
The document proposes modeling a positive process by making its logarithm an Ornstein–Uhlenbeck process. In this construction, the log value mean-reverts toward a constant level, so the corresponding process is positive and its long-run central level is the…