The Spectral_Barriers command prices barrier-style payoff structures using a
log-space spectral expansion. The model compares standard Black-Scholes vanilla option
values with several knock-out and barrier-sensitive contracts.
Barrier products are common in structured notes, derivatives trading, prediction-style payoffs, crypto-linked products, and digital event contracts. Many advertised products are built around a simple idea: the payoff depends not only on where the price ends, but whether it crosses a specified level along the way.
This command is for educational analysis. It helps show how spot price, strike, volatility, time, interest rates, yield, and upper or lower barriers affect the value of path-dependent payoffs.
Spectral_Barriers
The command opens an editable assumptions panel. After entering assumptions, press
Calc to refresh the valuation table.
Spot — current asset priceStrike — option strike priceLower Barrier — lower knock-out boundaryUpper Barrier — upper knock-out boundaryRate — risk-free interest rateYield — dividend or carry yieldVolatility — annualized volatilityYears — time to maturityCash — digital payoff amountThe result panel reports the assumptions, vanilla Black-Scholes call and put values, and a set of spectral barrier values. These may include double knock-out calls and puts, double no-touch values, digital knock-out payoffs, and asset-or-nothing knock-out payoffs.
Barrier values are highly sensitive to volatility and distance from the barriers. A contract that looks attractive because of a high advertised payoff may have a low fair value if the probability of touching the barrier is large.
This is especially relevant for products marketed around phrases such as “no-touch,” “knock-out,” “range-bound,” “digital payout,” or “event barrier.” The spectral method gives a disciplined way to value those payoff shapes rather than looking only at the headline payout.