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 asks for references surveying methods used to calibrate stochastic volatility models, including the Heston model. It notes that many calibration approaches exist and seeks a broad overview of research and practical projects. The response…
The document explains how to track relative implied volatility at a specific option delta over time, such as comparing a 10-delta put with an at-the-money put. The suggested process begins with collecting option quotes across strikes and expirations for each…
Convertible bond parity compares the value of the shares obtainable on conversion with the bond’s face value. When the stock and bond are quoted in different currencies, the share value must first be converted into the bond’s currency using the relevant…
The document asks how to infer a six-month LIBOR fixing from three-month Eurodollar futures. It identifies the futures-implied three-month rate as 100 minus the quoted futures price, expressed as a percentage, and asks how to extend that information to a…
The document considers a claim whose payoff is the time integral of an asset’s proportional price change. Its main replication argument is direct: hold one unit of the underlying’s inverse price, or equivalently one dollar of stock exposure, so the…
The document derives how delta hedging an options book can affect the underlying when hedge trades move its price. It starts with the delta-hedged profit and loss formula, then models price impact as proportional to the dollar demand created by rebalancing.…
The document discusses counterparty credit valuation adjustment for a European call bought from a counterparty. The key intuition is that the buyer has paid the premium and remains exposed to losing the value of the option if the seller defaults before…
The document considers whether a same-currency floating-for-floating interest rate swap has gamma, meaning sensitivity of value to changes in rates. It contrasts two views: distinct indices with different yield curves can create gamma, while a typical tenor…
The document explains how a bond’s cash flows can be valued using a sequence of forward rates. Each coupon is discounted by multiplying the accumulation factors for the forwards that span from today to that coupon’s payment date. By no-arbitrage, this…
The document asks whether overnight index swaps need a convexity adjustment when building an OIS curve, given that overnight rates are published after the accrual period. It presents an argument that OIS market quotes are coupon rates formed from compounded…
The document explains why a manually discounted cash-flow sum in QuantLib can differ from a bond’s dirty price, even when the same yield is used. The example uses a semiannual fixed-rate bond with an Actual/Actual ISMA day-count convention. The discrepancy…
The document addresses why labels such as long and short can be confusing for multi-leg option strategies. A debit or credit alone does not determine a strategy’s directional classification: spreads, butterflies, and similar structures combine bought and…
The document discusses whether an asset’s price, represented through risk-neutral valuation, must be below its expected discounted payoff under the real-world probability measure. The answer distinguishes how stocks and derivatives are priced: a stock’s…
The note clarifies that Black–Scholes gamma measures the change in option delta per unit change in the underlying price. It is an absolute sensitivity, so a large gamma value for a low-priced underlying does not itself indicate an error or describe a…
The document explains how to simplify the present value of a bond’s fixed annual coupons using the finite geometric series formula. Discounting each coupon produces a sequence with first term and common ratio equal to the one-period discount factor. Summing…
The document concerns a proof in a single-period mathematical finance setting: how a separating hyperplane theorem supports the connection between no-arbitrage and the existence of a risk-neutral probability measure. The question references normalized prices…
The document explains why Broadie–Kaya exact simulation is not automatically the practical choice for the Heston stochastic volatility model. Its main advantage is that it can simulate across arbitrary time steps without the time-discretization bias…
This note works through the stochastic differential of an exponential process built from an HJM forward-rate expression. It first differentiates the exponent, accounting for the time-dependent Brownian coefficient and the moving boundary of a nested…
This note explains why a QuantLib floating-rate coupon amount may differ from nominal multiplied by accrual period and the index forward. The coupon amount is calculated using the coupon’s rate, which can include a contractual spread; the index fixing or…
The document asks whether a receiver swaption is equivalent to a callable bond. The main response distinguishes the instruments: a callable bond is a security exposed to issuer default, while a swaption is an interest-rate option. It then describes an…
The document compares short- and long-dated straddles as ways to take a long-volatility position. Its answer links short-term straddles to profits from realized movements that exceed expectations, describing this exposure in terms of gamma. Longer-term…
The document considers an embedded equity conversion option in a bond issued by an Indian company. The bond is denominated and repaid in US dollars, while the underlying shares trade in Indian rupees; the conversion price uses a fixed USD/INR rate. One…
The document outlines how a variance swap works: the buyer exchanges a fixed variance strike for realized variance calculated from returns over specified observation dates. For liquid standard contracts, the market quotes the strike; for nonstandard expiries…
The discussion asks whether equity option valuation should account for uncertainty in interest rates, including in a risk-neutral expectation discounted by the path of the short rate. It explains that interest-rate sensitivity, measured by rho, is usually…