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.
12,303 documents
The document describes an attempt to reproduce a vendor price for a discrete arithmetic average price Asian call using the Haug, Haug and Margrabe approximation and Curran’s approximation. It lays out the inputs, reports the author’s calculated values and…
The document compares local volatility, stochastic volatility, and parameterized approaches for representing an implied volatility surface. Implied volatility is a transformed representation of European option prices, and interpolation in volatility space…
The document considers whether a single-factor Linear Gaussian Model calibrated to coterminal swaptions can price both payer and receiver Bermudan swaptions. The question arises because the two option types have different exercise boundaries and may respond…
The document clarifies the relationship between the drift of a price process and the drift of its logarithm under geometric Brownian motion. Starting from a stochastic differential equation for proportional price changes, Itô’s formula gives a log-price…
The document distinguishes the current VIX level from the behavior of VIX as market conditions change. VIX squared corresponds to a variance swap strike, and the answer uses an analogy with a stock whose current price does not depend on its instantaneous…
The document derives how skewness behaves when independent return increments are combined and how a forward-period skew can be recovered from observations over a longer horizon. For two independent, mean-zero increments, variances add and third central…
The discussion explains how several Heston model parameters affect the shape and level of the implied volatility curve. It focuses on producing a symmetric smile rather than a skewed smirk. The answer identifies correlation between the asset and its variance…
The discussion asks how a convex implied volatility smile relates to high kurtosis and the expected returns of options across strikes. Its answer says that assuming constant implied volatility alongside a symmetric, fat-tailed underlying distribution can…
The document asks how to estimate a stock’s price sensitivity to an earnings surprise when studying post-earnings announcement drift. It considers expected price-to-earnings ratios as a rough proxy for the price response to earnings, while noting that this…
The document addresses which S&P 500 options determine the settlement value of VIX futures with expirations beyond the nearest contract. It explains that each VIX future references the option maturity that will be the front month when that future expires. As…
The document clarifies the difference between instantaneous variance in the Heston model and the variance of cumulative log returns over a fixed horizon. In the model, the variance process describes local log-return variance; it should not be read as the…
The document surveys proposed uses of social media and online discussion data in trading. Suggested signals include investor attention, the popularity of individual stocks, shifts in discussion volume, and changes in sentiment. One cited behavioral…
The question concerns fitting a geometric Brownian motion model to historical stock prices, simulating future paths, and averaging those paths to create a forecast. The responses explain that the ensemble mean follows the model’s expected price path, while…
The note considers why a target call delta may fail to produce a strike in a dividend-paying Black–Scholes setting. With continuous dividend yield, call delta is bounded above by the discount factor for dividends, so a target above that bound cannot be…
The document outlines why variance swaps and volatility swaps are distinct products. Variance swaps became established instruments for volatility exposure and hedging, in part because variance can be related to prices of European calls and puts. A volatility…
The document explains how the Variance Gamma (VG) and Normal Inverse Gaussian (NIG) exponential Lévy models can approach the Black–Scholes model. In both cases, the log price is a Lévy process; removing or taking the limiting value of the jump-generating…
The document asks how EUR/JPY option skew relates to the skews of USD/EUR and USD/JPY options. It gives the standard variance relationship for a currency cross: the cross variance depends on the two component variances and their correlation. Rearranging this…
The document asks how to estimate the value of a put option if its underlying reaches the strike within a chosen future interval. It distinguishes the premium recorded as cost basis when the option is sold from the later market value relevant to buying the…
Black implied volatility is the volatility input that makes the Black pricing formula match an option’s observed market price, given the relevant strike, spot or forward, interest rate, and time to expiry. For options with payoffs resembling a call on a…
The document explains why repeatedly adjusting a delta hedge around a short call can lose money when the underlying price moves up and down. A short call position is described as short gamma and vega, and long theta. Delta hedging removes exposure to small…
The document proposes estimating the return distribution of a bonus certificate from the distribution of the underlying stock’s returns. The certificate is described as a combination of the underlying and a down-and-out put. The suggested bin-based procedure…
The document asks whether an options gamma exposure index can help forecast realized volatility and how to turn gamma exposure into an implied-move curve across underlying prices. It describes GEX as an aggregate of call and put gamma exposure, calculated…
The document asks for research on whether options open interest is related to implied volatility, proposing that heavy market-maker short positioning at a strike might lower implied volatility. The response highlights a basic identification issue: each open…
The document considers pricing a European put when the underlying follows geometric Brownian motion multiplied by a compound Poisson jump process. It proposes conditioning on the number of jumps over the option’s remaining life, then summing the conditional…