คลังความรู้

The document contrasts a funded equity collar with a margin loan used to build a stock position. In the collar, the client buys a put and sells a call to a bank; the bank may hedge its resulting exposure by borrowing and selling shares. A margin loan instead…

The document compares smoothing based on moving averages with two outlier detection approaches: global winsorization and local outlier factor analysis. Winsorization caps values at selected distribution quantiles, while a local method can flag unusual…

The document discusses a binomial no-arbitrage argument for pricing an option. A portfolio holds one option and shorts a quantity of the underlying chosen to offset the difference between the option values in the up and down states. If that hedge makes the…

The example considers a position short August puts, long August calls at a higher strike, and short futures. Its initial net delta, gamma, and vega are reported as slightly negative or close to zero. The question asks why the answer key says all three become…

The question asks how to sketch second-order Greek profiles for a European vanilla payoff, such as a butterfly, without computing a full profile. It is concerned with how Greeks vary as spot or volatility changes, including vanna, vomma, and the changes in…

The discussion describes several ways traders apply the Kelly criterion, while questioning how well its assumptions fit real trading. One approach links Kelly sizing to volatility targeting: expected return divided by a chosen Sharpe ratio sets a volatility…

The document examines the difference between an approximate daily P&L formula for a delta-hedged option and P&L calculated from changes in option and stock values. One response explains that the gamma-and-volatility expression gives an average P&L, so it…

The document raises a practical fixed-income curve-construction problem: bootstrapping forward rates from on-the-run Treasury securities when their coupon dates do not align. It describes a proposed workflow that bootstraps forwards and then applies…

The document asks how to find the expectation of the product of two integrals of standard Brownian motion over the unit interval, one weighted by time squared. The response evaluates the product as a double integral and moves the expectation inside the…

The document considers a two-step factor analysis: estimate factor returns from cross-sectional stock-return regressions on firm characteristics, then regress individual stock returns on those estimated returns. It describes this as resembling a reversal of…

The document explains how to account for inflation when calculating an internal rate of return. Its method is to build a price index from the inflation rate, convert each cash flow into real terms by deflating it with the corresponding index, and then…

The document describes difficulties implementing Black-Litterman with analyst-consensus views. The author reports portfolio weights that become negative or exceed the full portfolio allocation, as well as returns below a market-weighted benchmark. In one…

The document asks why a study of a two-factor Double Heston model calibrates against option-market observations from many Wednesdays across a year, rather than conducting a separate calibration for each date. It contrasts that setup with research using…

The document examines a static hedge for two short calls with the same strike but different expirations, using one call whose expiration falls between theirs. The example shows that matching total notional does not keep the hedge balanced over time: the…

The document describes how to estimate a foreign-exchange risk-neutral density from vanilla option data, in the context of comparing the distribution for GBP/EUR around two historical dates. The required inputs include option prices across strikes and…

The document considers an arithmetic Brownian motion with constant volatility and asks how often it is expected to move a fixed distance from its current level, resetting the reference band after each crossing. The question is framed in terms of repeated…

The document raises the hypothesis that trend-following strategies may perform better in low-volatility conditions and asks how a trader might switch between trend and range-bound approaches. It defines volatility as the standard deviation of the price rate…

The document explains that R-squared can be calculated for a robust linear regression, but its interpretation depends on how the fit statistic is defined. The conventional measure compares the sum of squared residuals with the total variation around the…

The document connects the fundamental theorem of asset pricing to a one-period binomial tree. Choose the probability of an up move so that the stock price discounted by the bond is a martingale under the resulting measure. Solving this condition gives the…

The document describes how practitioners can approximate a digital option using a narrow call spread around its strike. Buying the lower-strike call and selling the upper-strike call creates a payoff concentrated between the strikes; as the gap narrows, the…

The document explains a model-based route for estimating a European option’s value when its American counterpart is quoted. First, specify assumptions for the underlying’s risk-neutral dynamics, such as a diffusion or jump-diffusion model. Then select a…

The document considers why traders might choose American-style options, which allow exercise before expiry, over European-style contracts, which can be exercised only at expiry. It gives a proposed benefit for a short-dated option: exercising when the…

The document examines why the six-month point on a market-calibrated swap curve can differ from the published six-month LIBOR fixing. The explanation distinguishes the fixing from the market deposit rate used to calibrate the curve. A deposit instrument…

The document explains why commodity options commonly reference futures or forwards rather than spot prices. Futures can offer liquid, standardized contracts with established price discovery and settlement conventions, making them practical underlyings for…