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 note distinguishes two short-dated foreign-exchange swap tenors used to move settlement forward. Under the usual T+2 spot convention, a tomorrow/next swap exchanges currencies on the next business day and reverses that exchange on the following business…
The document addresses an attempt to derive stochastic differentials for integrals involving Brownian motion by treating the integral itself as a function of time and the current Brownian value. The response clarifies that the differential notation for a…
The discussion considers whether an economics researcher who prices options and calibrates models should learn C++ to speed computationally intensive work, and how to connect it with higher-level languages. One respondent recommends a derivatives-pricing…
The document works through the valuation of a forward rate agreement (FRA) that pays fixed and receives floating. It calculates the accrual fraction for the contract period, estimates a missing tenor’s Libor fixing by linear interpolation between available…
The discussion clarifies that risk neutrality is about how an interest-rate model is calibrated, rather than an inherent property of the Vasicek process. Calibrating parameters to traded instrument prices under pricing and hedging assumptions gives a…
The discussion explains how to calculate a corporate bond’s Z-spread when its yield to maturity and annual coupon schedule are known. The conventional approach is to solve numerically for the parallel shift to a reference swap curve that makes the present…
The document asks whether Black–Scholes call valuation should use a point estimate of variance from historical returns or average option values across the sampling distribution of that estimate. It describes treating the sample variance as uncertain, mapping…
The document explains what it means for forward swap rates to be realized and how that differs from the yield curve simply remaining unchanged. In its example, a pay-fixed swap is entered at the current par rate, and the relevant comparison after one year is…
The document raises a pricing question about bonds with constant-maturity swap (CMS) coupons in euros, where interest rates may be negative. It asks whether the convexity adjustment from Hull, which assumes lognormal rates, can be adapted to a normal-rate…
The document examines how a rise in implied volatility for a short-expiry option may affect a longer-expiry option with the same strike, assuming the event driving the move occurs within the shorter option’s life. The answer models volatility across time…
The note discusses the conditional-expectation formula that values a derivative as its future payoff discounted at the short rate under a risk-neutral measure. Its key distinction is between using a measure once it has been specified and establishing that…
The note distinguishes fitting an implied volatility surface at the current time from specifying how that surface changes as time passes and the underlying price moves. A cross section indexed by maturity and strike can be fitted to current market data, but…
The note applies the first fundamental theorem of asset pricing to explain why an attainable claim has the same value under every martingale measure. Given a replicating strategy, the theorem expresses its value at any time as the conditional expectation of…
The document works through an arbitrage-free valuation problem for a down-and-in claim paying the underlying stock value at maturity if a barrier is touched. The barrier equals the strike of a down-and-out call. The given market prices are for the…
The document asks what it means to say Black–Scholes overprices or underprices options when the option’s true value is not directly known. It presents research claims that the model can price deep in-the-money calls too high and deep out-of-the-money calls…
The document asks how to trade a violation of a stated no-arbitrage inequality involving three swaptions with the same strike and different option and swap maturities. The condition says the prices of two shorter-maturity swaptions, taken together, should be…
The document explains how to evaluate the probability that one of two correlated geometric Brownian motion stock prices will exceed the other at a future date. The key step is to take the ratio of the future prices: its logarithm is normally distributed,…
The document asks how to convert dollar P&L into percentage returns for a two-leg straddle strategy sized by vega notional. The strategy aims to stay vega neutral by balancing its legs, while positions are adjusted and delta hedged over time. The central…
The document asks why a forward contract’s value at delivery is not simply the spot price minus the contracted delivery price. It describes the holder’s apparent ability to buy at the agreed price and immediately sell at the market price, then questions a…
The document clarifies how USD LIBOR quote dates relate to loan periods and how business-day conventions affect swap dates. A non-overnight tenor quote is described as a forward rate whose accrual period begins two business days after the curve’s anchor…
The document asks how to handle the negative rate-times-value term in a Heston–Hull–White partial differential equation discretized with an alternating direction implicit (ADI) scheme. The paper described by the question allocates this term evenly among the…
The document asks when the conditional expectation of a terminal payoff given the full Brownian filtration can be expressed using only the current state of a diffusion. Its proposed argument relies on future Brownian increments being independent of the past…
The document clarifies how to calculate profit and loss for a continuously delta-hedged option position. Its central distinction is between the gains from holding a changing number of shares and the change in the market value of the final share position.…
The document explains why converting an FX option delta into a strike requires the market’s quoting conventions and the correct definition of at-the-money. In the example, the pair uses unadjusted deltas, and the at-the-money strike is delta-neutral: the…