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 asks how to interpret the rho parameter in the Surface SVI formula when the model is used to fit implied volatility. It notes two descriptions found in papers: rho is proportional to the implied-volatility smile's slope near at-the-money, and…
The answer clarifies that the familiar second-moment identity for a stochastic integral applies when the integrator is a martingale and the integrand satisfies suitable integrability conditions. It warns against applying the identity directly to a process…
The document poses a finite-state pricing question. It gives prices and payoffs across three possible states for three existing assets, then introduces a fourth asset whose payoff is zero in two states and positive in the third. The question asks how to…
The document discusses attempts to describe stock return distributions under the Heston stochastic volatility model, including a proposed unconditional density and later statistical comparisons with a lognormal distribution. It raises the concern that an…
The document explains how to select an interest rate when converting future cash flows into present values for U.S. securities. Its main guidance is to match each payment date with the corresponding zero-coupon rate from a yield curve, rather than applying…
Cubature approximates an integral by a weighted sum over selected points or paths, with the weights and locations chosen to reproduce integrals of a specified class of functions. In a stochastic differential equation setting, the target may be an expected…
The document asks what an expression involving the expected product of two stochastic differentials means, given that differentials of random processes are not ordinary standalone quantities. The answer explains a stochastic differential equation as…
The document asks how to follow a step in Piterbarg’s treatment of collateral agreements and derivatives pricing. The sticking point is a change in discount factor between two equations, and the questioner suspects integration by parts and notes that the…
The document asks how to interpret the time scale of a variance quantity computed from a local volatility formula, using the relationship between variance, volatility, and elapsed time. It wonders whether a value associated with a six-month horizon should be…
The discussion considers whether higher implied volatility for out-of-the-money calls and puts points to a particular options spread. It describes this pattern as a volatility smile and reasons within a Black–Scholes comparison: because option vega is…
The discussion asks whether a minimum-variance portfolio of currency derivatives can be optimized using the variance and correlation of each instrument’s value instead of its returns. The answer explains why covariance of asset values is unsuitable: changing…
The document describes common practical approaches to pricing European options. In liquid markets, practitioners often represent a vanilla option’s price through its forward price and Black-Scholes implied volatility for the relevant maturity and strike.…
The document considers how a payment delay affects discount-factor bootstrapping for SOFR swaps. It distinguishes the accrual period, which determines the interest amount, from the later cash-flow payment date. The answer argues that the payment lag’s…
The document addresses why simulating a stock price over one year in one step may appear to produce different variation from simulating twelve successive monthly steps. Under geometric Brownian motion, each interval applies the same drift and volatility…
The discussion considers how to account for convexity when bootstrapping a SOFR curve with futures and swaps. It distinguishes the task of calibrating to American options on SOFR futures from estimating futures convexity, and outlines approaches proposed by…
The document explains risk-neutral valuation as a pricing framework tied to replication and no-arbitrage assumptions. When a derivative payoff can be replicated, its market price corresponds to the cost of the replicating portfolio. A risk-neutral…
The document asks how volatility quants describe the shape of an equity options implied volatility skew using statistics beyond basic distribution summaries. It groups candidate features into level, represented by at-the-money implied volatility; skew,…
The document considers a perpetual binary claim that pays one dollar when a stock first reaches an upper barrier. It challenges the idea that the claim must be worth one dollar merely because a random-walk stock may eventually reach the barrier. With spot at…
The document considers numerical valuation of American options when the underlying model has multiple sources of randomness, such as stochastic volatility. One response argues that lattice methods can remain preferable to least-squares Monte Carlo (LSMC)…
The document explains why pricing a portfolio of swaptions by simulating several forward rates independently can be inconsistent. In the example, a swap rate depends on multiple forward rates, while under the relevant forward measure only one rate can retain…
The document presents a question about applying a regression from Asensio (2013) to test forecast bias in the VIX term structure, motivated by the possibility that VIX futures are overpriced. It identifies the equation’s forecast errors and its horizon…
The document clarifies how sticky strike, sticky moneyness, and sticky delta describe implied volatility changes when the underlying spot moves. Sticky strike holds implied volatility fixed at an absolute strike. Sticky moneyness instead holds it fixed at a…
The document discusses how a sell-side desk may hedge interest rate caps and floors without managing every caplet as a separate position. Its central practical point is that trades with similar risk are combined in a portfolio book, and the desk hedges the…
The document explains how forward premium enters currency option pricing and clarifies the role of overnight indexed swaps. In the Garman–Kohlhagen formulation, the domestic-minus-foreign interest rate differential determines the forward exchange rate…