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.
8,116 documents
This short exchange recommends books for readers seeking a practitioner-oriented history of modern finance and the ideas that shaped current markets. The questioner values accounts that explain the origins of influential concepts and provide context for…
The document identifies a derivative that pays the asset price at maturity when that price exceeds a strike, and pays nothing otherwise. This is an asset-or-nothing call, a binary-style option. In the Black–Scholes framework, one answer gives its value using…
The document examines a Monte Carlo simulation for pricing a European spread option whose payoff depends on three correlated assets. The initial attempt treats simulated normal returns as simple price multipliers, which does not model lognormal asset prices.…
The document explains how to estimate implied volatility for a VIX option using the market price of a VIX future with the same maturity. Since the option payoff depends on the VIX level at expiration, the response treats the matching-maturity futures price…
The document examines whether a variance swap is inherently long implied volatility skew. It describes the theoretical static replication of a variance strike as a weighted integral of out-of-the-money put and call prices, with weights inversely proportional…
The document shows why a standard Black–Scholes call formula can still apply when a stock is driven by several independent Brownian motions. If the stock’s volatility coefficients form a vector, their combined diffusion can be represented by a single…
The document explains why some rough-volatility papers write a stock-like process without an explicit drift. The answer says these models are focused on volatility and are often specified for a forward price under a terminal measure, where the forward has…
The document explains how to aggregate the deltas of individual options into a portfolio delta: multiply each option’s delta by its position quantity and sum across positions. The resulting exposure depends on the units and conventions used for each option,…
The document asks whether the VaR-equivalent volatility measure used in PRIIPs key information documents can be negative and what such a value means. The answer says it can occur when the loss at the measure’s 2.5th-percentile threshold is actually a gain.…
The document asks how to calculate a daily 30-day model-free implied volatility (MFIV) when listed options rarely have exactly 30 days to maturity. The described procedure selects out-of-the-money calls and puts by delta, fits a cubic spline to implied…
The discussion examines whether jumps in an asset’s returns explain the shape of its implied volatility surface. It presents competing views: jumps may create strike-dependent option prices because a continuous-hedging argument fails across discontinuous…
The answer derives a price-based condition for checking calendar arbitrage between European calls with different expiries. For a martingale underlying, the expected value of a call payoff cannot decrease with time. This follows from conditional expectation,…
The note addresses a QuantLib pricing error that occurs when a Black swaption engine is used with a negative forward rate. The error indicates that the Black model requires the forward rate, after any displacement, to be positive; with no displacement and a…
The document recommends academic texts for learning the foundations of derivatives, including forwards, futures, and options. Shreve’s two-volume Stochastic Calculus for Finance is presented as a suitable route for readers with a strong mathematical…
The document explains why local stochastic volatility (LSV) calibration may first fit a stochastic volatility model to a reduced version of the market volatility surface. This creates a lower partial surface that can be combined with one derived from local…
The document explains how to estimate the speed and half-life of mean reversion in an implied-volatility series. It proposes a discretized Ornstein–Uhlenbeck model, where changes in volatility depend on the gap between the current level and a long-run mean,…
The document derives no-arbitrage price bounds for European call and put options. It applies Jensen’s inequality to the convex option payoffs to obtain lower bounds equal to discounted intrinsic value, then compares each payoff with the underlying asset or a…
The document explains how to use QuantLib’s Cox–Ross–Rubinstein binomial approach when maturity is specified as a fraction of a year rather than by calendar dates. The questioner’s code constructs the process and lattice using a numeric maturity but gets…
The document asks why an arbitrage argument implies that a European call’s price cannot exceed the underlying share price. It compares a short call and long stock position with an alternative profit calculation that also includes investing the initial cash…
The document asks whether a year-on-year inflation option payoff, and its vega exposure, can be represented using zero-coupon inflation options. The response cautions that there is no direct payoff mapping. Converting zero-coupon inflation quantities into…
The document outlines two ways to infer yield volatility from bond option prices. One approach expresses a put payoff on bond price in terms of yield differences and the bond’s price sensitivity to yield. Assuming normally distributed yields, it then applies…
The document asks how a terminal stock price can serve as a control variate when estimating a financial quantity by simulation. The question focuses on the control-variate adjustment: if the expected terminal price is known, the writer wonders whether…
The document raises a research question about whether realized volatility relative to implied volatility is associated with changes in options skew. It reports an expected pattern—skew steepening when realized volatility exceeds implied volatility—but says a…
The note explains a result from the Hull–White stochastic volatility model: when the Brownian motions driving the underlying price and its variance are independent, an option can be priced by averaging Black–Scholes prices over the distribution of…