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20,364 dokumenter
The note gives an intuitive interpretation of the scaling used to make a symmetric random walk converge toward Brownian motion. As the time grid is refined, the number of independent coin tosses over a fixed interval rises, while the gain or loss on each…
The note explains how to estimate fair value for a futures contract using the cost-of-carry relationship. For an index future, it relates the spot index level to financing over the contract term, adjusted for income such as dividends. The same idea can be…
The document distinguishes two measures of a company’s financial performance and position. Book value per share divides common shareholders’ equity by the number of common shares and represents an accumulated balance-sheet amount. Earnings per share measures…
The document gives a broad overview of securitizing a loan portfolio, including how investor needs can shape tranche design. It describes a common sequential payment waterfall: senior bonds receive principal and interest first, while losses and, where…
The document shows how to calculate the unconditional expectation of an exponential Wiener process. For a process defined as the exponential of standard Brownian motion, the answer uses the moment-generating property of a normal random variable: the…
The document outlines a basic approach to trading markets believed to revert toward a central level. It recommends first testing whether the price series is mean reverting, with the Augmented Dickey-Fuller test offered as one possible check. If the…
The discussion frames ETF counterparty risk as a question of fund structure and replication method. It points readers toward a Financial Stability Board report, along with a related summary, as resources for examining different ETF designs. It also mentions…
The discussion explains a common source of discontinuities when building return series for standardized contracts such as IMM swaps or credit default swaps. A fixed-maturity CDS quote can remain stable across a roll date, while its label as an on-the-run…
The discussion addresses why a Chilean peso swap valuation built from flat discount and projection curves may differ substantially from market valuations. The response recommends constructing a curve from market quotes for the relevant CLP overnight indexed…
The discussion explains why Black–Scholes remains useful even though it cannot establish a uniquely fair option price. Its broader contribution is the dynamic hedging framework: under suitable assumptions, an option payoff can be replicated by adjusting…
The document asks whether tactical asset allocation ranges around strategic benchmark weights can be derived from asset-class correlations and information ratios without starting from proposed tactical weights or signals. It outlines two existing approaches:…
The document explains a volatility innovation as the part of future volatility that was not captured by the forecast made with currently available information. If realized volatility differs from its prediction, that forecast error is the innovation. In…
The document asks how to show that a power of a Black–Scholes stock price, normalized by its initial value, is a positive martingale under the risk-neutral measure. It assumes the stock follows the standard risk-neutral diffusion and sets the power using the…
The answer contrasts the former Australian dollar LIBOR benchmark with BBSW by describing how each rate was formed. BBSW is quoted by major Australian banks and is based on prices for discounted securities. The former AUD LIBOR, by contrast, relied on…
The answer distinguishes equality of option Greeks from equality of option prices. Greeks describe sensitivities, so two positions can have the same sensitivities while differing by a constant price offset. A replicating or hedging argument can support a…
The answer proposes simulating a price process with a fixed number of hourly steps and bounded daily returns. It sets the size of each step from the upper and lower daily limits and the number of steps, then uses Bernoulli draws to choose the direction of…
The answer explains that the Black–Scholes formula follows from the terminal-price distribution of a geometric Brownian motion (GBM). A Monte Carlo method simulates terminal prices under that process, applies the option payoff, averages the payoffs, and…
The document seeks a thorough and orderly treatment of Lebesgue-Stieltjes integration, bounded variation, and Stieltjes integrals as background for stochastic integration. It notes that one cited stochastic integration text lists relevant results without…
The document explains how to place a histogram and a probability density curve on a comparable scale. It connects the cumulative distribution function to its density: probability accumulated over a small interval is approximately the density at that location…
The document asks whether the sharp rise in long-term US Treasury yields during 1987 should be treated as a key cause of the stock market crash. It reports that the 30-year yield rose from 7.29% in January to 10.25% on October 19, a change of 296 basis…
The document examines a European call with a lower strike and a put with a higher strike, both expiring at the same time. It asks whether a condition linking their premiums to the gap between strikes could create a portfolio with a non-negative payoff and…
The document examines whether asset-level absolute risk contribution limits can be added to a return-maximizing portfolio optimization problem with a volatility cap. It defines portfolio volatility from the covariance matrix and weights, then derives…
The document addresses why forecasting each business line with its own compound annual growth rate can produce a different next-period total from forecasting the combined business with its aggregate CAGR. It defines each line’s CAGR from its starting and…
The document describes the exposure a broker takes on when a customer buys a contract for difference (CFD). Because a CFD passes through the underlying asset’s price change, the broker is short that exposure and may need to acquire a corresponding long…