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The document describes a pricing problem involving a multi-asset collar on European natural gas and US oil products, with an additional currency conversion because the contracts are denominated in different currencies. The questioner is considering Monte…
The document describes solving for the risk-aversion parameter in a mean–variance portfolio setup. Portfolio weights are expressed as a function of the parameter, expected returns, the covariance matrix, and a budget constraint. Those weights are substituted…
This document asks how to distinguish nominal growth in an equity index tracker from growth in purchasing power. Using a UK all-share tracker and UK inflation as an example, it considers whether historical tracker values can be adjusted by inflation measured…
This document examines how units and parameter choices affect the Avellaneda–Stoikov market-making model. It gives the reservation-price skew and optimal spread equations, then asks how price variance, order-arrival intensity, inventory, and remaining…
The document gives a finite-difference estimate of a fixed-income instrument’s convexity using its current price and projected prices after equal upward and downward parallel yield shifts. The central second difference, formed by adding the two shifted…
The document discusses portfolio optimization using an ETF and VIX futures, comparing minimum-variance and Sharpe-maximizing approaches across different rebalancing schedules. The response focuses on minimum-variance intuition: an asset’s weight is…
The example asks how to calculate the net present value of a property project with an upfront purchase, renovation payments over several months, and a later sale. The answer’s method is to place each cash flow on a timeline, convert the annual financing rate…
The document explains how to connect a zero-coupon bond’s price to the stochastic process for the short rate. If the rate follows an Itô diffusion under the risk-neutral measure, applying Feynman–Kac gives a pricing PDE with a terminal condition equal to…
The document considers how to validate a low-frequency crypto strategy with roughly 25 trades per year, focusing on the limits of statistical evidence from a small sample and the dependence introduced by adding correlated assets. One reply suggests extending…
The document asks how to express swap portfolio sensitivities in terms of bond and SOFR futures risks when the swap’s pricing model does not directly use those instruments. It frames the task as mapping risk between two instrument sets and explains that,…
The document clarifies what the time partial derivative means when applying Itô’s lemma to a function of a stochastic process. For a function written as f(S_t, t), the partial derivative with respect to t treats the process value S_t as the first, separate…
The document explains how correlation between two stocks’ Brownian shocks relates to correlation between their simulated price levels under correlated geometric Brownian motion (GBM). It gives formulas for each asset’s mean and variance, their joint…
The document outlines a variance-covariance approach to estimating volatility for a portfolio of cryptocurrencies. It starts from daily price changes, forms a covariance matrix of daily returns, and scales that matrix by 365 to estimate annual variance,…
The document discusses language choices for a pricing library that should support parallel pricing, control maintenance costs, and remain accessible to newer quantitative researchers. It argues that there is no single best language and suggests Python as a…
The document derives the instantaneous volatility of a zero-coupon bond price under a one-factor Hull–White short-rate model. It presents the bond price as a deterministic function of time multiplied by an exponential term in the current short rate. The…
The document considers how to calculate the correlation between a stock and an index reconstructed without that stock. It defines the reduced index return by removing the stock’s weighted return from the full index return and rescaling by the remaining index…
The document explains why annual rate labels can refer to different treatments of compounding. In the US usage it describes, nominal APR is generally a simple annualized rate, while effective APR or APY accounts for compounding; EAR is more commonly used…
The document explains how equity returns can be decomposed into an initial dividend yield, a change in valuation, and growth in dividends. Starting from the one-period return that combines the next stock price and dividend relative to the current price, the…
The document raises an unresolved scaling question for dynamic portfolio optimization using the Modified Sharpe ratio. Because that ratio depends on portfolio skewness and kurtosis, the author needs co-skewness and co-kurtosis arrays to construct the…
The document collects operational safeguards for an automated trading script interacting with an exchange API. The proposed controls include prioritizing exits and stop orders, checking whether orders reached the venue, handling failed requests, monitoring…
The document asks whether daily log returns can be presented directly as daily variation when the goal is not to report risk over a longer horizon. It distinguishes an individual return observation from a volatility estimate: one return shows a realized…
The document asks about an approximation discussed in a paper on delta hedging with a volatility smile: treating the sensitivity of implied volatility to the underlying price as equal to its sensitivity to strike. Under a downward-sloping smile, the cited…
The document explains how aggregate dealer gamma may affect hedging flows near options expiry. When dealers are long gamma, movements in the underlying can lead them to trade against the move, buying after declines and selling after rallies. When dealers are…
The document compares a manually discounted fixed-rate bond price with the output from RQuantLib. Its example uses a five-year bond with annual coupons, a flat interest rate, and a settlement date one day after the evaluation date. The manual calculation…