Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
10,263 documents
The document explains how to build and plot a Heston model volatility surface using Python QuantLib. The example creates a Heston process from spot, flat risk-free and dividend curves, and model parameters, then wraps it in a Heston model and passes it to a…
The document asks how swap rates relate to a textbook par-rate calculation and why market participants quote spreads against Treasury or swap curves. The response focuses on quoting conventions rather than deriving the swap rate formula. Historically, US…
The document explains a Monte Carlo check for an implementation of Dupire local volatility. Simulated underlying paths use the local volatility evaluated at the current simulated spot and time, with the process initialized at the market spot. For each…
The note explains a market convention for describing the right side of an implied volatility smile as call skew, even though put-call parity links those prices to in-the-money puts. The answer suggests that traders often build the smile from at-the-money and…
The note compares delta choices for hedging short-dated at-the-money options in an index dispersion trade, which pairs long single-stock variance with short index variance. It explains that using Black–Scholes delta with the option’s initial implied…
The document explains why the Black–Scholes call price contains two different probabilities: N(d2), the risk-neutral probability that the option finishes in the money, and N(d1), the corresponding probability under a measure associated with using the stock…
The document explains that option traders can seek directional gains as well as profit from volatility. Buying calls can express a bullish view with less upfront capital than buying the underlying or futures, while limiting the buyer’s loss to the premium…
The document asks how to choose volatility when using Black–Scholes deltas to hedge an option, and whether updating the volatility input with each day’s implied volatility changes expected profit and loss or its variance. It contrasts implied volatility,…
The document frames a relative-value trade between American-style options on different futures, potentially quoted in different currencies. The proposed view is to sell volatility in the option with higher implied volatility and buy volatility in the other,…
The document explains why a process introduced as the stock price under the real-world measure may later be written with a new name and then relabeled as the stock price in a Feynman–Kac representation. In the Black–Scholes PDE, the drift appearing in the…
The discussion explains why a bond’s measured duration can exceed its time to maturity, particularly when the instrument is nonstandard. The result depends on the duration definition and cash-flow structure. Embedded options may create asymmetric price…
The post asks how to hedge the cross gamma between interest rates and foreign exchange in a callable power reverse dual currency note. The brief answer is that this exposure may be difficult or impossible to hedge because the market has too few…
The document distinguishes a futures contract’s price from its value. At initiation, the contract is entered without an upfront payment between the parties, so its value is zero even though its agreed futures price is not. As the market price moves, the…
The document concerns pricing options under the Heston stochastic volatility model with an Euler Monte Carlo scheme. The question reports unstable convergence when using Sobol quasi-random numbers and asks whether a Brownian bridge can address apparent…
The document derives a formula for an asset-or-nothing European call when implied volatility varies with strike. It starts from the Black–Scholes prices for cash-or-nothing and asset-or-nothing payoffs, then applies a tight call-spread argument and the chain…
The document weighs whether a candidate can prepare for a quant interview on stochastic processes, stochastic calculus, and financial instrument pricing in a very short time. It argues that this is unrealistic for most learners unless they already have…
The document asks how to discount a cash flow at a tenor beyond the longest available LIBOR tenor, and whether interpolating quoted rates is appropriate when those rates reflect different payment periods. The answer frames the problem through the distinction…
The document explains an apparent violation of the no-arbitrage lower bound for a European put. For a put with strike K and maturity T, the cited bound is the greater of zero and the present value of the strike minus the current underlying price. A plotted…
The document asks how to estimate the early exercise premium for an American option when the underlying pays discrete cash dividends. The proposed approach integrates a probability term over possible asset prices and times before the ex-dividend date, then…
The document explains why treasury futures carry cannot be obtained simply by subtracting an implied repo rate from a deliverable bond’s yield. Under a strict definition, pure carry consists of known cash inflows and outflows from holding and financing an…
The document addresses numerical breakdown in SABR normal implied volatility calculations when the forward price equals the strike. In the cited formulation, the intermediate function chi depends on zeta, which becomes zero at this at-the-money point; direct…
The document explains option Greeks in the Heston stochastic volatility model, focusing on delta as the sensitivity of theoretical option value to the underlying price. It also defines gamma, rate sensitivity, theta, sensitivity to variance, vanna, and…
The document asks how to express time-sensitive inputs when using a closed-form option pricing approximation, specifically the Bjerksund–Stensland model. The question lists the risk-free rate, volatility, time to expiration, and cost of carry, and asks…
The document examines why European call and put prices are equal when the strike equals the asset’s forward price. Put-call parity states that their price difference is the spot price minus the discounted strike; setting the strike to the no-arbitrage…