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 discusses how an options market maker can manage vega after buying options from incoming customer flow while continuing to quote. Its main practical suggestion is to seek offsetting vega from other customers by quoting competitively on the side…
The document considers a calibration that maps a real-world cumulative distribution function into a fitted risk-neutral cumulative distribution by applying a beta CDF to the real-world CDF. It asks whether reversing that mapping uses the inverse beta…
This short exchange asks why a trader might hedge using Black–Scholes delta when pricing or modeling with a local volatility framework. The accepted response gives two practical reasons: Black–Scholes delta is straightforward to calculate from closed-form…
This exchange collects suggested references for learning about long-dated options, including contracts with maturities of six months or more. The original question focuses on pricing and speculative trading, with particular interest in how rho and theta…
The document explains the link between an option’s sensitivity to spot price and its sensitivity to the present value of dividends. It assumes the forward price equals spot less the present value of dividends, grown at the risk-free rate to maturity. For a…
The document considers an asset whose price follows a mean-reverting diffusion with a time-varying stable-process drift, then asks whether option values require a modified Itô formula. The answer says the stated price process remains continuous and has…
The document poses a model-selection problem for options market making: represent a volatility surface with five inputs, described as maximum put and call levels, skew, curvature, and at-the-money volatility. The author says the SABR model does not flex…
The discussion asks how to estimate historical volatility when electricity prices can be negative, making log returns undefined for some observations. It explains that the return measure should follow the assumed model: absolute price changes suit a model…
The document explains why the value at time t of a unit payment due at time T is expressed using the accumulated short rate from t to T. It defines the growth of a unit investment from time zero to each date, then obtains the discount factor by dividing…
The document develops a pricing route for a European call on a zero-coupon bond in the Vasicek short-rate model. The bond price is represented as an exponential-affine function of the current short rate, and the option payoff is split into a bond-value term…
The discussion considers what options a tail-risk fund might have used to profit during the March 2020 equity decline. The proposed structure centers on deeply out-of-the-money puts on the S&P 500 or another portfolio benchmark, with options potentially…
The document examines puzzling patterns in daily option quotes, including last prices equal to bid–ask midpoints, spreads that appear uniform across strikes and dates, matching bid and ask prices, and occasional violations of expected strike-price…
The document examines how implied volatility skew affects the valuation of a binary call and addresses conflicting signs in two published formulas. Its central method derives the binary price from the negative strike derivative of the vanilla call price,…
The document addresses why a normal-model swaption price may appear too high when compared with a lognormal Black-model price. The response identifies a likely source of the mismatch: normal and lognormal volatilities use different scales and cannot be…
The document shows how to infer the stock’s up-state price in a one-period binomial model when the current stock price, down-state price, strike, interest rate, and call price are given. It applies no-arbitrage pricing to both the stock and the call, using a…
The document proposes two possible adaptations of optimal transport methods for implied volatility surfaces. One concerns arbitrage-free projection methods that assume each maturity’s distribution integrates to one. When observed strike coverage is…
This document outlines trade-offs among three interest-rate option model families. It describes SABR as a formula-based approach used for European swaptions and some foreign-exchange vanilla options, with efficient computation and established hedging…
The document explains why a European put can become cheaper as time to expiry increases in a Black–Scholes example. With the stock and strike equal, volatility and the risk-free rate held constant, the reported put price falls as expiry extends from one year…
The document considers how to hedge a short, fixed-cash payoff that is triggered when a stock finishes above a specified strike. It identifies the contract as a binary call option and notes that, under Black–Scholes assumptions, its theoretical value can be…
The document considers how to calculate return on investment for a margin-backed short put that is closed and replaced with a new put. The example tracks the initial premium, margin posted, closing cost, returned margin, and the new trade’s premium and…
This question asks what “rate” means in the name of a lookback rate put option. It contrasts an average-rate put, whose payoff depends on the strike and the underlying’s average over the option’s life, with two possible interpretations of a lookback rate…
The document clarifies how put and call slopes are defined in the SVI-JW volatility parametrization. The key distinction is that the wing slopes refer to total implied variance, rather than implied volatility or variance divided by time. Differentiating the…
The document considers whether a financial institution could use a short-dated options position to reduce its reported exposure to a prescribed regulatory yield-curve shock. Its example is a strangle whose strike range corresponds to part of the shock,…
The document addresses a calibration step in the one-factor Hull–White interest-rate model: finding the critical rate that satisfies the equation used in an analytical swaption pricing formula. It explains that this root generally has no closed-form…