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 considers valuing a European call when its underlying asset cannot be traded, so the continuous-trading replication assumptions behind Black–Scholes are unavailable. Suggested inputs and approaches include estimating the underlying’s value from…
The document contrasts implied volatility from near-expiry, at-the-money S&P 500 options with the VIX. The response characterizes VIX as a discrete approximation to the square root of a theoretical fair variance swap strike, with its calculation window set…
The document discusses where to obtain constant maturity swap (CMS) swap prices for comparing theoretical valuations with market quotes. One response points to swap-rate ticker conventions for different maturities, while another suggests looking for spread…
The document describes how a simulated short rate can be used to obtain bond prices and the term structure of interest rates. Under the risk-neutral measure, a zero-coupon bond price is the conditional expected value of discounting one unit of payment by the…
The document explains why Bloomberg’s FXFA and SWPM screens can show different rates and basis figures for a EUR/USD cross-currency swap. FXFA uses floating EUR and USD yields, while the example SWPM setup uses two fixed rates, so the coupon rates are not…
The document considers a long call calendar spread when the underlying rises above the shared strike by the short option's expiration. It asks whether the spread necessarily loses its entire opening debit, using an example in which the near-dated call is…
The discussion addresses whether negative interbank rates should be floored at zero when valuing FX forwards or futures. The answer argues that market participants can lend and borrow at negative rates, so valuations must reflect those rates: replacing them…
The discussion explains how to interpret and scale Greeks for a GBP/USD call option. It emphasizes that the currency pair’s quotation and the chosen risk convention affect the sign and currency value of delta. A trader described as hedged by 50 deltas holds…
The document explains why a floating-rate bond is commonly valued near par just after a coupon reset or payment. It starts with a loan whose interest rate sets both its coupon and its discount rate: the discounted repayment equals principal, leaving the loan…
The document addresses numerical instability when a finite-difference method prices a call option using its terminal payoff, which has a kink at the strike. Near that point, a coarse grid can make a central approximation to the second derivative very large,…
The document asks how to compute higher moments of the time integral of an exponential Brownian motion, a quantity relevant to arithmetic Asian options. It first gives the expected value, then presents a general expression for the m-th moment using divided…
The document describes a QuantLib calibration problem for the G2++ interest-rate model in a negative-rate environment. The reported error arises because the cap helper uses shifted lognormal volatility with zero displacement, which requires the strike plus…
The document explains when European calls and puts with the same strike and maturity should have matching implied volatilities. Under put-call parity, their implied volatilities coincide at the at-the-money forward strike when the other pricing inputs are…
The document considers whether two cointegrated price series can be combined into a stationary spread and modeled with an Ornstein-Uhlenbeck process. The proposed workflow estimates a hedge coefficient through regression, constructs the residual spread, and…
The document distinguishes securities by the assets behind them and by how investors receive repayment. Asset-backed securities represent claims on pools of non-mortgage loans, such as auto or credit-card debt, while mortgage-backed securities represent…
The document asks whether a forward price for a financial product can be expressed as its current price divided by the price of a zero-coupon bond maturing at the settlement date. The proposed argument uses a conditional expectation under the…
The document shows how to price a payoff of the form (S_T f(S_T))^+ by changing from the money-market numeraire to the stock numeraire. Starting with a risk-neutral geometric Brownian motion, it defines the new measure using the discounted stock as the…
The document relates Merton’s structural credit model to European option payoffs. It models company asset value as a geometric Brownian motion and treats equity at maturity as a call on firm value with debt face value as the strike. Risky debt is represented…
The document explains the expiration profit and loss bounds for a collar, consisting of long stock, a long put, and a short call at a higher strike. At expiration, the call caps the position’s upside, while the put limits its downside. The stated maximum…
The document considers an option that pays the difference between two stock prices at maturity only if the first stock stays above the second throughout the option’s life. It presents a model-free replication argument: hold one share of the first stock and…
The answer demonstrates how a fixed-rate bond can be represented in QuantLib with an evaluation date, payment schedule, day-count convention, face amount, and coupon rates. The resulting cash-flow list contains coupon payments and the final principal…
The question concerns building an inflation-swap curve with QuantLib rate helpers and encountering an error because multiple instruments share a pillar date. The practical diagnostic is to inspect each helper’s pillar date, which is the date used as a curve…
The document describes a proposed product paying a notional amount times the change in the spread between 30-year and 10-year Treasury yields. The response frames the hedge as exposure to two future yields, corresponding to the 10-year and 30-year points on…
The document examines how to interpret the stock and money-market components of a portfolio formed by holding a call and discounted cash equal to the strike. Under Black–Scholes assumptions, it combines the call price with the present value of the strike and…