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.
8,116 documents
The document addresses calibrating the SABR parameters rho and nu when beta and alpha are fixed. The target is to minimize the sum of squared differences between observed market volatilities and model-implied volatilities. The questioner’s R call supplies…
The document compares approaches for calculating American-option implied volatility repeatedly in a production setting. It discusses closed-form approximations, including Barone-Adesi–Whaley, Roll-Geske-Whaley, Ju–Zhong, and Bjerksund–Stensland, while…
The document asks how today’s implied volatility for a forward-start call relates to the implied volatility observed when the option begins. The call’s strike is set as a multiple of the stock price at a future start date, and its payoff depends on the stock…
The document considers the no-arbitrage relationship between prices of call options on the same stock with the same expiry but different strikes. A lower-strike call should be worth at least as much as a higher-strike call, since its payoff is never smaller.…
The document explains why an autocall with a linear payoff can still have volatility exposure. The payment date is determined by whether a second index crosses a barrier: with low volatility it may never cross, while higher volatility increases the chance of…
The document raises a pricing question about crypto options: whether a reported discount rate around 10% is unusually high, and whether observed option quotes imply a rate near 12% when checked against put-call parity. It presents bid and ask snapshots for…
The document contrasts two mathematical characterizations of the perpetual American put discussed in a stochastic calculus text. The analytical treatment describes the option value through partial differential inequalities and linear complementary…
The document proposes a staged way to learn Monte Carlo methods, while emphasizing that the right material depends on the problem. It starts with simple simulations such as dice, coin tosses, estimating areas, and pricing a vanilla option. It recommends…
The document concerns Monte Carlo valuation of a barrier option when the underlying follows a jump-diffusion process. The question reports a simulated value that differs from the cited paper and jump probabilities that sometimes fall outside the valid…
The document diagnoses a QuantLib error raised while building a Black variance surface from option implied volatilities. The reported validation requires expiry dates to be unique and arranged in chronological order. In the supplied schedule, one-year expiry…
For standard European calls and puts, the document explains why a higher ask price usually implies a higher ask implied volatility than bid implied volatility. The key link is that, holding other inputs constant, these option prices increase as volatility…
The document asks whether a derivative can have a payoff that is quadratic in the underlying asset’s price, including a version floored at zero. The responses explain that a bespoke payoff could be requested from a bank, while emphasizing that the buyer…
The document asks whether European call prices at a single maturity uniquely determine a time-independent local-volatility function, given that Dupire’s formula ordinarily uses a surface across maturities. One answer cites a result establishing a unique…
The document distinguishes the risk-reversal trading strategy from the market convention used to quote a risk reversal on a volatility surface. A risk reversal combines a call and a put, often selected at specified delta points, while the quotation…
The document compares the spot sensitivities of American and European calls when the stock pays a single dividend before expiry and interest rates are zero. It represents the American call as the expected value of the better choice at the dividend date:…
The contract pays the positive part of the difference between the stock price at an earlier date and its price at maturity. At the earlier date, the strike is known, so the claim becomes an ordinary European put with a strike equal to that observed stock…
A binary option pays a fixed amount when the underlying finishes on one side of its strike, so its value is tied to the risk-neutral probability of that event, discounted for interest rates. Under a lognormal Black–Scholes model, increasing volatility can…
The document addresses a kink that can appear when combining call and put implied volatilities to build a fixed-tenor smile from American SPY options. The response recommends deriving one forward price for the option maturity from dividends and the market…
The response discusses how implied volatility differences between expiration dates can affect calendar spread pricing. It suggests that when front-month implied volatility is below back-month volatility, calendars may have broader profit ranges and higher…
A replicating portfolio matches an option’s payoff only under idealized assumptions, including continuous trading, no transaction costs, unlimited divisibility, and known constant volatility. Actual markets violate these conditions, so an option combined…
Whether an option has a closed-form price depends on both its payoff and the assumed dynamics of the underlying asset. Some European vanilla options have tractable formulas under certain models, while other combinations of payoff and dynamics do not. The…
The document shows how a payer swaption can be expressed as an option on a coupon bond. It starts from a fixed-for-floating swap with reset and payment dates, writes its value as the difference between a floating leg and a fixed leg, and uses the forward…
The document addresses a common sign confusion in put-call parity: when constructing a synthetic forward by buying a call and selling a put at the same strike, the put’s premium is not itself negative. Option premiums are positive prices by definition;…
The document clarifies the probability terms in the Heston call pricing formula. It decomposes the call payoff into two expectations, then uses a change of numéraire to express the price through probabilities under the risk neutral measure and a stock…