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20,364 dokumenter
The document discusses using the Heston stochastic volatility model to estimate Value at Risk and Conditional Value at Risk. It contrasts Heston’s joint stochastic modeling of asset prices and volatility with GARCH, which models conditional volatility from…
The document addresses whether portfolio weights should be optimized using asset returns or returns measured relative to a benchmark. Its answer favors raw portfolio returns when the goal is to evaluate a complete investment strategy without a specific…
The document considers a contract paying the average stock price over an interval ending at maturity. It introduces a running integral of the stock price as an additional state variable and applies Itô’s lemma to a price function of time, spot, and that…
The document considers how to estimate a bond’s price sensitivity to changes in credit risk and whether duration and convexity are sufficient. It suggests using a credit default swap, when one is available on the bond, as a market indicator of credit risk…
The document explains how to calculate account performance when deposits, withdrawals, and currency conversions can occur at any time. It recommends treating the account like a fund: track the number of units outstanding and the net asset value per unit in a…
The document discusses whether Malliavin calculus has practical value in finance, especially for computing Greeks on exotic derivatives. Its main use case is a payoff with nonsmooth features, where finite-difference estimates can be difficult or unstable.…
The document asks whether correlation swaps respond differently to stochastic volatility than to local volatility. Its answer identifies a decorrelation effect: under stochastic volatility, each underlying’s volatility varies over time, increasing the…
The document describes an application of a multivariate GARCH-BEKK model to spot and futures price returns. It presents estimated model parameters and asks how to derive the conditional variance and covariance matrix from them. The stated hedge ratio is the…
A digital option pays a fixed amount if it finishes in the money and nothing otherwise. The note explains that the payoff diagram’s height is this fixed payment, often denoted by δ. The underlying price determines whether the payment is triggered, while the…
The document describes a terminal-wealth portfolio allocation problem with a quadratic penalty for falling below a target wealth level. It approximates expected utility under normally distributed portfolio returns using Gauss–Hermite quadrature, then…
The note distinguishes the bid–ask spread from the mid-price: the spread is the difference between the best offer and bid, while the mid-price is their arithmetic midpoint. It then cautions that this quote midpoint is only a simple proxy for fair value,…
The discussion concerns joint maximum likelihood estimation of the drift and volatility of a geometric Brownian motion from simulated log prices. Although the likelihood can identify volatility clearly, it may appear nearly flat in the drift direction when…
The note explains why the Black–Scholes call pricing formula is dimensionally consistent, despite an apparent problem involving the square root of time in the normal cumulative distribution inputs. The option price, underlying price, and strike are all…
The document explores the Grossman–Stiglitz paradox: if prices fully reflect information and trading cannot earn excess returns, investors may have little incentive to gather information or trade. Responses offer several reasons trading can persist.…
The document presents an insurance ruin theory exercise using a compound Poisson model. Claim arrivals follow a Poisson process, while claim sizes are exponentially distributed. The exercise asks for claim frequency over different time intervals,…
The document asks whether an app giving every investor the same supposedly optimal stock portfolio could distort markets. It raises two possible effects: stocks excluded from the recommended portfolio might lose investor demand, and favored stocks might…
The document addresses how to describe coupon and amortization income relative to the amount originally paid for a bond, while distinguishing that measure from the bond’s current market value. It proposes realized holding period return for cash flows…
The document compares two annualized yield measures for a short maturity zero-coupon security. Bond equivalent yield scales the return relative to the purchase price by the fraction of a year represented by the days to maturity, reflecting simple interest.…
The document poses a practical question about calculating a Sharpe ratio from a portfolio’s daily observations over a year. The investor has annualized log returns and a risk-free rate for the same year, and proposes dividing their difference by the standard…
The document explains how to specify correlated Brownian drivers for a two-asset Heston model. Since each asset has a price process and a variance process, the simulation uses four stochastic drivers and therefore requires a joint four-by-four correlation…
The document considers how to report 95% VaR when a return sample contains no losses. Under a historical quantile calculation, the measured lower-tail return may still be positive; the accepted answer recommends flooring reported loss VaR at zero under a…
The document explains how to derive a local volatility surface from a smooth implied volatility surface and how to handle its derivatives in numerical work. It recommends using finite differences across expiry at fixed moneyness for the time derivative,…
The document describes a portfolio investor’s uncertainty about which standard deviation belongs in an annual Sharpe ratio when returns are recorded daily over a long historical period. The investor compares the dispersion of annual returns across years with…
The document asks how to infer negative-moneyness implied volatilities for interest-rate swaptions when broker data provide at-the-money volatility and payer and receiver spreads only at positive offsets from the at-the-money forward. It considers lognormal,…