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 asks whether differences in higher moments of returns can support relative-value trades. It proposes dividing observations into groups using an external variable, such as volatility regimes, and comparing the return distributions. If one group…
The document asks how to select inputs for calculating Black–76 implied volatility on an SPX option. The author describes using a continuously compounded rate interpolated from the US Treasury par yield curve, deriving the forward from that rate and put–call…
The document asks how the one-period no-arbitrage condition in a binomial model changes when interest is expressed with continuous compounding and the option maturity is not one period. The response converts the gross risk-free return over the period to its…
The document considers calibrating Heston stochastic volatility parameters to an option volatility smile when the available pricing implementation uses Monte Carlo simulation. The proposed approach is to fix the random numbers across calibration iterations,…
This discussion explains why a QuantLib Black calculation for a Treasury futures option can appear to disagree with Bloomberg on price and gamma. The accepted answer attributes the apparent mismatch to quote conventions and Greek settings: Bloomberg may show…
This note asks how the adjusted Poisson parameter arises when a European call is priced under Merton’s jump-diffusion model. It starts from a valuation expressed as a sum over the possible number of jumps, with each term weighted by a Poisson probability and…
This note examines how spot delta and forward delta relate through put–call parity. Differentiating the parity relationship with respect to spot gives a call-minus-put delta of one, while differentiating with respect to the forward gives a discounted…
The document explains the replication error that arises when an option priced with Black–Scholes volatility is delta hedged while the underlying realizes a different path of volatility. Between hedge adjustments, the option’s gamma exposes the portfolio to…
The document describes an American call or put whose strike resets to the stock price when the stock falls to a specified fraction of the current strike during a defined period. Reset events can occur repeatedly, although the problem statement allows…
The document proposes allocating a limited budget across long call options on three correlated assets: an equity fund, government bonds, and gold. Its workflow estimates a covariance matrix with a multivariate GARCH model, uses that matrix to simulate…
The document separates investor risk aversion from movements in implied volatility. It describes risk aversion as a relatively persistent feature shaped by an investor’s circumstances, while option prices can change when many market participants revise their…
The document examines a USD-settled payoff tied to the return of the EUR-denominated DAX and asks whether it removes foreign-exchange risk. Under constant interest rates and volatilities, it sets out correlated diffusion models for the FX rate and index,…
The document analyzes a forward-start call whose strike is set as a multiple of the underlying price at the start date. Under a pure stochastic-volatility model, conditioning on that date and using the homogeneity of the Black–Scholes price shows that the…
The payoff that rises with the underlying above a lower strike and then stops increasing can be decomposed into a long call at the lower strike and a short call at a higher strike. The upper strike is the lower strike plus the payoff cap. This identity makes…
The document considers whether prices for Wells Fargo stock and options with a shared expiration violate put-call parity. It compares the stock price plus put value with the strike price plus call value, neglecting interest rates, and asks how an apparent…
The document examines how to derive a pricing equation for an option when the underlying asset follows a mean-reverting process in log price. It contrasts a delta-hedging argument with a risk-neutral valuation argument and discusses when the model’s physical…
The document poses a valuation problem for a call option with a three-year life that cannot be exercised during its first two years, but may be exercised at any time during the final year. It supplies assumptions for the underlying price, strike, risk-free…
The document discusses the claim that an at-the-money option’s time value scales with the square root of time and asks whether the idea extends to in-the-money and out-of-the-money options. One answer connects the rule to volatility scaling: under a…
The document introduces risk-neutral pricing for a European call when the underlying follows Merton’s jump-diffusion model. It explains that, under a risk-neutral probability measure, an option’s value is the discounted expected payoff. Because jumps make…
The document resolves a reader’s confusion about a delta-hedged option example in a chapter on dynamic hedging. The described position combines calls at two strikes with a forward hedge, but the stated long and short directions do not match the accompanying…
The document derives the distribution of a time-averaged stock value rescaled by the terminal stock price, under the stock measure in a Black-Scholes market without dividends. The key step is to write the average and terminal price using the same Brownian…
The document asks whether a European call’s Black-Scholes price, as a function of volatility, covers every price allowed by static no-arbitrage bounds. With the stock price, strike, maturity, and continuously compounded rate fixed, the admissible call-price…
The note asks whether sellers of options tied to California earthquakes should price them using real-world earthquake probabilities. Its central point is that standard derivative pricing is most tightly constrained when an option payoff can be replicated by…
The document considers whether a warrant holder’s gain necessarily means another party loses money. It distinguishes exchange-traded options, which are treated as zero-sum between counterparties, from company-issued warrants that create new shares when…