Payoff scripting

Write a structured product's terms as a short script (observation dates, barriers, memory coupons, autocalls, issuer calls and holder exercise) and value it by Monte Carlo on up to five correlated assets under Black-Scholes, local volatility or Heston, with Longstaff-Schwartz for early redemption. Templates for Phoenix autocallables, reverse convertibles, callable notes, twin-wins, Napoleons and shark fins.

Inputs

Start fromPayoff script (pays per 1 of notional)S(t), perf(t), worst(t), best(t), pay(amount, t), stop(), call(price, t), exercise(amount, t), df(t), yf(t1, t2); loop over dates; T is the last date.ParametersNames the script reads, separated by semicolons.

Currency

Notional

Maturityy

Observation datesModel

Correlation ρ

Paths

Random seed

Curve

Curve: flat rate% cc

Asset (as the script names it)	Spot	Vol %	Dividend %

Results

Every input and result then gets a + calc button.

Explain this result

Get a plain-English reading of the numbers above and what drives them.

Preview: rule-based reading. AI-assisted explanations run on the analytics core.

Methodology

Conventions

The script runs once over all Monte Carlo paths at the same time: an if on a path condition runs each branch on the paths it holds for.
pay(amount, t) pays per 1 of notional on an observation date; stop() ends the trade on those paths.
call(price, t) and exercise(amount, t) are valued backward by Longstaff-Schwartz regression on the assets' performances.
Black-Scholes paths take exact lognormal steps between dates; local vol and Heston paths take weekly steps.

References

Longstaff and Schwartz (2001)
Glasserman, Monte Carlo Methods in Financial Engineering

Formulas

Assets: dSᵢ/Sᵢ = (r − qᵢ)dt + σᵢ dWᵢ, dWᵢ dWⱼ = ρᵢⱼ dt
Value: V = N · E[Σ D(tᵢ) CFᵢ]