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 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 document distinguishes the broad category of cash instruments from deposit rates used to calibrate a yield curve. Cash can refer to several short-term instruments, including deposits, Treasury bills, commercial paper, and repos; their yields differ, so…
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 explains how an interest rate swap’s market value can respond to its projection curve and discount curve, particularly when the swap’s value is near zero. It separates the fixed and floating legs: fixed coupons are known and their present value…
The document explains why a parallel shift in a forward curve does not necessarily produce the same change in a forward swap rate. The effect depends on how the shift is defined: the answer defines it through overnight rates implied by discount factors, then…
The document discusses how to measure the risk left when a government bond is hedged with a bond future, even when their DV01s match. Matching DV01 addresses first-order sensitivity to yield changes, but does not make the positions behave identically. 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 post asks whether a QuantLib vanilla swap needs an explicit curve-linking step when a discount curve handle has already been created. Its code builds a zero curve, applies a spread, uses a discounting swap engine, and constructs a swap, but does not show…
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…
The document asks how to choose the exponent in a discounted-cash-flow formula when bond payments do not fall on a simple sequence of whole coupon periods. It gives a semiannual coupon bond example with a settlement date between payment dates, then contrasts…
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 note works through the drift of a forward LIBOR rate when changing between forward measures associated with two bond maturities. It identifies the rate multiplied by its maturity bond as a tradable asset, then uses the bond as numeraire to express the…
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…