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
The document raises a question about very negative AUDJPY market strangle volatility quotes at long maturities. It gives examples for 25-delta and 10-delta strangles, alongside an at-the-money-forward volatility level, and asks whether the resulting concave…
The document describes a zero-coupon-style claim on mortgage principal that pays when the borrower prepays or, if no prepayment occurs, at maturity. It models the prepayment time as a stopping time triggered when a mortgage reference rate falls below a…
The document asks whether Novikov’s condition holds for a proposed Girsanov kernel in the Heston model. The stock’s market price of risk leads to an exponential-integrability requirement involving the time integral of the reciprocal variance. The variance…
The document discusses how a learner studying derivatives can practice hedging and trading in a simulation or demo account. The answer describes Interactive Brokers’ paper account as an option for customers with a live account, noting that it had broad…
The note describes several reasons to trade a risk reversal, which combines a put and a call to express a view on implied-volatility skew. A delta-hedged risk reversal can be viewed as a wager on realized spot–volatility covariance relative to the covariance…
The document proposes extending the Heston stochastic volatility model by making its long-run variance level itself a mean-reverting stochastic process. The spot variance mean-reverts toward that changing level, while the asset price follows a diffusion with…
The note outlines a procedure for estimating an empirical pricing kernel, also called a stochastic discount factor, for an index. It estimates the physical density from index observations over a historical interval and the risk-neutral density from option…
The document examines whether negative probabilities can support pricing a European call in a finite-state, one-period market. The proposed calculation replicates the option payoff with a portfolio and assigns it a price from the portfolio’s initial cost. A…
The response corrects the premise that ordinary, or real-world, valuation avoids taking expectations of future cash flows. It states that asset valuation in either framework involves expected discounted cash flows; the key distinction is how risk is handled…
This question compares a perpetual American put’s exercise threshold under Black–Scholes assumptions with the value of waiting for a finite period. The author argues that, from a price above the perpetual threshold, there should be some horizon for which…
This question considers Monte Carlo valuation of a payoff based on the positive part of the difference between domestic and foreign forward rates. It assumes a domestic zero-coupon bond maturing at the later tenor date is used as numeraire, and describes the…
The document examines the limits of replicating variance exposure with a weighted strip of out-of-the-money calls and puts, a construction associated with log-contract replication and the VIX calculation. The cited explanation says the continuous static…
The document examines whether a calendar spread can provide a stable way to trade changes in implied volatility while remaining delta- and gamma-neutral. The responses explain that neutrality holds only under particular market conditions and can deteriorate…
The document asks how to estimate covariance when optimizing a minimum-variance portfolio over weekly or fortnightly cumulative returns. It contrasts calculating covariance directly from returns sampled at the target frequency with scaling a daily covariance…
The document discusses how to estimate risk inputs for an option on the difference between two futures. It presents three approaches to spread volatility: calculate it from historical spread returns, combine the futures’ implied volatilities with a…
Fourier inversion prices European options by transforming information from a model’s characteristic function into option values. The discussion describes why the approach can be fast and accurate for European contracts, and notes its broad applicability to…
This note examines how Bloomberg’s swaption volatility quotes relate to Black-model prices, focusing on a EUR cash-settled payer swaption. It defines the normal cumulative distribution and Black formula, then distinguishes the physical-settlement annuity…
The document describes difficulties in deriving pseudo-European implied volatility slices from American option prices through de-Americanization. The method may produce different European implied volatilities at the same strike when both calls and puts are…
The document asks why a stock-price diffusion changes when a model includes correlation between interest rates and stock returns. In the uncorrelated case, the stock diffusion coefficient is constant; in the correlated case described, it is scaled by the…
The document distinguishes pricing models used for equity options from parametric fits used to store and retrieve implied volatility data. It identifies Black–Scholes, including time-dependent versions, and local volatility as common industry choices, with…
The document explains how a delta-neutral position with long call options can generate gains through repeated stock rebalancing. In its example, the trader starts long calls and short shares; a price decline reduces call delta, so buying shares to restore…
This discussion considers whether VIX-style volatility indices could be created for individual S&P 500 industries. Since the VIX is derived from index option prices, the proposed analogue would likewise depend on an adequate market in options on the relevant…
The document explains why bid and ask quotes can matter when fitting option prices in an incomplete market. Rather than forcing a model to match each quote’s midpoint exactly, a calibration can allow model values to lie within the quoted spread. This…
The document develops a pricing approach for a derivative whose payoff is the positive part of the stock price squared minus strike times stock price. It first changes from the risk-neutral measure to the stock measure, splitting the payoff into an…