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20,364 dokumenter
The note considers how to compare stock ranking models intended to surface candidates for later fundamental analysis. Its central recommendation is to define the predictor and its outcome separately, then test whether the predictor ranks or classifies future…
The note addresses how to value an uncollateralized swap when the bank must fund its exposure. It describes two equivalent framing choices: discount cash flows using a curve that reflects the bank’s unsecured funding rate, or use OIS discounting as the base…
The document sets up an equity log-price as a function of firm asset value and time, plus a mean-reverting market-noise component. It gives real-world dynamics for the asset value and noise, then applies Itô’s lemma to obtain the drift and two diffusion…
The document explains how a change from the real-world measure to a risk-neutral measure can alter diffusion drifts while preserving instantaneous volatility and correlation. In a geometric Brownian motion example, the market price of risk shifts the…
The document asks whether a payoff equal to the square of the terminal stock price is worth the initial stock price squared grown at the risk-free rate. The response explains that taking a power does not commute with taking an expectation: convexity makes…
The document addresses why returns computed from MSCI World subindices may not match the published parent-index return when weights are based on each subindex’s index level. The answer states that MSCI indices are market-cap weighted, so a rough…
The document examines how the Heston stochastic volatility model changes when moving from the historical probability measure to the risk-neutral measure used for derivative pricing. It describes how the variance risk premium shifts the variance process…
The document clarifies the intercept in a time-series regression of portfolio excess returns on the Carhart four-factor returns. The intercept, or estimated alpha, is the portion of the portfolio’s average excess return that remains unexplained by its…
The document explains how to value an American call on a non-dividend-paying stock with a risk-neutral binomial tree. At each node, the option value is the greater of its immediate exercise value and its discounted expected value at the next step, using…
The document asks how to read a vector autoregression impulse response when the variables are log differences, using exchange-rate volatility and interest rates as an example. It focuses on the vertical-axis value and whether a plotted response should be…
The document asks how to simulate a mean-reverting Ornstein–Uhlenbeck process driven by a Lévy process. It proposes a basic Euler step: approximate the drift over each time interval using the current process value, then add an increment sampled from the Lévy…
The document sets up a short-rate model with mean reversion, square-root diffusion volatility, and independent positive jumps whose sizes follow an exponential distribution. It presents the pricing PIDE for a security paying a function of the terminal rate…
The document discusses a one-period, two-state replication of a forward using stock and cash. The stock holding is chosen to match the difference between the forward payoffs across the two future states, and the cash position makes the combined portfolio…
The document asks whether an option buyer who initially delta hedges using the option’s implied volatility should keep using that original volatility or update the hedge as implied volatility changes. The response says accurate dynamic hedging requires…
The document explains a simple parametric VaR calculation for normally distributed portfolio returns. At a 99% confidence level, the standard normal quantile is about 2.33, so the return standard deviation is multiplied by that factor and the expected return…
The document asks how to model the distribution of ending wealth from a starting investment when an asset’s arithmetic mean return and standard deviation are known. It suggests running repeated simulations in a spreadsheet and plotting their cumulative…
This note explains how to read forward-rate volatility and drift in the Heath–Jarrow–Morton framework, starting from instantaneous forward-rate dynamics and zero-coupon bond prices. It gives the link between bond-price volatility and forward-rate volatility:…
This note derives a relationship between Conditional Value at Risk (CVaR), Value at Risk (VaR), and the expected excess of a random loss over its VaR threshold. It defines VaR through an upper-tail probability and CVaR as the average of VaR quantiles over…
This note addresses whether log returns or simple returns are more appropriate as the dependent variable in a regression studying factors such as dividend yield and stock index returns. It corrects a common misunderstanding about regression assumptions: the…
The document discusses Fourier-based pricing of European calls using a model’s characteristic function. It presents an integral representation that expresses the call price through two probability terms and asks how the formula is derived, when it applies,…
The document explains how to estimate simulation error when pricing an option with Monte Carlo. It identifies the relevant quantity as the standard error of the estimated price, calculated by dividing the estimated standard deviation of simulated outcomes by…
The document asks how to adjust discounting and projected forward rates when valuing collateralized derivatives under a CSA currency with no directly quoted swap or OIS curves. Its response says that FX forwards, local-currency rates, and collateral discount…
The document compares simulated returns from a multivariate BEKK process and geometric Brownian motion with observed stock returns. The author finds that default BEKK output appears too volatile and that both approaches fail to reproduce the excess kurtosis…
The document asks how to estimate the parameters of a coupled square-root diffusion model for an interest rate and its stochastic volatility. It considers rearranging discretized equations for VAR or OLS estimation, but recognizes that these transformations…