How does Shoals price options?

Shoals uses a 128-step Cox-Ross-Rubinstein (CRR) binomial tree with Broadie-Detemple smoothing for American option pricing. The tree incorporates term-structure volatility, moneyness skew, and discrete dividend adjustments. Stock prices follow geometric Brownian motion with optional Merton jump diffusion and Heston stochastic volatility.

What are the option Greeks?

The Greeks measure an option's sensitivity to different factors. Delta measures price sensitivity to the underlying stock. Gamma measures the rate of change of delta. Theta measures time decay. Vega measures sensitivity to volatility changes. Rho measures sensitivity to interest rate changes. Shoals displays all five Greeks in real time across a 21-strike, eight-expiry options chain.

What is the Heston stochastic volatility model?

The Heston model treats volatility as a random process that mean-reverts over time, rather than being constant as in Black-Scholes. This produces realistic volatility clustering (periods of high and low volatility) and a non-flat implied volatility surface. Shoals implements Heston with configurable mean reversion speed, long-run variance, and volatility of volatility.

What market events does Shoals simulate?

The offline registry currently contains roughly 350 curated events across Federal Reserve, macro, market, firm, political, investigation, media, HCN, tip, trait, and interjection domains. Events may change price-process parameters, world state, institutional standing, followup eligibility, or player choices; decision events are queued as popups.

How do I build a multi-leg options strategy in Shoals?

Open the Strategy tab, select an expiry, and click stock, bond, VXHCN, call, or put cells to add long legs; use sell mode or right-click for short legs. The combined view updates payoff, Greek overlays, max profit or loss, and break-even estimates.

Does Shoals collect any personal data?

Offline modes keep simulation state in the browser. Dynamic (LLM) mode stores the supplied Anthropic key in browser local storage and sends generated market/world context directly to Anthropic's API; the portfolio site may also record aggregate page-view metadata separately.

Is Shoals free and open source?

Yes. Shoals' source is available on GitHub under the GNU Affero General Public License v3.0.

How does Shoals build its pricing-volatility surface?

Shoals derives an effective term volatility from the Heston variance state, mean reversion, and volatility of volatility. It then applies first-order correlation skew plus a curvature term by log-moneyness before pricing each contract. This is a constructed pricing surface, not an inversion of observed market option prices.

Shoals — Options Trading and Politics Simulator

What is Shoals?

Shoals is an options trading simulator that models derivatives pricing under realistic market conditions. Stock prices evolve with stochastic volatility and jump diffusion while a narrative event engine introduces market shocks, connecting abstract pricing theory to real-world dynamics.

Pricing Models

The underlying stock follows geometric Brownian motion with optional Merton jump diffusion (sudden large moves) and Heston stochastic volatility (time-varying vol that mean-reverts). Interest rates follow a Vasicek process. American options are priced on a 128-step CRR binomial tree with term-structure volatility and moneyness skew adjustments.

Strategy Builder

The multi-leg strategy builder supports spreads, straddles, strangles, condors, butterflies, and custom combinations. Each strategy displays a payoff diagram, Greek overlays showing how sensitivity changes across strikes, maximum profit and loss, and break-even points. A margin system tracks portfolio-level exposure and buying power.

Market Events

Roughly 350 curated events span Federal Reserve, macro, market, firm, political, investigation, media, HCN, tip, trait, and interjection domains. Depending on the event, they can change process parameters, world state, institutional standing, followup eligibility, or player choices; decision events are queued as popups.

Price Impact

Shoals records decaying cumulative volume separately for stock, bonds, VXHCN futures, and each option contract. Square-root fill costs and valuation overlays model execution impact; option delta changes generate market-maker stock hedges, and very large gross exposure can add temporary capped parameter overlays.

Narrative Framework

The simulation is set at Meridian Capital during the Barron administration. The event registry combines Poisson arrivals, scheduled pulses, portfolio triggers, one-shot conditions, and followup chains. Twelve permanent convictions, six dynamic reputation tags, and six institutional-standing dimensions shape later eligibility and consequences, culminating in one of six ending types with a five-page adaptive epilogue.

Accessibility

Shoals provides keyboard shortcuts, light and dark themes, labeled controls, numerical market and portfolio readouts, and focus trapping for narrative popups and the epilogue. The live candlestick chart, sparklines, typewriter treatment, and other animated feedback create continuous motion.

See also: Geon for particle physics, Cyano for cellular metabolism, Gerry for electoral fairness.

Learning Outcomes

After using Shoals, students should be able to: explain why American exercise is handled with a binomial tree; interpret delta, gamma, theta, vega, and rho for single options and multi-leg positions; distinguish spot volatility, term volatility, skew, and VXHCN futures; connect margin and execution impact to position sizing; and trace how market events and institutional decisions propagate into portfolio value.

Prerequisites

Basic probability and statistics (expected value, standard deviation, normal distribution). Familiarity with compound interest and present value. No prior knowledge of options or derivatives is required.

Volatility Surface

Shoals computes a contract-specific pricing volatility rather than plotting or reverse-engineering a market-implied surface. The Heston variance state and mean reversion produce the term component; price/variance correlation and volatility of volatility add moneyness skew and curvature. Events can shift those underlying parameters, after which the configured decay and mean-reversion mechanisms act on them.

References

F. Black and M. Scholes, "The Pricing of Options and Corporate Liabilities" (1973). S. L. Heston, "A Closed-Form Solution for Options with Stochastic Volatility" (1993). J. C. Cox, S. A. Ross, and M. Rubinstein, "Option pricing: A simplified approach" (1979).