คลังความรู้

The discussion considers how to build an equity volatility surface when American and European options are listed on the same underlying and provide separate implied volatility observations at each maturity. One practical preference is to use European options…

This discussion examines why MATLAB’s actual/actual date-to-time calculation may not match QuantLib’s actual/actual day-count variants when code is ported between the two platforms. The example compares a period spanning 2006 to 2036 and reports different…

The discussion asks whether a strategy with many successful trades gives stronger evidence of skill than one with few trades but similar returns. One answer invokes the law of large numbers: as independent observations accumulate, a sample average tends to…

The document asks whether any established financial ratios involve kurtosis and seeks academically discussed examples. The response does not name a particular ratio that uses kurtosis as an explicit component. Instead, it directs readers to a paper section…

The document considers whether Least Median Squares (LMS) regression is useful for financial estimation, such as estimating the beta between two securities. LMS minimizes the median of squared residuals rather than their mean, with the intended benefit of…

The document explains how to infer implied correlation from an observed Margrabe option price. Given the two assets’ volatilities, prices, yields, and time to maturity, correlation determines the option’s relative volatility. The response notes that this…

The document clarifies the proof that the first time an American derivative’s value equals its payoff is an optimal exercise time in a finite-period binomial model. The price process is constructed as the Snell envelope: at each node it is the greater of…

The document describes how to identify the underlying asset, strike, and maturity of French traded warrants when only their ISINs are available. Its suggested workflow uses Bloomberg: look up the ISIN in the terminal to open the security record, then view…

The discussion examines why Black–Scholes can produce implausibly high values for very long-dated options. One explanation is that the model holds interest rates and volatility constant, even though both can change over time. The more detailed argument…

The discussion distinguishes terminology by context. In bond and swap trading, the terms notional and nominal may refer to the same reference amount used to calculate contractual cash flows. In macroeconomics, nominal commonly describes a rate or value…

The discussion considers why an exchange rate might be modeled with geometric Brownian motion, a process whose proportional changes have a drift and a volatility term. With constant coefficients, its solution is an exponential of a drift-adjusted time…

The discussion explains why the risk-free rate can be expressed as the reciprocal of the summed prices of state-contingent claims. Each claim pays one unit of currency in one possible state and nothing in the others. Buying a claim for every state therefore…

The discussion asks whether traders can legally short stocks promoted through unsolicited emails. The answer says that, in the respondent’s experience of Canadian markets, there is no rule barring the trade. It shifts attention from legality to whether a…

The document explains why derivative pricing in a risk-neutral framework discounts expected future payoffs at the risk-free rate. Its central idea is that changing from real-world probabilities to risk-neutral probabilities accounts for risk premia in the…

The document explains how to find the global minimum variance portfolio from two risky assets. It represents the portfolio with weights w and one minus w, then expresses portfolio variance using each asset’s variance and their covariance, represented through…

The document investigates when the phrase “Modern Portfolio Theory” entered use, distinguishing the label from the ideas associated with Markowitz. It notes that Markowitz’s early work used different terminology and reports a 1965 article by Herbert Grubel…

The document derives the dynamics of a stock forward when the underlying stock pays a constant dividend yield. Starting from a geometric Brownian motion for the stock, it states the forward price as the spot price adjusted by the financing and dividend…

The document describes a portfolio-selection problem: individual strategies can be profitable yet generate trades in bursts, leaving gaps in activity and uneven profit growth. The author wants to combine strategies so that trades and returns are distributed…

The document explores how to include callable bonds in a historical-simulation risk model. For plain bonds, the questioner proposes applying historical changes in the currency zero curve and issuer or rating spreads, then repricing. Callable bonds add…

The document asks whether the Black–Scholes risk-neutral probability that a call expires in the money, expressed using N(d2), can be adapted to estimate the real-world probability. The reply says this is possible if the asset's real-world drift is known. The…

The document examines how to relate options written on reciprocal currency pairs. It asks whether the delta of a USDJPY put corresponds to the delta of a JPYUSD call at the reciprocal strike and with the same maturity. The answer derives the terminal payoff…

The document asks how to derive an option-pricing probability expression in Gatheral’s framework by directly performing a complex inverse Fourier integral. It compares that route with the Gil-Pelaez inversion theorem and focuses on the boundary condition at…

The document considers estimating a riskless interest rate from spot and forward or futures prices using the relationship between the forward price, spot price, rate, and time to maturity. Rearranging that relationship gives an implied rate from the…

The document raises a portfolio-construction problem from a life-insurance asset and liability model: whether a large bond portfolio can be represented by a smaller set of zero-coupon bonds with approximately matching cash flows. The motivation is to reduce…