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.
10,263 documents
The document asks whether Vega-Vanna-Volga methods are used beyond foreign exchange derivatives and why they are common in FX. The response connects FX risk-reversal asymmetry to the possibility of central-bank intervention around exchange-rate levels. It…
The document sets up a ratio between a geometric Brownian motion with time-varying volatility and a Brownian bridge, then asks how to derive its stochastic differential. The bridge has a drift that pulls its value toward a fixed endpoint as the terminal time…
The document introduces volatility dispersion trading through a position that sells at-the-money straddles on an equity index and buys straddles on its component stocks. It asks how the payoff of this combination relates mathematically to implied correlation…
The document gives an intuition for why averaging can reduce the volatility exposure of an Asian call option with an average-strike payoff. It uses the fact that the time average of standard Brownian motion over a fixed horizon has standard deviation…
The document raises the difference between a Eurodollar futures implied three-month rate and a forward rate inferred from the yield curve. It identifies convexity adjustment as a possible explanation and asks how to calculate its size without relying on…
The question concerns pricing a US three-month Libor cap under euro collateral, where the discounting and forward curves reflect the collateral agreement. It asks whether the volatility quoted for a US-collateralized cap can be reused, given that the pricing…
The document clarifies why the variance of changes in a spread between two correlated geometric Brownian motion assets includes the asset price levels. For the spread defined as the first asset price minus the second, its instantaneous change is the…
The document explains why a same-strike FX call and put do not generally have offsetting deltas, so their straddle is not automatically delta neutral. Put-call parity links call and put deltas through the discounted forward, and a delta-neutral straddle…
The document asks how to calculate the probability that a geometric Brownian motion starting above a lower barrier touches it by a fixed time. It maps the problem to the minimum of a drifted Brownian motion by taking logarithms, then applies a…
The document examines whether a double-barrier cash-or-nothing option can be priced by subtracting an upper-barrier knock-in binary from a lower-barrier knock-out binary. It defines lower and upper first-hit times and expresses the payoff as the amount paid…
The document addresses which zero rates to use when bootstrapping a default probability curve from credit default swap spreads. The response recommends discounting with the curve relevant to collateral remuneration, typically the applicable overnight indexed…
The document asks whether arbitrage freedom implies completeness in a general binomial model and how the condition that the risk-free return lies between the down and up moves matters. The main response states the standard relationship: existence of a…
The document discusses pricing a call option on a stock expected to pay a fixed cash dividend during the option’s life. It presents two approximations: convert dividends to a percentage yield when payments move with the share price, or subtract the present…
The document compares two EUR/USD option hedges for a short-euro exposure: a call spread and a risk reversal consisting of a long call and short put. It explains that neither structure is automatically delta neutral. The option legs have their own deltas,…
The document asks how a UK investor can express the spread on a US dollar bank loan in sterling terms. The example is a five-year loan paying three-month USD LIBOR plus 100 basis points, with the desired result stated as three-month GBP LIBOR plus an…
The document describes an attempt to estimate an option premium by replicating a strategy using futures order-book snapshots. The data consist of daily observations at noon over one month for futures with different delivery periods. The central question is…
The document shows how to value a call whose payoff applies leverage and a shift to the terminal underlying price. For a positive leverage factor, the payoff can be factored into the leverage multiplied by a standard call payoff. This transforms the original…
The question asks how to price a European call when the underlying follows mean-reverting arithmetic dynamics with constant absolute volatility. The answer frames option valuation through a change to a risk-neutral process: in a complete market with…
The document explains how the risk-neutral measure prices a stock when its terminal value is discounted at the short rate. Under an equivalent martingale measure, discounted asset prices are martingales, so the stock value is the conditional expectation of…
The document explains the one-period binomial model’s no-arbitrage condition: the risk-free gross return must lie strictly between the down and up factors. If both possible stock returns exceed the risk-free return, borrowing at the risk-free rate to buy the…
This exchange discusses a discounted cashflow model for pricing a floating rate note and estimating interest rate and credit duration. The proposed model uses today’s reference rate in every projected coupon and discounts those cashflows using a discount…
The document raises a fixed income pricing question: why a nearly expiring 10 year Treasury note futures contract appears to imply a yield different from the yield on recently auctioned notes. The author recognizes that the futures contract assumes a…
The exchange considers whether daily EURIBOR 3M fixings can be compounded into a total return index, including whether to use a quarterly rate or a daily accrual convention. The answer explains that EURIBOR is a reference fixing for the cost of term…
This exchange examines why realized volatility can support profits from a long gamma position and why volatility alone does not determine the result. The questioner understands that scalping requires buying after a decline and selling after a rise, and asks…