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 discussion clarifies whether the VIX is leading or lagging. Because it is calculated from option prices and represents the market’s implied expectation of volatility over the coming period, it is forward-looking in that sense. It does not independently…
Treasury futures allow the short to choose which eligible bond to deliver, creating a quality option for the short and affecting the futures price. If the cheapest-to-deliver bond is already known, pricing can be based on that bond’s forward price adjusted…
The discussion explains why out-of-the-money VIX puts expiring on a given date can lose value even when the spot VIX falls sharply. The key distinction is that VIX options are tied to the VIX futures contract for their expiration, not directly to the spot…
The document asks how to price a European claim that pays the natural logarithm of a stock price at maturity, including the possibility of a negative payoff when the stock finishes below one. It presents the general risk-neutral valuation rule: discount the…
The answer describes how to derive a forward rate from a simulated Hull–White short-rate path. At each simulated future time, use the current short rate in the model’s zero-coupon bond pricing expression, with the model’s time-dependent A and B terms, to…
The document raises a question about constructing a variance-swap replication portfolio from options. It describes an apparent jump in implied volatility when the option wing switches from puts below a strike to calls above it. The quoted explanation is that…
The document investigates whether an FX option’s time to expiry in an at-the-money delta-neutral strike calculation includes hours and minutes or counts only whole days. It applies the standard forward-based strike formula to a one-day example, using the…
The document reconciles several formulations of Durrleman’s condition for preventing butterfly arbitrage in an implied volatility surface. It explains how expressions differ when volatility is represented as raw volatility, total volatility, or total…
The document compares ways to choose the drift parameter in a recombining binomial tree. It describes the Cox–Ross–Rubinstein construction, which uses symmetric log-price steps, and an alternative that adds a fixed drift to the up and down multipliers. It…
The document asks how to price a one-year call when a stock can move to either of two values, given a risk-free rate and equal real-world probabilities. It uses a one-step binomial model: calculate the call payoff in each state, form a replicating hedge, or…
The document asks why volatility models often treat out-of-the-money calls and puts as a group even though their implied volatilities can differ. It identifies liquidity as a reason for focusing on OTM contracts and notes that OTM puts commonly carry higher…
The document clarifies how gross basis relates a bond’s cash price to a bond futures contract. It gives the relationship as bond price minus futures price multiplied by the bond’s conversion factor. This frames gross basis as the difference between the bond…
The document asks why an American call on a stock paying continuous dividends has a finite stock price above which early exercise is optimal. It contrasts the option’s value, which cannot fall below intrinsic value, with the possibility that the two values…
The document asks how to infer zero-coupon discount factors from clean and dirty prices of coupon bonds with annual coupons and staggered maturities. It proposes expressing a bond's dirty price as the sum of its coupon and principal cash flows, each…
The document discusses maintaining interest rate curves built from swap and other market data, with particular attention to calibration failures and kinks. It recommends keeping user-adjustable configuration manageable, supported by instrument symbology and…
The document explains how to convert a perturbative approximation for a vanilla call's equivalent Black volatility into an expansion centered at the midpoint between the current forward and strike. The original approximation expands the local volatility…
The document sketches why a market with stochastic volatility may be incomplete when volatility risk is driven by an independent source of randomness that cannot be traded directly. In a one-stock setting, changing the risk premium associated with the…
The document investigates a Python QuantLib TypeError raised while constructing Heston model calibration helpers for options. The replies point to mismatched input types or values as the likely cause and identify code issues to check, including an…
The response distinguishes two interpretations of a share purchase plan in which the bank can terminate during the purchase period. If the customer’s price is the average only through the termination date, the answer argues that termination does not create…
The document explains why a Black–Scholes option price is not the discounted expected payoff under real-world probabilities. That calculation uses the stock’s physical drift, which reflects expected returns, but ignores how traded assets and hedging…
The document asks what drives the price of a bond futures calendar spread when both contracts share the same deliverable basket and cheapest-to-deliver bond. The accepted answer identifies the forward repo rate implied by term repo rates extending to each…
The document clarifies how SVI parameterizations describe implied volatility data. Raw and natural SVI parameterizations represent total implied variance across strikes for a single expiry, while SVI-Jump-Wings represents implied variance for a single…
The document explains why binary option quotes that appear inconsistent with a simple Black–Scholes volatility range may still be reasonable. It gives the digital call price in terms of the forward price, strike, time to expiry, rates, and volatility, then…
The document examines a terminal payoff formed by taking the positive part of the stock’s gain over its current price, subtracting a fixed notional, and capping the result at zero. It asks how to price this payoff under risk-neutral valuation, while noting…