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 whether Heston parameters estimated from stock returns under the real-world measure can be used to price vanilla options under the risk-neutral measure. The response explains that option pricing requires risk-neutral dynamics and outlines a…
The note explains that a mandatory break in an interest rate swap generally does not change the swap’s ordinary valuation or hedge. It can, however, reduce counterparty valuation adjustment and funding valuation adjustment charges because the contract is…
The document explains how to obtain raw moments of a future short rate in the Cox–Ingersoll–Ross model by differentiating a conditional transform. It defines a function as the conditional expectation of the exponential of minus λ times the future rate. This…
The document tests whether a stock, a put, and a call with different strikes create an arbitrage opportunity. The example gives a stock price of USD 30, a put struck at USD 28 priced at USD 1, a call struck at USD 29 priced at USD 8, and a one-year risk-free…
The document explains why the difference between two correlated Brownian shocks can be represented by a single Brownian motion when pricing an exchange option. The payoff can be rewritten using the ratio of the two stock prices, and Itô’s lemma gives that…
The document explains why a farther-dated option can show lower implied volatility than a near-term option while still having a higher premium. It describes an inverted volatility term structure: near-term implied volatility is elevated, while the market…
The document considers adding vanilla interest rate swaps to an existing Monte Carlo VaR process for foreign exchange and commodities. The proposed simplified method estimates volatility and correlation from daily changes in par swap rates, simulates rate…
The document presents asymptotic boundary conditions used when numerically solving generalized Black–Scholes models on a truncated price domain. At the low-price boundary, the call value tends to zero. At the high-price boundary, it approaches the discounted…
The document concerns a covariance matrix used in a Gaussian construction for stratified Monte Carlo sampling, motivated by simulating a barrier option under Black–Scholes dynamics. The answer identifies a normalization error: the stated result assumes the…
The document considers how to assess a proposed interest-rate cap volatility surface for arbitrage. A cap consists of caplets, and the response recommends stripping caplet values from cap prices across maturities. In a simplified setting with a flat yield…
The document asks how to find the fair value of a three-month futures contract on a two-stock index when each stock pays a dividend before expiry. The answer gives the cost-of-carry approach: express financing costs and expected dividends in index points,…
The document asks how to estimate future values for a portfolio containing a stock, a long-term coupon bond, and a European call option. It provides example daily inputs for the stock price, required yield, volatility, and short-term interest rate, and asks…
The document works through a derivation of the price dynamics of a zero-coupon bond in the Ho–Lee short-rate model. The question starts from the model's short-rate process and a conditional expectation representation of the bond price, then applies Itô's…
The document clarifies why geometric Brownian motion (GBM) produces nonnegative, lognormally distributed prices, and why it is not exactly equivalent to multiplying price by a sequence of normally distributed simple returns. Exponentiating Brownian motion…
The document identifies a modeling connection between interest-rate options and volatility options: both markets have term structures. It points to a variance-curve model in which variance across maturities evolves as a martingale driven by Brownian shocks,…
The document discusses whether equity option prices can reveal the stock lending rate faced by a market maker hedging short positions. Put-call parity links a matched call and put to the underlying, financing, dividends, and borrow costs, so deviations from…
This document explains the convention used by QuantLib's zero-yield structure when it converts a zero rate into a discount factor. The implementation applies the exponential discount formula, which corresponds to continuous compounding. The question is…
The document interprets a formula that extracts an annual longevity risk premium by comparing discounted risk-neutral and physical expectations of a longevity index across payment dates. The risk-neutral expectation is described as inferred from traded…
The document explains a parity relationship for asset-or-nothing binary options. The call pays the underlying asset at maturity when its price is above the strike, while the put contributes a negative asset payoff when the price is below the strike.…
The note asks how to take a directional view on volatility while limiting exposure to the underlying’s direction. It points out that straddles, strangles, and iron condors respond to volatility but also carry exposure to other option risk factors, including…
The note explains how a stochastic volatility model distinguishes physical-measure dynamics from risk-neutral dynamics used for option pricing. It describes a volatility risk premium that shifts the variance process’s drift, while the stock drift is adjusted…
The discussion asks whether U.S. Treasury cash flows should be discounted using SOFR or a security-specific repo curve. One answer emphasizes that Treasuries are liquid and trade at observable market prices, so practitioners generally do not need to infer…
The document clarifies how FX spot delta relates to option delta and settlement timing, using GBP/USD and USD/CHF examples. Its answer explains that spot itself has delta one by definition: its value changes one-for-one with the spot rate. FX option delta…
The document asks whether Black–Scholes pricing remains relevant for an over-the-counter call when the option buyer cannot delta-hedge. The responses distinguish the venue where an option trades from whether its underlying asset is liquid: the accepted…