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 how Bloomberg calculates implied volatility smiles for equities and mentions a possible lognormal-mixture model for stock prices. The replies point readers to Bloomberg’s BVOL equity implied volatility calculations paper as the available…
The document explains two related ideas for European options settled in bitcoin: put-call parity for identifying a conversion or reversion mispricing, and delta hedging to manage exposure to the underlying. For matching calls and puts, parity relates their…
The document discusses how to hedge a long American put in a two-period binomial stock and cash market while repaying a loan used to buy the option. The central method is dynamic replication: calculate the option's stock hedge at each node, then rebalance as…
The document describes using QuantLib’s SABR swaption volatility cube with an at-the-money volatility matrix, strike spreads, volatility spreads, and SABR parameter vectors. It discusses calibrating normal at-the-money volatility by fixing beta at zero and…
The document asks how to approximate a function from values observed at a finite set of points using a weighted sum of call-like payoff functions at selected strikes. It frames the goal as a super-replication problem: find coefficients so that the…
The document discusses implied-volatility calculations from option-chain prices and spot values sampled at potentially different times. Its example shows a call quote below its discounted intrinsic value, so the inputs violate the no-arbitrage lower bound…
The document raises foundational questions about pricing a call or put in a two-state binomial model. The method described is replication: combine positions whose payoffs match the option's payoff in each possible future state, then infer the option value…
The document asks whether Heston parameters estimated from stock returns under the real-world measure can be used to price vanilla options under the risk-neutral measure. The response explains that option pricing requires risk-neutral dynamics and outlines a…
The document tests whether a stock, a put, and a call with different strikes create an arbitrage opportunity. The example gives a stock price of USD 30, a put struck at USD 28 priced at USD 1, a call struck at USD 29 priced at USD 8, and a one-year risk-free…
The document explains why the difference between two correlated Brownian shocks can be represented by a single Brownian motion when pricing an exchange option. The payoff can be rewritten using the ratio of the two stock prices, and Itô’s lemma gives that…
The document describes a Bloomberg workflow for identifying European equities that have listed options. It recommends using the securities finder to select equities, open the equity options category, and filter by fields such as currency or exchange before…
The document explains why a farther-dated option can show lower implied volatility than a near-term option while still having a higher premium. It describes an inverted volatility term structure: near-term implied volatility is elevated, while the market…
The document presents asymptotic boundary conditions used when numerically solving generalized Black–Scholes models on a truncated price domain. At the low-price boundary, the call value tends to zero. At the high-price boundary, it approaches the discounted…
The answer explains the tendency for equity volatility to move inversely with stock prices by comparing equities with credit. For credit, falling prices can reflect growing concerns about whether borrowers can meet obligations; uncertainty can increase…
The document concerns a covariance matrix used in a Gaussian construction for stratified Monte Carlo sampling, motivated by simulating a barrier option under Black–Scholes dynamics. The answer identifies a normalization error: the stated result assumes the…
The document considers how to assess a proposed interest-rate cap volatility surface for arbitrage. A cap consists of caplets, and the response recommends stripping caplet values from cap prices across maturities. In a simplified setting with a flat yield…
The document identifies a modeling connection between interest-rate options and volatility options: both markets have term structures. It points to a variance-curve model in which variance across maturities evolves as a martingale driven by Brownian shocks,…
The document discusses whether equity option prices can reveal the stock lending rate faced by a market maker hedging short positions. Put-call parity links a matched call and put to the underlying, financing, dividends, and borrow costs, so deviations from…
The document explains a parity relationship for asset-or-nothing binary options. The call pays the underlying asset at maturity when its price is above the strike, while the put contributes a negative asset payoff when the price is below the strike.…
The note asks how to take a directional view on volatility while limiting exposure to the underlying’s direction. It points out that straddles, strangles, and iron condors respond to volatility but also carry exposure to other option risk factors, including…
The note explains how a stochastic volatility model distinguishes physical-measure dynamics from risk-neutral dynamics used for option pricing. It describes a volatility risk premium that shifts the variance process’s drift, while the stock drift is adjusted…
The document clarifies how FX spot delta relates to option delta and settlement timing, using GBP/USD and USD/CHF examples. Its answer explains that spot itself has delta one by definition: its value changes one-for-one with the spot rate. FX option delta…
The document asks whether Black–Scholes pricing remains relevant for an over-the-counter call when the option buyer cannot delta-hedge. The responses distinguish the venue where an option trades from whether its underlying asset is liquid: the accepted…
The explanation links sticky-delta implied volatility to scale invariance in asset-price models. If scaling the initial spot and strike by the same factor scales a European option’s value by that factor, the option price is homogeneous of degree one.…