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 which bond price belongs in a duration calculation. It defines modified duration using the derivative of price with respect to yield divided by price, and identifies that price as the dirty price, which includes accrued coupon…
The document explains a sign confusion in a put–call parity arbitrage argument. A trader considers a position involving a call, a put, and the underlying stock, and asks whether the terminal expression represents a debt or a gain when the call is exercised.…
The document studies a European payoff that is zero below a lower threshold, declines linearly between two strikes, and pays a fixed amount above the upper strike. It first expresses the price as discounted risk-neutral expectations over the relevant…
The document raises a question about two option sensitivities: dual delta, described as the derivative of option price with respect to strike, and epsilon, described as sensitivity to dividend yield. It asks whether these measures have practical uses and…
The document asks which implied volatility surface should serve as the target when calibrating the leverage function in a stochastic-local volatility model. It describes a two-stage setup: first calibrate pure Heston parameters, then fit the leverage…
The document distinguishes carry from roll-down for forward-starting interest rate swaps. Before the swap begins, its floating leg has no certain payments over the investor’s holding horizon, so the response describes the position as having no earned carry…
The document explains how to estimate a Treasury futures contract’s modified duration when its cheapest-to-deliver (CTD) bond is known. Under the simplifying assumption that futures track the CTD’s forward price perfectly, the conversion factor cancels from…
The document explains how to value a European option whose payoff is determined at expiry but paid later. It distinguishes the option expiry date from the cash settlement date and expresses the value at expiry as the payoff multiplied by the price of a…
The document describes a request to value a Chilean peso fixed floating swap in QuantLib when the fixed leg pays as a single coupon through the first eighteen months and semiannually afterward. The question includes code for constructing a discount curve…
The document presents Python code intended to value a European call or put using a time and asset-price grid. It sets the payoff at expiration, then attempts to step backward through the grid while estimating option sensitivities and applying boundary…
The question asks how to obtain a zero-coupon curve for Italian government bonds in order to calculate Z-spreads, including how to treat a bond’s next coupon date. The answer clarifies that the “z” in Z-spread refers to zero volatility, rather than…
The discussion describes what makes options strategy backtesting more demanding than testing a simple underlying asset. A credible simulation needs historical option chains, including contract terms and market prices, alongside underlying prices used to…
The document compares Monte Carlo prices for a European call under constant volatility and under volatility sampled once per path from a lognormal distribution. It raises the question of why the random-volatility estimate is slightly below the…
The document discusses valuing the floating leg of a daily compounded overnight-indexed swap when payment occurs after the accrual period, under the one-factor Hull–White short-rate model. One derivation rewrites each daily accrual factor using a ratio of…
The document explains why an equity index future may appear to fall far less than its underlying index during a sharp market move. For a global index such as MSCI World, constituent markets trade in different time zones, so many index prices can remain fixed…
The document raises a model-validation question: whether stochastic-volatility option models produce more accurate market-price estimates than the standard Black–Scholes–Merton model. It highlights two practical costs of more complex models: greater…
The question asks whether one can derive the Black–Scholes partial differential equation without invoking Girsanov’s theorem, and whether a stock with nonzero drift is a martingale. The answer distinguishes the original replication argument from later…
The document considers how a bank might price a ten-year EUR/DEV cross-currency basis swap when there is no established swap market in DEV and the proposed hedge is to roll daily borrowing and deposits at the two risk-free rates. Its central point is that…
The document challenges the claim that an option’s Black–Scholes price is the discounted expected payoff under real-world probabilities. The response recommends comparing this claim with risk-neutral valuation, which uses a pricing measure consistent with…
The document asks why a stock-price model with drift μ can be expressed under a different probability measure with drift equal to the risk-free rate r, while retaining the same volatility. This is the risk-neutral change of measure used in derivative…
The document asks when a Black–Scholes market with two risky assets driven by the same Brownian motion and one risk-free asset is arbitrage-free and complete. The question highlights a modeling issue: the setup has one source of randomness, which does not…
The document raises a practical question about estimating spread option Greeks by applying finite differences to Kirk’s spread option approximation. The author reports that, for options with deltas between 0.45 and 0.6, the resulting gamma estimates fall…
The document considers the lower price bound for a claim in an incomplete market, where multiple risk-neutral measures may be consistent with observed prices. It asks whether sub-replication is the counterpart to super-replication: while the…
The document describes a general way to value a call option when the underlying’s terminal price distribution is known. The option value is the discounted expected payoff under a risk-neutral probability distribution: integrate the payoff above the strike…