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 how to recover FX option strikes from broker volatility quotes, forward points, deposit rates, and delta conventions. It explains that the ATM strike formula depends on the convention: a delta-neutral strike with premium-adjusted delta…
The document explains how to obtain a quantile of an exponentiated normally distributed variable. If the logarithm of a positive variable is normal, its quantile is found by taking the exponential of the corresponding normal quantile. Because the exponential…
The document asks for a route from beginner-level C++ to quantitative trading, from a learner who already programs professionally in Visual Basic and has trading experience. The response suggests starting with a general C++ text, then studying resources…
The document examines how the value of an inflation-linked payment can differ from expected inflation multiplied by a discount factor when inflation and interest rates are correlated. It presents a simplified convexity adjustment for a fixing paid after a…
The document applies Itô’s lemma to an exponential function of an integrated short rate under the Vasicek model. It derives the stochastic differential of the intermediate process, then uses its drift and diffusion terms to obtain the dynamics of the…
The document answers whether a bond can begin amortizing after an initial period of interest-only payments. It confirms that such structures exist, while noting that they do not have a single standard name in the response. The timing and pattern of principal…
The document compares ways to calculate a bond’s yield to maturity from price when repeated updates make speed important. One approach computes yields for three selected prices, fits a quadratic price–yield relationship, and uses it to estimate yields for…
The document considers pricing a callable range accrual whose coupon depends on how often a spread between long- and short-tenor constant-maturity swap rates stays above a threshold. The question notes that a LIBOR Market Model can be slow and that a…
The discussion examines whether Black–Scholes–Merton derivations require an unproven self-financing condition. It describes replication arguments in which a portfolio holds stock and a money-market account, and its changes in value come from gains on those…
The document asks how to interpret theta and gamma for a portfolio holding one call while dynamically hedging its delta with the underlying and financing trades. It gives the local P&L relationship in which theta contributes over time and gamma contributes…
This derivation uses an exponential-affine form for a zero-coupon bond price in the Vasicek short-rate model and substitutes it into the risk-neutral bond pricing PDE. Matching the constant and rate-dependent terms yields differential equations for the time…
Junior tranches of a credit default swap index absorb losses before more senior portions, so a small change in the underlying portfolio can produce a much larger proportional change in the tranche’s value or spread exposure. The document illustrates this…
This discussion addresses a payoff paid at a later date that uses the underlying price at both an earlier and a later date. The standard risk-neutral valuation formula still applies when the payoff is measurable at the payment date: by then, both observed…
This brief spreadsheet example shows how to make a Bloomberg BDP query use a strike stored in another cell instead of a fixed value. The method is to concatenate the ticker’s text components with the cell reference, while formatting the ticker with spaces as…
The discussion considers how to infer implied volatility from option bid and ask quotes across strikes, expiries, calls, and puts. It covers estimating forwards through put-call parity, choosing representative option prices, and fitting a consistent…
The question concerns valuing an interest rate swap whose schedule began before the valuation date. It raises two implementation issues: representing a declining notional and including a floating coupon whose rate was fixed earlier. The response gives a…
The question asks how to obtain the volatility input needed to calculate an option’s Black–Scholes delta. The replies explain that this input is commonly implied volatility: the volatility value consistent with the observed market price of the option and the…
The document discusses pricing a European exchange option that pays the positive difference between two stock prices at expiry. The assets follow correlated geometric Brownian motions. One answer changes to a measure using one asset as numeraire; under that…
The question asks how to estimate the jump intensity in a Black–Scholes–Merton setting from observed jump counts across three consecutive months. The response points to a compound Poisson process as the model for jumps and directs readers to a statistical…
The document shows why European calls and puts with the same strike and maturity have equal gamma under put-call parity. It starts from the parity relation between the call, put, spot price, discounted strike, and interest rate. Differentiating once with…
The document explains the no-arbitrage argument that a claim with a replicating portfolio must have the same initial price as that portfolio. If the claim is overpriced, short the claim, buy the replicating portfolio, and invest the surplus at the risk-free…
The document asks why some derivatives references express option prices on an undiscounted basis. It contrasts a density formula using the strike derivative of an undiscounted call price with the version using discounted prices, which includes a…
The example applies Feynman–Kac to a terminal-value partial differential equation with a fourth-power terminal payoff. The PDE contains a second derivative term proportional to the square of the asset price, and the proposed solution represents the value as…
The document explains how to value a CMS indexed range accrual when simulated zero-coupon rates follow a short-rate model under the risk-neutral measure, while the desired probability is expressed under the payment-date forward measure. The payoff event is…