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 reports a comparison between a Python implementation of the binomial option pricing model and observed prices for SPY calls. The author says in-the-money and near-the-money options had relatively small absolute errors, while errors appeared to…
The document asks how to interpret Rebonato’s approximation for swaption volatility when using a factor-reduced or multifactor Libor Market Model. It questions whether each factor should be represented by a separate volatility function tied to a tenor, with…
The document explains why a Heston model does not always produce lower implied volatility at longer maturities. Its variance process is mean reverting toward the long-run variance level, so the relationship between current variance and that target influences…
The document discusses where researchers might obtain sample or market data for swaption valuation, focusing on the difficulty of finding free public data for these over-the-counter instruments. Suggested sources include examples bundled with textbooks or…
The document explains a way to interpret an annual yield calculated from the difference between NDF bid and ask rates relative to spot. It connects the calculation to the familiar practice of expressing forward points as a proportion of spot, then…
The document explains why the European Black–Scholes relationship between vega and gamma generally does not carry over to American options. Early exercise creates a boundary that changes the option’s value and sensitivities. For a put with a positive…
The document gives a concise explanation for why a floating-rate loan is generally valued near par on a coupon reset date. At that date, the loan’s coupon is reset to the prevailing market rate. In the basic bond-pricing argument, an instrument whose coupon…
The document explains how to value a payment of LIBOR fixed at time T and paid at T plus an accrual period. After the rate has been set, its value is the discounted payment amount. Before the fixing date, the price is the value of a portfolio holding a bond…
A zero-coupon bond makes a single payment of face value at maturity and has no interim coupon payments. Its issue price reflects the present value of that future payment. With a positive yield, discounting makes the issue price lower than par; the discussion…
The document asks how practitioners might extend a long-dated foreign exchange option hybrid model that captures volatility level and skew but may not reproduce the full smile. The questioner wants to retain a three-factor setup, avoid stochastic volatility,…
The document asks whether a plain-vanilla European option can have negative time value, defined in the discussion as option value minus intrinsic value. One response constructs a deep in-the-money put case: with a positive interest rate, the discounted…
The document explains that option Greeks are sensitivities of the Black–Scholes–Merton price to model inputs. It defines delta, gamma, rho, vega, theta, and sensitivity to the dividend rate as partial derivatives, then works through the call delta…
Put–call parity links prices of European calls and puts with the same strike to the value of a forward contract. With the risk-free rate and time to expiry known, the parity relationship gives the forward price and can be rearranged to infer the asset’s…
The document asks how to choose a probability measure when pricing derivatives with Monte Carlo simulation. It starts from risk-neutral valuation, where price is the discounted expected payoff, and notes that simulations may require modeling state variables…
The document poses an inverse pricing problem: fitting a Black–Scholes model to binary option prices observed across strike prices when the time to maturity, volatility, risk-free rate, and underlying price are all unknown. The stated goal is to predict…
The document explains why a single expiration payoff diagram may not fully describe a portfolio containing short American-style options or options with different maturities. A short American option can be exercised by its holder before expiration, so the…
The document explains how to obtain the Radon–Nikodym derivative when changing from a probability measure associated with numeraire M to one associated with numeraire N. The derivation uses the martingale property of asset prices expressed in units of the…
This note addresses the European call formula for a dividend-paying stock and whether an expected stock growth rate should replace dividend yield. It explains that the dividend-adjusted Black–Scholes formulation and a cost-of-carry formulation are equivalent…
This note explains why a plain floating-rate bond can have interest-rate duration close to the time until its next coupon reset. Under a single-curve assumption, future coupons are projected from forward rates and discounted using the same curve.…
The note discusses how options traders describe exposure to changes in implied volatility skew and volatility convexity. Skew refers to differences in implied volatility across strikes, such as between out-of-the-money puts and calls. Traders may…
This note clarifies how to set up valuation equations for an asset whose dividends follow a Markov process. Its central distinction is between cum-dividend value, which includes a payment made today, and ex-dividend price, which excludes it. The investor’s…
The discussion describes how to think about risk in a single-currency swap exchanging floating payments based on different tenors, such as six-month and three-month rates. It separates sensitivity to changes in the tenor basis from outright rate delta. A…
The document explores representing Brazilian DI1 interest rate futures with rateslib for curve calibration and sensitivity analysis. It proposes a zero-coupon swap representation and distinguishes the futures’ annualized compounded internal rate of return…
The document explains why quasi-Monte Carlo methods use low-discrepancy sequences: these points fill a space more evenly than random samples, reducing large gaps. It defines discrepancy as a measure of how closely the fraction of points in a region matches…