คลังความรู้

The document explains how to aggregate ordinary monthly returns into quarterly returns. For each quarter, add one to every monthly return, multiply those gross returns together, and subtract one. This captures the effect of sequential returns; simply summing…

The document gives an approximation for the probability that a stock touches a short strangle’s higher strike without touching its lower strike. It defines events for touching each side and expresses the desired probability as the probability of touching the…

For normally distributed asset returns with known means and covariance, the document relates portfolio VaR optimization to familiar portfolio objectives. When VaR is defined as a return quantile centered on the portfolio mean, maximizing it is equivalent to…

The document examines why a finite-step Taylor expansion for an option price can include the squared asset-price increment, while a continuous-time Itô calculation uses quadratic variation. It distinguishes two ways to express a change in a smooth function:…

The document asks how to compare strategies whose capital usage differs over time. It contrasts strategies with stable allocations against an event-triggered strategy whose invested capital varies, noting that return as a percentage of capital is easier to…

The document considers how to specify the mean equation when forecasting stock index return volatility with a GARCH model. One workflow first selects AR and MA terms for the mean using an ARIMA procedure, estimates that equation by least squares, and checks…

The document proposes a heatmap for showing how often obligors remain in each credit rating class from one period to the next. Ratings occupy one axis and time intervals the other; color represents the proportion that kept the same rating. This puts many…

The document distinguishes martingale assumptions used in derivative pricing from assumptions used in trading and risk management. For pricing, it describes a risk-neutral probability measure under which an underlying asset is a martingale, linking that…

The document describes a proposed way to compare an algorithm’s backtest with a simple benchmark portfolio. The benchmark buys some or all stocks in a selected universe at the start of the test period, then closes positions at the end, with transaction fees…

The document asks whether an FX swap can be priced by subtracting spot from the theoretical FX forward rate. The proposed forward calculation uses spot and the two currencies’ interest rates, and the question frames the swap value as the forward-minus-spot…

The document asks how to apply stratified sampling, a variance reduction technique, when pricing Asian options by Monte Carlo simulation. It contrasts stratifying the terminal Brownian motion value for a European option with stratifying the average of…

The document addresses how to execute a large futures order in a thin order book while limiting market impact. It recommends splitting an order algorithmically instead of submitting a large market order. VWAP is presented as a straightforward, widely…

The discussion examines a long-dated equity index call whose hedged profit and loss appears sensitive to interest rates. It questions whether a standard Black–Scholes formula using a current LIBOR rate and ordinary delta hedging remains appropriate when…

The document concerns estimating parameters for a stochastic volatility model in which variance follows a Cox–Ingersoll–Ross (CIR) square-root process. The question asks for estimation from time-series data rather than option prices, with quasi-maximum…

The document explains why gross basis tends to decline as a bond futures contract approaches delivery. It defines gross and net basis and relates the implied repo rate to the bond’s invoice price, cash price, and time remaining. Because time to delivery…

The document asks how to set the fixed-leg payment frequency when pricing an interest rate swap in MATLAB. The accepted response identifies a reset-frequency name-value setting as the relevant parameter, rather than the period option used in a bond-pricing…

The document explores why historical replay alone may not faithfully test market-making or other microstructure strategies. A replay uses recorded order-book events, but cannot fully capture how other participants would react to the strategy's orders. The…

The document examines how to simulate multiple geometric Brownian motion price paths with a specified correlation structure. The attempted R approach draws independent normal shocks, applies a Cholesky factor of the input correlation matrix, and uses the…

The document asks whether volume-based bars can make fixed-parameter strategies more responsive to changing market activity. It starts from the observation that equal calendar periods may represent very different conditions, then suggests volume bars as a…

The document explains free cash flow as operating cash flow after capital expenditures. Operating cash flow reflects cash generated through business operations, while capital expenditures are spending on long-lived operating assets. It distinguishes free…

The document addresses the lack of long histories for Treasury bond ETFs, especially leveraged funds, when backtesting portfolios over periods earlier than those products existed. It suggests using long bond futures as a proxy source of historical exposure…

The document considers how to calculate returns from one-minute price bars when a trading session begins after a long market closure. The first observed price of a session and the prior session’s final price produce a return spanning far more than one…

The document asks how to build a simple parametric value-at-risk estimate for comparison with ISDA SIMM initial margin. It specifically raises whether the profit-and-loss distribution should be normal or asymmetric, and whether a model should include option…

The document distinguishes a stock’s return over an individual year from its annualized return across multiple years. It describes an example with an initial investment, a change in year-end price, and no purchases or sales during the holding period. The…