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 discusses foresight, or look-ahead, bias in least-squares Monte Carlo valuation of American options. In the Longstaff–Schwartz approach, regression on the same simulated paths used for valuation can overfit continuation values and make estimated…
The document considers how to estimate Treasury yields beyond the longest available bond maturities, using a theoretical 40- or 50-year yield as an example. The questioner reports that Nelson–Siegel and Svensson curve fits gave unsatisfactory, unstable…
The question challenges the idea that an American option should always be worth more than its intrinsic value, making sale preferable to early exercise. The key correction is that at an optimal exercise point, the option’s value equals its exercise value.…
The discussion considers how to build an equity volatility surface when American and European options are listed on the same underlying and provide separate implied volatility observations at each maturity. One practical preference is to use European options…
This discussion examines why MATLAB’s actual/actual date-to-time calculation may not match QuantLib’s actual/actual day-count variants when code is ported between the two platforms. The example compares a period spanning 2006 to 2036 and reports different…
The document explains how to infer implied correlation from an observed Margrabe option price. Given the two assets’ volatilities, prices, yields, and time to maturity, correlation determines the option’s relative volatility. The response notes that this…
The document clarifies the proof that the first time an American derivative’s value equals its payoff is an optimal exercise time in a finite-period binomial model. The price process is constructed as the Snell envelope: at each node it is the greater of…
The document describes how to identify the underlying asset, strike, and maturity of French traded warrants when only their ISINs are available. Its suggested workflow uses Bloomberg: look up the ISIN in the terminal to open the security record, then view…
The discussion examines why Black–Scholes can produce implausibly high values for very long-dated options. One explanation is that the model holds interest rates and volatility constant, even though both can change over time. The more detailed argument…
The discussion distinguishes terminology by context. In bond and swap trading, the terms notional and nominal may refer to the same reference amount used to calculate contractual cash flows. In macroeconomics, nominal commonly describes a rate or value…
The discussion explains why the risk-free rate can be expressed as the reciprocal of the summed prices of state-contingent claims. Each claim pays one unit of currency in one possible state and nothing in the others. Buying a claim for every state therefore…
The document explains why derivative pricing in a risk-neutral framework discounts expected future payoffs at the risk-free rate. Its central idea is that changing from real-world probabilities to risk-neutral probabilities accounts for risk premia in the…
The document derives the dynamics of a stock forward when the underlying stock pays a constant dividend yield. Starting from a geometric Brownian motion for the stock, it states the forward price as the spot price adjusted by the financing and dividend…
The document asks whether the Black–Scholes risk-neutral probability that a call expires in the money, expressed using N(d2), can be adapted to estimate the real-world probability. The reply says this is possible if the asset's real-world drift is known. The…
The document examines how to relate options written on reciprocal currency pairs. It asks whether the delta of a USDJPY put corresponds to the delta of a JPYUSD call at the reciprocal strike and with the same maturity. The answer derives the terminal payoff…
The document asks how to derive an option-pricing probability expression in Gatheral’s framework by directly performing a complex inverse Fourier integral. It compares that route with the Gil-Pelaez inversion theorem and focuses on the boundary condition at…
The document considers estimating a riskless interest rate from spot and forward or futures prices using the relationship between the forward price, spot price, rate, and time to maturity. Rearranging that relationship gives an implied rate from the…
The discussion considers whether a constant displacement can adapt a standard LIBOR market model to negative interest rates. It proposes applying the shift to the forward rates used in the diffusion and drift numerators, while the accepted response clarifies…
The discussion clarifies the difference between a cross-currency swap and a cross-currency basis swap, then illustrates how a basis swap can convert a foreign-currency bond exposure into a USD funding comparison. In the example, an investor exchanges USD…
The document raises whether the price of a call or put butterfly can indicate the likelihood that a stock will finish near the butterfly’s middle strike. It questions a casual explanation based on at-the-money option delta and asks how to construct an…
A non-deliverable interest rate swap exchanges fixed and floating interest cash flows linked to one local currency, but settles the net amount in a deliverable currency such as USD or EUR. The example describes paying a fixed local-currency rate and…
The discussion derives the distribution of a future asset price under geometric Brownian motion and clarifies the relationship between the distributions of log price and log return. Integrating the Black–Scholes dynamics from the current time to maturity…
The discussion asks whether a payer Bermudan swaption’s chance of exercise at its first exercise date rises or falls as interest rates increase. Its answer gives an intuitive example: for a payer option with a fixed strike and a flat curve, low swap rates…
The document explains a payoff decomposition for a secured barrier call. The product pays the positive difference between the terminal stock price and the strike if the upper barrier is never reached; if the stock reaches that barrier before expiration, it…