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 surveys several forms of liquidity provision. It describes cross-market arbitrage, where a trader posts a limit order in one venue and hedges a fill by taking liquidity elsewhere, and rebate trading, which seeks exchange payments for passive…
The document explains a practical reason dealers may quote vanilla options in implied volatility rather than in currency amounts. Option prices depend on several inputs, including the underlying or futures price, rates, volatility, and the shape of the…
The document distinguishes historical or realized volatility from Black–Scholes implied volatility. In the model, volatility scales the standard deviation of log returns with the square root of time; implied volatility instead is inferred by matching option…
A borrower’s par call right can reduce the value of a floating-rate loan’s floor: when rates fall and the floor becomes valuable, refinancing may cause the loan and its floor to disappear. The response recommends valuing the callable instrument on a grid,…
This explanation distinguishes the timing option from the switch option in bond futures and clarifies that the end-of-month option is another form of switch option. The timing option concerns when to deliver; the switch option concerns which eligible bond to…
The question asks how to extend a put-call symmetry known at the initial time to an arbitrary time before expiry in a Black-Scholes model with zero interest rate and zero dividend yield. With the current asset value used as the starting value, it asks…
The document states a calendar-spread inequality for European calls on the same non-dividend-paying stock with different maturities. The shorter-dated option uses a lower strike, discounted to account for the interval between expiries; the claim is that its…
The note sketches a pricing expression for an up-and-in put under a stochastic volatility model in which the asset return and volatility share a Brownian driver, with an additional independent return component. For a barrier at or above the current asset…
This document discusses pairing European call and put observations from separate price files when their option identifiers differ. It recommends matching on valuation date, expiration, and strike, with the underlying security also included where relevant.…
This document asks how a Taylor expansion produces a short-time P&L formula for a delta-hedged option. The setup combines the change in option value with financing and underlying-position cash flows, including interest and repo or dividend yield. Choosing…
This document considers relative-value trading between options on two similar, but nonidentical, indices. Matching equivalent strikes may allow a position in one index’s option to be offset with an option on the other, yet movements in the indices’ basis…
The document raises two related questions about volatility smile terminology. First, it asks whether skew has a generally accepted definition and whether it means the derivative of implied volatility with respect to strike, with maturity held as an argument…
The document discusses why gamma and vega for a European call can have similar shapes when plotted against delta. It presents Black–Scholes expressions and summarizes an answer that describes both sensitivities as largest near at-the-money and smaller in the…
The document asks why a short iron condor on the Nifty 50 showed an all-positive payoff diagram when constructed in the morning, while the same strikes on the same instrument showed the familiar central-loss, outer-profit shape an hour later. The author…
The document asks whether the Fokker-Planck forward equation used in local volatility calibration still holds when the diffusion coefficient depends on time as well as the state. The accepted response says that time dependence is allowed and outlines a…
The document explains delta hedging of a long gamma option position. As the underlying moves, the option’s convex value change can exceed the linear gain or loss on the stock hedge. Rebalancing the hedge captures this convexity, while the option’s theta…
The document presents a constructive way to represent a piecewise linear European payoff as a portfolio of calls. Begin to the left of all strike points, where call payoffs are zero, and move through the underlying price levels where the target payoff’s…
The document distinguishes a position that is delta neutral when opened from a strategy that stays delta neutral as the underlying price changes. A call and a suitably sized put can offset each other’s deltas at a chosen spot price, volatility, maturity, and…
The document raises a question about whether cross-gamma effects belong in curvature calculations under the Fundamental Review of the Trading Book standardised approach. It describes an FX option whose risk is represented in the two currency legs relative to…
The document shows how a change of variables converts the Black–Scholes partial differential equation into a dimensionless form. It defines log price relative to the strike, rescales time using volatility, and expresses option value relative to the strike.…
The document compares two bullish vertical option spreads: buying a call spread for a debit and selling a put spread for a credit. It outlines their maximum gains and losses and explains that, when prices are fair, their payoff profiles can be equivalent.…
The answer explains how to identify inputs for a European at-the-money currency option using spot FX, implied volatility, and deposit rates. For an option on a currency forward, it first derives the forward level from spot and the interest-rate differential…
The document addresses how to identify the full range of listed SPX option strikes, including strikes with no trades or open interest. The contract description says in-, at-, and out-of-the-money strikes are initially listed, with additional series generally…
The document sets up a quanto put with a fixed exchange-rate conversion in its payoff and describes candidate hedge instruments involving the foreign stock, exchange-rate conversion, foreign cash, and domestic cash. It applies Itô’s lemma to the proposed…