คลังความรู้

The document collects suggestions for software and services that can be used to backtest investment strategies. The examples span a mobile portfolio tool, a Python framework, a form based service, standalone engines, and a brokerage platform with strategy…

The document studies a two factor stochastic growth model in which the growth component follows a mean reverting diffusion and the level also has direct Brownian noise correlated with that diffusion. The answers derive the conditional expected change in the…

The document asks how a risk surface can turn sensitivities from a model’s implied volatility function into sensitivities to market quoted volatilities. The described method adds an interpolated surface of risk bumps to the model volatility. At the base…

The document raises a question about delta for American-style exotic options whose holders can make choices at specified times during the option’s life. The holder is assumed to follow an optimal policy that maximizes the option’s value, described in terms…

The document asks how to choose the trade size that maximizes profit when exploiting a price difference between two constant-product market-making pools. Because each pool’s quoted rate changes with the amount traded, a small trade can receive a different…

The document explains a two-period definition of arbitrage: a portfolio must have nonpositive value initially, a nonnegative payoff in every later state, and a strictly positive chance of producing value rather than zero throughout. This framework clarifies…

The document compares approaches to retrieving SEC 10-K information, depending on whether a researcher needs standardized financial data or the original filings. For historical fundamentals such as income statements, balance sheets, and cash flow statements,…

The document asks how to size a four leg iron butterfly and warns that expiration payoff calculations alone do not capture risks while the position is open. The response highlights execution costs, liquidity, assignment, margin, and the possibility of forced…

The document distinguishes an analytic swap PV01 from a market risk measure calculated by shifting rates. Analytic PV01 measures the value change from moving the fixed coupon by one basis point while holding discount factors unchanged; it is useful for…

The document considers whether an equities focused algorithmic firm could earn very high annual returns, including a claim of 100% returns from event driven trading and text mining. Its responses say such outcomes may be possible but emphasize that returns…

The document explains how an observer could estimate the gross premium associated with a reported SPY call trade using option-chain data. The key inputs are the option’s trading volume, the contract multiplier, and the option price. In the example, the cited…

The document discusses estimating the volatility and mean-reversion parameters of a Hull–White short-rate model when the market has daily overnight rates and a swap-based zero-coupon curve but no actively traded options. It distinguishes estimation from…

The document derives probabilities for the first observation date on which a geometric Brownian motion underlier exceeds an autocall barrier. It writes the asset as an exponential of drift and Brownian motion, then converts the barrier condition at each…

The document examines whether combining a long butterfly, which benefits from a price near its center at expiration, with a long straddle, which benefits from a large move, can produce a profit across all terminal prices. The accepted answer explains the…

The document considers the limit of a discrete sum involving two geometric Brownian motions, with a constant offset applied to one process. It defines a partition of the time interval and rewrites the sum using increments of the second process. As the…

The document presents a mean-variance framework for a fully invested portfolio, then decomposes holdings into benchmark weights and active weights. Under the stated setup, the active-weight optimization maximizes expected active return while penalizing…

The document explains why summing SPY’s daily close-minus-open changes does not match the difference between its first opening price and final closing price over the same period. The calculation captures only price movement within each regular session, so it…

The document addresses how to prevent an order-tracking system from recording the same execution more than once when a broker does not provide a separate identifier for each lot. The example includes fills with matching quantities and prices, showing why a…

The document asks whether negative short-term risk-free rates require changes to the Black-Scholes option pricing formula. Its answer says the standard model does not require the rate to be positive, so a negative rate can be used directly. Under the stated…

The document addresses why interest rate swaps are often valued using forward rates derived from today’s yield curve instead of simulating each future floating payment. It explains that spot rates are bootstrapped from traded instruments and imply forward…

The document explores whether a high price-to-earnings multiple can benefit shareholders when a company’s earnings rise. It reasons that, if the multiple stays unchanged, each additional unit of earnings per share translates into a larger price change at a…

The document introduces the risk-neutral density as the probability distribution of an asset price under an equivalent martingale measure. It asks whether that distribution can be described by a density with respect to ordinary length on the price axis, and…

The note explains how to use trade-level profits with PerformanceAnalytics, whose functions generally expect return data rather than a raw list of trade P&L values. One suggested workflow is to record transactions in the blotter package, calculate cash P&L,…

The note asks whether a government bond yield can be divided into an expectations component and a term premium within the Heath–Jarrow–Morton framework. It distinguishes a real-world view of yields, in which investors may describe yields as expectations plus…