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 explains how interest enters the overnight profit of a delta-hedged option position. It represents the portfolio as a short option combined with a position in the underlying sized by the option’s delta. The net portfolio value determines whether…
The document examines why an at-the-money European call and put on a non-dividend-paying stock can have equal value when interest rates are zero, despite their different-looking payoff diagrams. Its central explanation is that option prices reflect both…
The post asks how to transform one risk-neutral pricing expression for a derivative with funding and collateral rates into another expression using collateral-rate discounting and an adjustment based on the difference between funding and collateral rates.…
The document derives a risk-neutral price for a contract that pays the average underlying price over an interval ending at maturity. It discounts the payoff at the final payment date and uses linearity to move the expectation inside the time integral. Under…
The document explains why jump intensity cannot be interpreted independently of the assumed jump-size distribution. To estimate a model’s jump frequency, it recommends fitting intensity and the other model parameters jointly, using maximum likelihood or…
The document investigates how to reproduce CBOE’s discontinued single-name 30-day normalized skew field using historical options data. It describes the target as the 25-delta put implied volatility minus the 25-delta call implied volatility, divided by…
The document explains how an unpublished floating-rate fixing creates P&L exposure for an interest rate swap, measured as the difference between the published fixing and the market forecast. Once the fixing is known, the associated cash flow is fixed; the…
The document explains why a receiver swap's return is not naturally computed as a percentage change in its market value: the swap can begin at zero value and later have positive or negative value. It presents change in swap value divided by notional as one…
The document asks how to define an arbitrage-free price process for an American-style derivative when the buyer may make payments over its lifetime and choose a random exercise time. It proposes selecting a process so the supremum over exercise times of…
The document explains the relationship between the par fixed rate of a spot-starting fixed-for-floating interest rate swap and its DV01. It gives the par-rate expression as one minus the final discount factor divided by the swap DV01, and expresses DV01 as…
The example shows how put-call parity and relationships across option strikes can be used to infer some option prices from quoted market data. Ignoring discounting, the response applies parity at the 70 strike to the given futures level and straddle price,…
The document discusses background reading for someone struggling with a mathematical finance text. It frames Shreve’s work as a calculus-based treatment of finance and suggests building mathematical preparation before tackling it. For derivatives-focused…
The document explains that PV01 and DV01 both describe value changes associated with a one basis point interest-rate move, but usage depends on the instrument and calculation. One response frames DV01 as the yield sensitivity of an individual bond, while…
The document considers a claim paying the time average of squared Brownian motion when the underlying follows standard Brownian motion and the interest rate is zero. It gives the initial fair value as the expected payoff, then uses Itô calculus to rewrite…
The document asks how to judge whether a derivative-pricing model improves on Black–Scholes when traders already use implied volatilities and interpolation to fit option prices. It distinguishes pricing from prediction: a pricing model can interpolate or…
The document examines how pull to par affects a bond's spot price and forward price when yields remain unchanged. The question relates the spot price, accrued interest, and financing to a fixed-date forward price, then asks how a long cheapest-to-deliver…
The document raises a foundational question about defining the Malliavin derivative on two probability spaces. One construction starts from canonical Wiener space, consisting of continuous paths equipped with Wiener measure. Another works on a general…
The problem asks for Black–Scholes prices of two terminal payoffs: the square of the stock price and a unit payment when the stock finishes below a strike. It applies risk-neutral valuation by discounting each payoff’s expected value. The squared payoff uses…
The discussion asks whether a market is complete when a stock price is exposed to two independent Brownian motions: one drives returns directly, while another drives a mean-reverting stochastic drift. With only the stock available for investment, one…
The note explains how to read a quoted sovereign five-year credit default swap spread and how it relates, in broad terms, to perceived credit risk. It interprets a quote of 42.520 as basis points and says that a lower spread generally signals a lower premium…
The document explains how options systems represent time remaining on expiration day. Rather than using whole-day buckets, pricing and risk software generally represents expiry tenors fractionally and may measure time internally in years, seconds, or…
The document explains how day count conventions apply when pricing cross-currency forwards and swaps. Its central method is to calculate the accrual factor for each currency leg using that currency’s convention, then form the forward price as the domestic…
The document explains an instantaneous forward rate as the limiting forward rate over an interval whose length approaches zero. Starting from the no-arbitrage relationship between two zero-coupon bond prices and a simply compounded forward rate, it derives…
The document explains how a Wiener process can have continuous paths while lacking a derivative at every point with probability one. It distinguishes continuity, where nearby input times produce nearby function values, from differentiability, which…