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 considers whether options can reveal the market’s expected volatility from one close to the following open. It explains that an option’s implied variance over its life represents variance accumulated across the full interval to expiry. A quoted…
The document asks whether a volatility skew creates expected profit from buying an at-the-money option and delta hedging it. Its answer separates implied volatility from the path of realized prices: a move to a particular terminal level does not reveal how…
The document discusses the consumption-based asset pricing equation and why an asset’s payoff covariance with consumption matters for its price. In the model, an investor chooses asset holdings to maximize current and expected future utility, yielding a…
This document examines why an American call on a non-dividend-paying stock is generally not exercised before expiration. Its central correction is that comparing the proceeds from early exercise with a hypothetical payoff at maturity mixes a known current…
This document presents a bond portfolio duration calculation and asks how to hedge its interest-rate exposure with a fourth bond. The accepted answer distinguishes Macaulay duration, which measures the weighted timing of cash flows, from modified duration,…
The document clarifies how long and short CDO tranche positions relate to credit exposure and credit protection. For cash CDO tranches, an investor buying a tranche takes on credit exposure and receives a spread as compensation. For a synthetic CDO, the…
The document examines the basis risks in a SEK–USD cross-currency swap collateralized in euros. It reasons from the collateral currency: discounting the SEK cash flows may involve a SEK–EUR basis, while discounting the USD cash flows may involve a USD–EUR…
The note examines why an equity option’s annualized at-the-money implied volatility can be higher for a shorter expiry than for a longer one. It distinguishes a downward-sloping volatility term structure from negative forward variance: comparing two implied…
The document raises a question about using a non-flat term structure when pricing options on bonds with a normal short-rate model. The author describes a proposed mapping for a ten-year bond: at each future point before maturity, use a zero-coupon yield…
The document explains the economic reason bid and ask sides may appear reversed when deriving implied interest rates from an FX forward. A long AUD forward is described as a sequence: borrow USD, exchange USD for AUD at spot, and lend AUD. Each leg has its…
The document compares two ways to estimate the price of a European call at a strike and maturity absent from the market: interpolate neighboring option prices directly, or interpolate model inputs such as implied volatility and then reprice with…
The document explains where practitioners can obtain dividend and repo assumptions when pricing vanilla equity options. It identifies broker quotes or contract terms as sources for repo rates, noting that the standard rate may apply when the underlying is…
This brief exchange asks what price to charge for an option whose expected payoff is zero. The reply gives a minimal market-based answer: a seller would accept the smallest positive amount buyers are willing to pay. It treats the question as one of…
This post raises two practical challenges when using QuantLib from Python: inspecting the market inputs inside a Black–Scholes–Merton process and determining the conventions used to calculate a vanilla option’s Greeks. The author says the library’s C++…
The response offers several theoretical research areas for someone seeking mathematical finance problems grounded in analysis, probability, and optimization rather than statistical modeling. It suggests investigating convergence questions in simulation-based…
The discussion explains how price alignment interest (PAI), paid on variation margin, changes the funding interpretation of cleared interest rate swaps. With perfect collateralization, where collateral tracks the derivative’s net present value, the…
The answer interprets “near choice” as dealer jargon for a spread whose midpoint is close to zero. For a risk reversal, the proposed meaning is that buying one direction of the spread or the reverse direction costs roughly the same, with the trader…
This discussion addresses European swaption pricing under normal volatility, including how to derive a receiver swaption value from a payer value and whether an at-the-money strike equals the forward swap rate. The answer identifies the Bachelier formula as…
This discussion examines a negative yield returned by QuantLib for a fixed-rate bond when the user expected a small positive yield. The replies identify several input and convention issues to check: the coupon is divided by 100 after already being described…
The document asks how to price a long-maturity fixed-for-floating interest rate swap when the available LIBOR curve quotes extend only to short maturities. Its answer is to use quoted market swap rates beyond the end of the Eurodollar futures strip,…
The document derives the fair delivery price for a three-year forward on thirty dividend-paying assets using a replication argument. Buy the assets at spot by borrowing their cost, invest the interim dividends, and compare the resulting time-three cash flows…
The document describes a binary option valuation in RQuantLib where a European contract returns a full set of Greeks, but an American contract displays numeric values only for value, delta, and gamma. The response identifies the cause in the library wrapper:…
The document works through the normalized gains process for a stock paying continuous dividends, using a bank account as numeraire. It starts with geometric Brownian motion under the real-world measure, applies a change of measure, and identifies the…
The document explains how interest rate derivatives use historical index fixings for dates already observed and projection curves to estimate future fixings. It then considers valuing a derivative at a simulated future date, when the fixing history available…