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The document frames discrete delta hedging as a tradeoff: more frequent rebalancing can reduce hedge error but raises transaction costs, while less frequent trading lowers costs and leaves greater residual risk. It argues that there is no single practice…
The document answers whether Python trading libraries can support forex strategies. It describes three routes: combine plotting tools with a broker's REST API, use a backtesting framework that accepts OHLC data regardless of instrument, or run Zipline…
The document discusses numerical instability when optimizing a custom GARCH quasi-maximum-likelihood objective in R. Its proposed safeguard is to clamp each filtered conditional variance to a chosen lower and upper limit, preventing extreme parameter values…
The document asks how to apply multidimensional Itô’s lemma when a function maps a vector of stochastic processes to another vector. It illustrates the question with a vector of assets divided by a stochastic numeraire, a transformation that can arise when…
The document addresses how to tell whether listed call options are European or American when searching for real market data. Its key distinction is that US options on individual securities are generally American, while options on indexes are generally…
The document asks about obtaining long historical daily price series across thousands of instruments and several asset classes. The response says that paid vendors do offer historical datasets, but that assembling prices is only part of the task. Data…
The document derives the value of a floating-rate note before its next coupon reset in a continuous-time zero-coupon bond framework. Each future floating coupon is represented as the difference between discount bond prices at its reset and payment dates.…
The document asks whether methods besides principal component analysis are standard for decomposing interest-rate term structures. The response names the Nelson–Siegel model as another commonly used approach. This points readers toward a parametric way to…
The document asks whether a sharply inverted credit default swap curve can create arbitrage. Its example compares protection at two maturities: buying longer-dated protection and selling shorter-dated protection may appear to leave a positive premium balance…
The document discusses how the move from LIBOR to risk-free reference rates affects swap discounting and curve construction. It describes the market shift to SOFR discounting for US swap quotations and cleared swaps, and explains that an existing projection…
The discussion explains why an arbitrage-free call price curve should be convex in strike. A butterfly spread combines calls at neighboring strikes so that its payoff is nonnegative across terminal prices and positive over an intermediate range. If the call…
The document explains an ACT/365 deposit-interest calculation when settlement timing and a business-day convention affect the maturity date. In the example, a deposit is quoted for seven days, but T+2 settlement falls on a weekend, so the answer treats the…
The document poses an idealized optimization problem: given the historical prices of a small set of assets over a fixed interval, find the sequence of trades that maximizes terminal wealth from an initial cash amount. The investor may hold up to a limited…
The discussion considers what mathematical background can help a reader understand and implement models in Brigo and Mercurio, including HJM, LMM, and local volatility models. The questioner has studied introductory stochastic calculus and is working through…
The document raises a market design question: could an exchange collect orders during fixed intervals and match them together at each interval’s end, instead of processing each incoming order immediately? It contrasts this proposed batch process with…
The discussion distinguishes two simple price differences over a bar or other observation period. The high–low range is the period’s highest price minus its lowest price, so it is nonnegative and describes the span of observed prices. The open–close…
The discussion explains why corporate actions can distort daily returns when a price series is adjusted incorrectly. A stock split should be reflected consistently across historical prices; a discontinuity caused by a mismatched close and adjusted close can…
The document describes how to combine three asset return series into a portfolio index with fixed weights of 50%, 25%, and 25%. It recommends calculating each asset's simple percentage return, taking the weighted sum at each time step, adding one to obtain…
The document explains how to value a payoff equal to a forward LIBOR rate fixed and paid at the start of its accrual period by translating it into a payoff at the period's end. Under the assumed risk-neutral framework, the rate known at the start can be…
The document addresses whether an exchange rate and its reciprocal, such as a currency pair and the inverted pair, should have the same at-the-money implied volatility. It models one exchange rate as a diffusion with proportional volatility and applies Itô's…
The document explains how to calculate portfolio drawdowns from cumulative returns and find both the deepest decline from a prior peak and the longest period spent below a peak. It identifies a common pandas indexing error: integer access can fail when a…
The document describes an R workflow for estimating a CARMA(2,1) model with the yuima package from daily market price data. The initial attempt passes a price column directly into the package and produces an error while constructing the model data. The…
The document asks whether every twice-differentiable call-price surface across maturities and strikes can be generated by a local volatility function of time and the underlying asset price. It points to the assumption used in Dupire’s approach and seeks a…
The document asks which representation of interest rates should be used when applying principal component analysis or other stress tests to interest rate swaps: par swap rates, spot rates, or forward rates. It notes that the studies the author has…