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 explains the arbitrage argument behind a proof that forward and futures prices are equal under a constant interest rate. The proof compares two strategies that produce the same final capital. If their initial costs differ, an investor can take…
The document explains the basic construction of a bull spread using European calls with a common expiration. For the two-call example, the proposed position buys the lower-strike call and sells the higher-strike call. The intuition offered is that the…
The document examines the expiry payoff and a proposed Black-style valuation for a payer option on a credit default swap index. It identifies two issues: whether the payoff’s running-spread component should reflect the surviving index factor, and how the…
The document discusses how someone without access to an OTC derivatives desk can study prices and payoff risks for customized options. It explains that dealers generally quote only to established desk customers, who may need product-specific legal agreements…
The document clarifies the distinction between daily futures accounting and final settlement. Futures are settled at expiry, while their positions are marked to market each day. The daily mark to market changes the balance in the trader’s margin account,…
The document corrects a proposed variance formula for a stock modeled with geometric Brownian motion. Under Black–Scholes dynamics, the terminal price is lognormally distributed. Its conditional mean is the current price grown at the risk free rate less the…
For European interest rate options, the document distinguishes pricing from hedging. Vanilla prices across strikes can be represented by an implied volatility surface or interpolated total variance, so stochastic volatility is not required to price each…
The document questions whether risk-neutral valuation remains adequate as derivatives become actively traded. It argues that the classical view treats derivatives as replicating portfolios, while trading in derivatives can produce volatility skews, smiles,…
The document asks why an up-and-out call is said to have a lower delta than a standard call, while a down-and-out call is said to have a higher delta. The answers reason from how the underlying’s movement affects both the call payoff and the chance that the…
The document sets up a small Treasury futures example to investigate whether parallel yield curve shifts can change which bond is cheapest to deliver. It uses two hypothetical deliverable bonds, prices them from a shifted curve, applies conversion factors,…
The answer introduces Lévy processes as a way to model jumps in asset prices and connects them to risk-neutral pricing. It contrasts two constructions of price dynamics in the Black–Scholes setting, then describes generalizing them by replacing Brownian…
The answer distinguishes standard interest rate swap valuation from non-deliverable swaps, explaining that a library supporting ordinary swaps may not directly handle the latter. It outlines the fixed and floating leg present values for a standard swap,…
The document lists several basic ways to offset the interest rate exposure of a long bond position. Besides selling the same bond or a different bond, it names paying a swap and buying a payer swaption as possible hedges. Bond futures are also included in…
The explanation clarifies that interest rate swap pay and receive conventions refer to the fixed leg. A pay-fixed position has positive DV01 under the convention described: when market rates rise, the fixed payments become relatively less costly than current…
The document explains a measure change from the risk-neutral measure to an alpha measure used with a power numeraire in option pricing. It starts from a geometric Brownian motion for the underlying and expresses the Radon–Nikodym derivative in terms of the…
The document examines whether bookmaker odds can inform option prices when an underlying asset moves up or down in response to a binary event. The proposed setup combines a real-world probability for the positive event outcome with an assumed expected…
The discussion explains how one-way collateral terms affect the funding valuation adjustment (FVA) for an interest-rate swap. Its central distinction is whether the swap is hedged with a standard, fully collateralized market hedge or with an uncollateralized…
The document shows how to calculate positions in two derivatives that offset an option portfolio’s delta and gamma. It sets up a pair of linear equations: the hedge instruments’ weighted sensitivities must cancel the portfolio’s existing delta and gamma.…
The document illustrates how borrowers with different relative advantages in fixed and floating rate markets can use an interest rate swap to improve their borrowing costs. Although one party has lower borrowing rates in both markets, the comparison of their…
The document considers whether characteristic function methods used to price options can be adapted to interest rate derivatives, especially swaptions. It explains the key difficulty: many interest rate models describe short rates or zero coupon bonds, while…
The discussion addresses how to set an upper-domain boundary when numerically pricing options with finite differences. It recommends using linear behavior in an extreme model state as a generic boundary approximation for many products. In mathematical terms,…
The discussion distinguishes estimating implied volatility from observed option prices from using machine learning to approximate prices for complex derivatives. Inverting a standard option pricing model to find implied volatility is described as a simple,…
The document compares a call credit spread and a put debit spread, whose expiration payoff diagrams can appear similar. It explains that the call spread places both strikes above spot, while the put spread places both below spot. The call credit spread…
The document poses a risk measurement question about a portfolio of plain interest rate floor options. It asks whether the change in economic value under a one basis point parallel rate shock should equal the sum of value changes under one basis point shocks…