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 addresses whether a swap’s fixed rate remains independent of a spread deducted from its floating leg, such as LIBOR minus a stated amount. The answer explains that the par fixed rate is set so the swap’s fixed and floating legs have…
The document asks what “NPV of the deliverable swap” means in the quoted price of a MAC swap future. It contrasts the discounted-cash-flow meaning of net present value with an expectation of future cash flows, using a stock futures price as an analogy. The…
The document describes how option pricing is used in practice, emphasizing that model choice depends on the contract and market. It notes that standard Black-Scholes-Merton pricing can be sufficient for European-style listed index options, while…
Malliavin calculus extends differentiation to random processes such as Brownian motion, which are not differentiable in the ordinary sense. The document presents it as a stochastic counterpart to Itô calculus: where Itô calculus provides tools for stochastic…
The document considers a European-style payoff that is positive when twice the log of the terminal asset price exceeds a strike parameter. Under geometric Brownian motion, the answer avoids solving a modified Black–Scholes partial differential equation…
The document asks whether an option model can represent volatility as a deterministic function of strike alone. It distinguishes this idea from local volatility, which the author understands as deriving a volatility surface from market prices with dependence…
The question asks whether converting a mean-reverting Ornstein–Uhlenbeck (OU) process to a risk-neutral measure works by replacing its drift with the risk-free rate, as is often done for geometric Brownian motion. The response points to a discussion that…
The document reviews a commonly cited set of empirical regularities in asset returns, including heavy tails, volatility clustering, slow decay in the autocorrelation of absolute returns, leverage effects, and relationships between volume and volatility. It…
The document examines a proof claiming that a positive martingale can be expressed as an exponential driven by a Brownian stochastic integral. The proof applies the martingale representation theorem to write the martingale differential in terms of Brownian…
The document describes a problem generating Monte Carlo paths from a QuantLib Black variance surface. The surface is interpolated and extrapolated from market data, with checks for decreasing total variance across maturities and butterfly irregularities, yet…
The discussion considers estimating implied volatility at each intraday option tick when end-of-day implied volatility and Greeks are available alongside tick-level option and underlying prices. One shortcut estimates volatility changes from option price…
The discussion concerns software choices for building fixed-income portfolio risk analytics when QuantLib and its Java interface are unavailable. The questioner reports problems with JQuantLib, including a bond-yield calculation error, and asks for pure Java…
The note asks how the Black–Scholes framework extends to a stock paying a continuous dividend yield. It outlines a proposed construction that converts the dividend-paying stock into an auxiliary process by reinvesting the yield, then applies a change of…
The document distinguishes a delta-neutral hedge from a self-financing trading strategy in the Black–Scholes setting. A portfolio holding an option and a changing number of shares may cancel local price risk, but changes in the share position create…
The document explains how to calculate the time-zero delivery price of a bond forward in a discrete-time, risk-neutral fixed-income model. Its pricing relation takes the expected discounted value of the underlying bond at the forward date and divides it by…
Historical default rates are probabilities under the real-world measure, but they cannot be converted directly into risk-neutral probabilities using Girsanov’s theorem alone. A model for the underlying process and its dynamics under the real-world measure…
The exchange considers how to estimate a CDS spread between quoted maturities, such as a spread for an intermediate tenor between shorter and longer quotes. It asks whether hazard rates calibrated to quoted CDS contracts can support a direct spread…
The post asks how to convert a US Treasury bond yield into a price by discounting the remaining coupon and principal cash flows. The author reports a calculated value that differs from a quoted market price and tests alternative day-count and compounding…
The document raises a modeling question about computing option theta from the Black-Scholes partial differential equation when market implied volatility varies across strikes. It compares three approaches: standard Black-Scholes Greeks with implied…
The discussion explains three common criticisms of the Heston stochastic volatility model: limited flexibility when fitting observed option volatility surfaces, unusual behavior in its forward volatility skews, and limited usefulness for some exotic pricing…
The document raises a fixed-income valuation question: whether CDS spreads quoted in different currencies can be subtracted to adjust a bond’s credit margin for a change in issuer country. The example compares five-year U.S. and Polish CDS quotes, then adds…
The document derives the logarithmic dynamics of a geometric Brownian asset and explains how to change probability measure so its drift becomes the risk-free rate. Applying Itô’s lemma to the asset’s stochastic differential equation gives the log return a…
The document shows how a narrow call spread approximates a cash-or-nothing digital option: subtract the call price at a slightly higher strike from the call price at the target strike, then divide by the strike interval. In the limit, this becomes the…
The document asks whether American option prices must increase with volatility whenever European option prices do, and seeks intuition for proving the result in more general models. The answer states that a standard American option under Black–Scholes is…