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 clarifies a common misunderstanding of the Feynman–Kac theorem in a stochastic calculus text. The theorem is not asking the reader to discover an unknown terminal function: the payoff function is specified as part of the problem. A derivative’s…
The document addresses which options to use for research on S&P 500 index options, comparing contracts on the index, its futures, and exchange-traded funds. It offers a concise liquidity assessment based on electronic-market bid-ask spreads measured in…
The document explains how a risk-neutral probability density for the underlying at expiration can be recovered from the second strike derivative of call prices, under a constant interest-rate assumption. Once recovered, the density can be integrated against…
The document asks how useful implied volatility remains when the Black–Scholes assumptions do not fit the market. It uses stock-borrowing fees as an example: different borrowing and lending rates can change the pricing equation, so an option price must be…
The document poses a risk-neutral pricing problem for a derivative that pays the square of a non-dividend-paying stock price at maturity. It proposes discounting the expected terminal payoff, but the attempted expression does not satisfy the Black–Scholes…
The document examines whether a portfolio that is neutral to vega is also neutral to gamma and theta. One response gives a specific result for portfolios of calls and puts sharing the same maturity: under the Black–Scholes framework, gamma neutrality and…
The document introduces an ATM implied-volatility correction in a free-boundary extension of SABR, motivated by pricing under negative rates. It describes a small-time heat-kernel approximation and gives a first-order correction for the at-the-money case…
The discussion explores estimating one-day downside risk for a portfolio that combines linear assets with short option exposure. It contrasts fitting a generalized Pareto distribution to the tail of repriced historical portfolio returns with simulating…
The discussion considers how to price same-day-expiry options on futures across equity indexes, energy commodities, and Treasury markets. The response says many futures options are European and can be priced with Black–Scholes, while some contracts are…
The document asks why long-horizon realized excess returns on agency mortgage-backed securities may fall below their average option-adjusted spread over duration-adjusted Treasuries. The response attributes the gap to borrower prepayment behavior changing…
The document raises a mathematical question about deriving an asymptotic option-price expression used in the Hagan SABR implied volatility formula. It focuses on a partial differential equation for option value, with terms involving the forward price,…
The document compares two ways to extract risk-neutral information from option prices. Breeden-Litzenberger (BL) uses the curvature of call prices across strikes to estimate an entire risk-neutral density. Bakshi-Kapadia-Madan (BKM) methods estimate…
The document sketches a multifactor geometric Brownian motion framework for pricing options whose payoffs depend on multiple assets. Each asset has its own volatility, while shared Brownian factors create dependence; factor loadings determine the modeled…
The document considers whether a risk system can simplify a multicallable bond by treating an assumed call date as its maturity. For small interest-rate sensitivity calculations, one possible shortcut is to identify the exercise date associated with yield to…
The document discusses hedging a perpetual up-and-out call with a strike of 110 and barrier of 120. One proposed static hedge buys stock in an amount intended to cover the option’s maximum intrinsic payoff at the barrier. This is a buy-and-hold superhedge…
The document discusses which financing rate belongs in option valuation and whether call and put quotes can be used to infer it. It starts from European put-call parity, then compares that relationship with observed option bids. One answer says the inferred…
This discussion explains how to interpret at-the-money swaption volatility quoted under normal and Black conventions. Normal volatility is expressed in rate units, commonly basis points, while Black volatility is relative to the forward swap rate. The…
The document raises a derivatives calibration question by analogy with joint modeling of the S&P 500 and VIX. Since the VIX is derived from S&P 500 options, the author asks whether the Euro Stoxx 50 and VSTOXX should likewise be calibrated together. The…
The document addresses whether Python users can price compound options through QuantLib's CompoundOption class. The accepted answer reports that the class is not exposed in the Python module: attempting to access it through the QuantLib namespace raises an…
The document clarifies competing conventions for dollar gamma. It distinguishes dollar gamma, commonly expressed as gamma multiplied by the square of the underlying price, from the half-dollar-gamma coefficient used in the second-order approximation of…
The document discusses how phoenix and snowball autocallable notes can be valued and hedged. It describes the note price as a combination of a zero-coupon bond, coupon exposure, a short down-and-in put that may be terminated by autocall, and issuer profit.…
The document works through a question about deriving a continuous-time equation for the value of an investment with an option to stop. It presents a Bellman relation that compares immediate stopping value with the value of continuing, including profit flow…
The document asks how to check a Python implementation of delta hedging for a short European call, offset by a long position in the stock sized to the option’s delta. It proposes examining the distribution of the combined hedge-and-option profit and loss…
The document asks how to interpolate implied volatility between listed maturities to construct a volatility surface for a Black–Scholes delta-hedging experiment. It considers bilinear interpolation and seeks guidance on methods that can fill values between…