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.
5,701 documents
The document asks how to derive the price dynamics of a claim whose payoff depends on the short rate, and how to show that its price divided by the money-market account is a martingale under the risk-neutral measure. The answer applies Itô’s rule to the…
The document compares ways to value the tax savings created by corporate interest deductions and asks whether they should be discounted at the cost of debt or at WACC. One explanation treats the shield as a consequence of a borrowing decision: when borrowing…
The document discusses selecting historical index data for testing portfolio optimization methods and benchmarking a 60/40 equity and fixed-income allocation. It emphasizes that the appropriate series depends on the portfolio the simulation is meant to…
The document considers how to include single-name emerging-market corporate bonds in a multi-asset portfolio when their histories are short, missing, or unreliable and trading is illiquid. Because these holdings make up a material share of the portfolio,…
The document raises a credit-risk modeling question about calibrating a stochastic default-intensity model. The author considers the Cox–Ingersoll–Ross process because its intensity is nonnegative when the model parameters satisfy the Feller condition. They…
The document derives a zero-coupon bond price for a Gaussian short-rate model with constant mean reversion and volatility, and a time-varying deterministic drift. Under the risk-neutral measure, it writes the short rate as a mean-reverting process and values…
The document explains the conversion-factor adjustment in a duration hedge using bond futures. With a single cheapest-to-deliver bond and no delivery optionality, the futures price is the CTD bond delivery price divided by its conversion factor.…
The document considers calibrating a structural Merton jump-diffusion model to credit default swap spreads. The modeled firm value combines diffusion with compound Poisson jumps, and default is defined by the first time firm value reaches a barrier. The…
The document explains the risks a protection seller takes on in a single-name credit default swap and the limits of hedging that exposure. Selling protection leaves a position short credit spread; there is no generally available instrument that isolates and…
The document derives why debt and equity values in the Merton framework satisfy the Black–Scholes partial differential equation. It applies Itô’s lemma to each claim, then forms a self-financing portfolio of debt and equity whose exposure to the firm’s…
The document explains that key rate duration or DV01 can be calculated by shocking different representations of the interest-rate curve. The appropriate choice depends on the purpose of the measure and on how the curve is constructed, so there is no single…
The document compares buying a one-year Treasury and holding it to maturity with buying a three-year Treasury and selling it after one year, assuming the yield curve stays unchanged and funding costs are zero. It explains that the longer bond earns its…
The document addresses how to identify an issuer, rather than an individual security, in Bloomberg Symbology. A search for a company such as Apple can return many instrument records, and the question asks whether an entity-level identifier can be found in…
The response explains how a sharp currency depreciation can threaten banks when their assets are largely in local currency but their liabilities include deposits or bonds denominated in hard currency. Depreciation raises the local-currency burden of those…
The document explains the rationale behind bond futures conversion factors: they translate the futures invoice price into a comparable amount for eligible delivery bonds with differing coupons and maturities. The cited explanation says maturity and coupon…
The document formulates a two-state stochastic differential equation model in which the short rate mean-reverts toward a second state variable, while that state variable mean-reverts toward a long-run level. It asks whether the resulting affine system admits…
This note describes the state of the US dollar interdealer swaps market during the transition away from LIBOR. Earlier conventions included swaps paying semiannual 30/360 or annual Actual/360 rates, as well as spreads over Treasury securities. A 2021…
The response defines spread to maturity as a bond’s yield to maturity minus the government yield at the same maturity. It distinguishes this measure from yield to worst, which accounts for repayment at the least favorable available date or call scenario, and…
The document introduces yield to maturity as the single continuously compounded rate that equates a bond’s market price with the present value of its fixed payments. It clarifies that each payment time marks when a coupon or other cash flow is received,…
The document asks how to derive the stochastic dynamics of a zero-coupon bond when the short rate follows the Cox–Ingersoll–Ross model and the bond price has an exponential-affine form. A direct Itô expansion differentiates the time-dependent coefficients…
The document discusses how to value uncollateralized over-the-counter derivatives after LIBOR cessation. Under the older convention, a LIBOR curve could serve as a discount curve to reflect unsecured funding, while collateralized trades were discounted using…
The document addresses where to find historical US savings account interest rates and suggests using four-week Treasury bill rates as a proxy for US dollar cash interest. It points readers toward Federal Reserve historical interest-rate data. The rationale…
The document poses a methodological question about applying principal component analysis to daily yield curve changes. It compares using observable par rates, as in influential work on common factors in bond returns, with first bootstrapping a curve and…
The document discusses how to construct historical simulation scenarios for value at risk when an instrument may approach zero or become negative. Applying multiplicative price ratios to rates can produce implausible scenarios, so it distinguishes between…