คลังความรู้

The discussion considers why experience with poker may be relevant to equity and options trading. Its central analogy is that both activities involve decisions under uncertainty against other participants, where the quality of a choice depends on more than…

The question asks how to estimate the jump intensity in a Black–Scholes–Merton setting from observed jump counts across three consecutive months. The response points to a compound Poisson process as the model for jumps and directs readers to a statistical…

The document shows why European calls and puts with the same strike and maturity have equal gamma under put-call parity. It starts from the parity relation between the call, put, spot price, discounted strike, and interest rate. Differentiating once with…

The document explains the no-arbitrage argument that a claim with a replicating portfolio must have the same initial price as that portfolio. If the claim is overpriced, short the claim, buy the replicating portfolio, and invest the surplus at the risk-free…

The document asks why some derivatives references express option prices on an undiscounted basis. It contrasts a density formula using the strike derivative of an undiscounted call price with the version using discounted prices, which includes a…

The example applies Feynman–Kac to a terminal-value partial differential equation with a fourth-power terminal payoff. The PDE contains a second derivative term proportional to the square of the asset price, and the proposed solution represents the value as…

The discussion considers Java options for basic time-series analysis, including moving averages, standard deviations, correlations, charting, and exponential smoothing. Suggestions range from implementing common statistics directly to using libraries that…

The document explains how to value a CMS indexed range accrual when simulated zero-coupon rates follow a short-rate model under the risk-neutral measure, while the desired probability is expressed under the payment-date forward measure. The payoff event is…

The discussion distinguishes a put diagonal spread from a put calendar spread and explains why a proposed pair of puts with different expirations but the same strike is a calendar spread. The original example uses different strikes, but the answer notes that…

The document asks how to obtain implied volatility for a specific overnight period in foreign exchange, such as the night before a particular trading day. It then asks how to translate an overnight volatility quote into an implied breakeven exchange-rate…

The document asks whether hourly observations can be used to estimate dynamics that matter over a horizon of several days, particularly mean reversion or cointegrating relationships. It refers to a proposed analogy between estimating monthly relationships…

The document asks why a forward price is chosen so that a newly signed contract has zero value, and whether the explanation comes from no-arbitrage or from both parties being indifferent between taking the long and short sides. It also asks why the parties…

The document sets up a structural credit model in which a firm’s asset value follows geometric Brownian motion and default occurs when it reaches an absorbing barrier. A coupon bond pays coupons while the firm survives, pays principal at maturity if it has…

The discussion asks whether a liquid interest rate swap curve can exist without a liquid government bond market, and how dealers hedge the risk they absorb. One answer describes the typical development of local currency markets: governments issue short-dated…

The document asks whether corporate events that change a U.S. common stock’s price or shares outstanding occur during the trading session or predominantly overnight. Its brief answer is that events affecting shares outstanding happen overnight, giving a…

The document explains how to obtain a zero-coupon yield curve and distinguishes observed spot rates from a curve calibrated to traded instruments. A curve can be interpolated from spot rates when they are available, but spot rates are generally not directly…

The document asks how option Greeks, especially delta, should be interpreted under Merton and Kou jump diffusion models. Its central explanation is that a continuous hedge cannot offset a discrete price jump instantaneously. A riskless-portfolio argument…

The document compares two descriptions of risk remaining around a commodity futures hedge. It describes “basic risk” as residual exposure after hedging, including the difference between futures and spot prices if a futures position is closed early. The cited…

The document distinguishes an asset’s expected arithmetic return from its compounded growth rate. Under the return model described in the question, the expected return over a short interval is given by the drift, while the continuously compounded rate…

The document asks how to understand and implement calibration of the SABR model for volatility smiles across equity, foreign exchange, and interest rate markets. Its response points readers toward several papers and practitioner resources, and mentions a…

The document presents a beginner’s question about why summing rate-of-change values multiplied by trading signals gives a different return from the price change between a stated entry and exit. The example uses Bollinger Bands, stochastic indicators, and…

This collection of answers challenges widely used ideas in quantitative finance, including correlation-based diversification, CAPM as an allocation rule, normally distributed independent returns, value at risk, efficient markets, copulas, and perfect delta…

The document illustrates how a company with dollars can use an FX swap when it needs francs to settle a bond purchase and later expects to receive foreign-currency proceeds. In the example, the company exchanges dollars for francs for near-term settlement,…

The question asks whether regional central banks provide programmatic access to their statistical data, after the author encountered CSV downloads and web scraping. The response points to the Federal Reserve Bank of St. Louis’s FRED service as a widely used…