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20,364 dokumenter
The document explains three conditions used to characterize a diffusion process: continuity of paths, the local average movement, and the local variance of increments. It relates these conditions to an SDE model for a stock price, distinguishing the process…
The document discusses valuing the floating leg of a daily compounded overnight-indexed swap when payment occurs after the accrual period, under the one-factor Hull–White short-rate model. One derivation rewrites each daily accrual factor using a ratio of…
The document asks how to estimate a stochastic volatility model from historical daily returns without using an implied volatility surface or computationally intensive MCMC. It specifies a latent log variance that follows an autoregressive process with…
The document explains why an equity index future may appear to fall far less than its underlying index during a sharp market move. For a global index such as MSCI World, constituent markets trade in different time zones, so many index prices can remain fixed…
This discussion considers whether a candle-based strategy backtest can rely on mid-prices, especially when modeling stop losses, or should use bid and ask prices to reflect the side at which a trade executes. The author reports that replacing mid-price highs…
The document raises a model-validation question: whether stochastic-volatility option models produce more accurate market-price estimates than the standard Black–Scholes–Merton model. It highlights two practical costs of more complex models: greater…
The question asks whether one can derive the Black–Scholes partial differential equation without invoking Girsanov’s theorem, and whether a stock with nonzero drift is a martingale. The answer distinguishes the original replication argument from later…
This discussion examines whether downside market capture should use compounded returns or sums of periodic returns. One answer explains that simple percentage returns do not add to produce cumulative wealth: compounding uses the product of one plus each…
The document compares AAPL historical data from two vendors and asks why their recorded activity differs. The examples show discrepancies in timestamps, reported trades or quotes, and prices. Replies propose several possible causes: one vendor may provide a…
The document discusses ways to reduce the runtime of repeated mean-variance portfolio optimizations, such as daily rebalancing for a universe of fewer than one hundred assets. It suggests first considering whether the work can be parallelized, then using the…
The document considers how a bank might price a ten-year EUR/DEV cross-currency basis swap when there is no established swap market in DEV and the proposed hedge is to roll daily borrowing and deposits at the two risk-free rates. Its central point is that…
The document examines a convex optimization formulation for constructing a portfolio with a target risk budget. The stated objective combines portfolio variance with a logarithmic penalty weighted by each asset’s desired budget. The questioner imposes a…
The document considers how to assess performance when an investor adds money at uneven intervals and holds a mix of securities, including ETFs and options, potentially with leverage. Its response separates investor cash flows from the return series used for…
The document asks which interest rates are appropriate for empirical covered interest parity testing between Canada and the United States across several forward maturities. It raises a practical concern with Treasury bill rates: their lending yield may not…
The document challenges the claim that an option’s Black–Scholes price is the discounted expected payoff under real-world probabilities. The response recommends comparing this claim with risk-neutral valuation, which uses a pricing measure consistent with…
The document considers a long-run relation between exchange rates and purchasing-power parity whose residual appears stationary only when a deterministic trend is included. It asks whether that trend is acceptable and how to justify its inclusion. The…
The document asks why a stock-price model with drift μ can be expressed under a different probability measure with drift equal to the risk-free rate r, while retaining the same volatility. This is the risk-neutral change of measure used in derivative…
The document describes a shareholder’s concern about convertible notes exchanged for common shares at a conversion price far below the market price. It cites a company filing that identifies a beneficial conversion feature under ASC 470-20, records its…
The document asks for a rule of thumb for the share of a stock’s daily return variance explained by market movement, framed as the typical correlation between a stock and the market. The accepted response cites historical risk-model research and reports that…
The document discusses whether Yahoo Finance data accessed through a Python package is reliable for historical daily open and close prices. The questioner distinguishes actual closing prices from adjusted closes and asks about alternatives. Responses suggest…
The document asks when a Black–Scholes market with two risky assets driven by the same Brownian motion and one risk-free asset is arbitrage-free and complete. The question highlights a modeling issue: the setup has one source of randomness, which does not…
The document raises a practical question about estimating spread option Greeks by applying finite differences to Kirk’s spread option approximation. The author reports that, for options with deltas between 0.45 and 0.6, the resulting gamma estimates fall…
The document considers the lower price bound for a claim in an incomplete market, where multiple risk-neutral measures may be consistent with observed prices. It asks whether sub-replication is the counterpart to super-replication: while the…
The document asks how the CAPM relates an asset’s beta and the equity risk premium to its expected future spot price, including continuous dividend yield. It contrasts a simple one-period return calculation, which gives a linear expression, with an…