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 investigates why a simulated call price comes out as zero when the Black–Scholes calculation gives a positive value. Its proposed remedy is to simulate the underlying under the risk-neutral geometric Brownian motion process, using the risk-free…
The document answers whether local volatility can be estimated using only the spot price at a particular time. It explains that Dupire’s approach derives local variance as a function of option maturity and strike from a surface of call prices, rather than…
The document outlines a Monte Carlo approach for valuing performance share units whose payout depends on a company’s share-price performance relative to a peer group. It estimates daily log-return means, volatilities, and correlations from historical prices,…
The document examines why a finite-step Taylor expansion for an option price can include the squared asset-price increment, while a continuous-time Itô calculation uses quadratic variation. It distinguishes two ways to express a change in a smooth function:…
The document distinguishes martingale assumptions used in derivative pricing from assumptions used in trading and risk management. For pricing, it describes a risk-neutral probability measure under which an underlying asset is a martingale, linking that…
The document asks whether an FX swap can be priced by subtracting spot from the theoretical FX forward rate. The proposed forward calculation uses spot and the two currencies’ interest rates, and the question frames the swap value as the forward-minus-spot…
The discussion examines a long-dated equity index call whose hedged profit and loss appears sensitive to interest rates. It questions whether a standard Black–Scholes formula using a current LIBOR rate and ordinary delta hedging remains appropriate when…
The document explains why gross basis tends to decline as a bond futures contract approaches delivery. It defines gross and net basis and relates the implied repo rate to the bond’s invoice price, cash price, and time remaining. Because time to delivery…
The document asks how to set the fixed-leg payment frequency when pricing an interest rate swap in MATLAB. The accepted response identifies a reset-frequency name-value setting as the relevant parameter, rather than the period option used in a bond-pricing…
The document asks how to build a simple parametric value-at-risk estimate for comparison with ISDA SIMM initial margin. It specifically raises whether the profit-and-loss distribution should be normal or asymmetric, and whether a model should include option…
The document discusses how to infer implied volatility from an option’s bid and ask prices. It compares averaging the prices before solving for implied volatility with solving for each quote’s implied volatility and averaging those values. Although the…
The document raises a conceptual question about the one-factor and multi-factor Hull-White interest rate models. The author understands that the one-factor model has limited ability to represent yield-curve movements, and asks which parameters govern a curve…
The document asks how to express a receiver interest rate swap as a sequence of forward rate agreements. It starts from the swap’s discounted fixed-minus-floating cash flows, then compares those payments with forward-rate terms based on discount factors. The…
The document poses a valuation problem for a software investment whose daily revenues depend on an exchange rate and whose costs depend on a commodity price. The proposed simulation models both underlying prices as geometric Brownian motions estimated from…
The document considers whether a swap must be hedged with another derivative or can instead be hedged using cash products such as equities or foreign exchange. Its answer is contract dependent: the key issue is whether the swap’s underlying exposures…
The document explains the terminal value of a forward contract that requires its holder to buy one share for a fixed cash price at a specified date. At maturity, the holder receives a share worth the prevailing stock price and pays the contracted amount, so…
The document asks how to interpret a model-independent representation of a twice-differentiable payoff as a combination of terms involving the payoff and its derivative at zero, the underlying stock, and an integral of calls across strikes. The questioner…
The document asks how to read derivative notation in conditions from a theorem on arbitrage-free SVI volatility surfaces. One condition uses a time derivative of a parameter and requires it to be nonnegative. Another bounds the derivative with respect to…
The document presents a question about deriving the dynamics of a process defined as the exponential of a stochastic integral and a quadratic-variation adjustment. The process is parameterized by an integrand and a driving process, in the setting of an…
The document raises a boundary-condition question about using a finite element method to price an up-and-out call. It refers to an appendix that demonstrates the method for a straddle and focuses on a boundary vector containing the difference between option…
The document asks whether the expected payoff of a multi-leg option position, such as a spread or condor, equals the sum of the expected payoffs of its individual options. It represents each leg’s payoff as a function of the same market value at expiration…
The document presents a question about the relationship between a long call butterfly and a short iron butterfly. It gives a four-option position consisting of a long lower-strike put, short middle-strike put and call, and long upper-strike call, then…
The discussion separates a stock-price model from the martingale condition. A Brownian-motion-based model can include drift under real-world probabilities; having nonzero drift does not mean the process ceases to be Brownian motion. The first answer connects…
The document outlines how Lévy processes can model log stock prices through exponential Lévy models. It explains that these processes combine drift, diffusion, and jumps, and distinguishes finite-activity jump models from models with infinitely many jumps.…