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20,364 documente
The document explains how an FX options collar can hedge a foreign-currency receivable while preserving some favorable exchange-rate movement. It contrasts the structure with a forward, which locks in a conversion rate, and with leaving the receivable…
The document surveys ways to estimate the price impact of large trades in liquid markets. A commonly used family relates impact per unit traded value to volatility and the trade’s share of volume during the execution interval, with an exponent between…
The document explains the factor of one half in a mean-variance portfolio objective that subtracts a risk penalty proportional to portfolio variance from expected return. The factor is a mathematical convenience: when differentiating the quadratic variance…
The document asks how to compute an option-value expectation expressed as a path integral. The central practical answer is to use Monte Carlo simulation: generate many possible realizations of the stochastic process and estimate the expectation with a…
The document compares simple price proxies for estimating short-term price movement. One proposal weights the best ask price by bid size and the best bid price by ask size; the last traded price is offered as another useful predictor. These measures are…
The document explains how to estimate a variance risk premium when the available inputs are probability densities rather than volatility estimates. It defines the premium, loosely, as the difference between objective and risk-neutral variance of future…
The document considers insurance payoffs that combine a financial asset with survival or death, such as an endowment paying a stock-linked amount if the policyholder survives. Its answer explains a simplifying approach: assume financial and mortality risks…
The document explains how to value the EUR leg of a EUR-GBP cross-currency swap when GBP collateral is specified. The EUR leg needs both a three-month EURIBOR forward curve and a EUR discount curve that are consistent with GBP collateral. In theory, these…
The document asks how to estimate execution-price deviations and slippage for stock strategies when only daily OHLCV data is available. The proposed starting point in the question relates the daily high-low range to trading volume, with a restriction on…
The document outlines how to build an equity curve for a two-stock pair-trading backtest. It starts from entry and exit signals, assigns long and short portfolio weights, and estimates share quantities using initial capital and prices at entry. It then…
Implied volatility is the volatility input that makes an option pricing model, such as Black–Scholes, match an option’s market price. Because each strike, maturity, and option type is a distinct contract, each can trade at a different price and therefore…
The document explains how obligor asset correlations in a Vasicek single-factor credit model can be assigned under the Basel II Internal Ratings-Based framework. It presents a correlation rule that varies with probability of default, along with an adjustment…
The document discusses adding a penalty proportional to absolute portfolio changes to a mean–variance objective, while retaining constraints such as long-only holdings and fully invested weights. Its central modeling idea is to represent each position change…
The document considers whether a trader who needs tight spreads should post non-marketable limit orders inside the quoted bid–ask spread instead of crossing it. It explains why the chance and timing of a fill are difficult to estimate in spot foreign…
The document describes difficulty obtaining stable parameters when calibrating a two-factor Hull–White interest-rate model to cap prices. The five parameters are two mean-reversion rates, two volatility parameters, and the correlation between factors.…
The document asks whether two assets with equal return volatility can be combined into a product with greater percentage-return volatility, without simply using cash leverage. It considers a long-only linear combination and derives its variance from the…
The document discusses foresight, or look-ahead, bias in least-squares Monte Carlo valuation of American options. In the Longstaff–Schwartz approach, regression on the same simulated paths used for valuation can overfit continuation values and make estimated…
The document asks how to simulate a credit spread series that tends to tighten when stock returns exceed their average and widen when returns fall below it. It proposes a linear model: a positive baseline spread minus a positive coefficient times the…
The document considers how to estimate Treasury yields beyond the longest available bond maturities, using a theoretical 40- or 50-year yield as an example. The questioner reports that Nelson–Siegel and Svensson curve fits gave unsatisfactory, unstable…
Subadditivity says that the risk assigned to a combined position should be no greater than the sum of the risks assigned to its components. The document explains the right-hand side as the separate risks of two positions, whether those positions are held in…
The document asks how to form a confidence interval for a set of long-window moving averages when adjacent values are dependent. The questioner is unsure whether a simple standard deviation based interval is appropriate, given the overlap among observations,…
The document discusses how to make yield curve stress shocks meaningful when the current rate level differs from the historical level used to define a shock. It contrasts applying a proportional change to rates, which can exaggerate moves at low levels, with…
The document clarifies a calculation for estimating volatility in a PRIIPs Category 2 stress scenario. The questioner first forms overlapping 63-day log returns, then calculates the standard deviation of those returns. The response says to calculate daily…
The question challenges the idea that an American option should always be worth more than its intrinsic value, making sale preferable to early exercise. The key correction is that at an optimal exercise point, the option’s value equals its exercise value.…