options-pricing Checked

[STUB] Options pricing models including Black-Scholes, binomial trees, Monte Carlo, implied volatility surfaces, and Greeks for crypto options

Options Pricing

> **Status: STUB** — This skill provides a basic Black-Scholes implementation and an overview of planned capabilities. Full implementation is awaiting community contribution.

Options pricing is the quantitative foundation of derivatives trading. For crypto markets, options on BTC and ETH trade actively on Deribit, Lyra, and Aevo, while Solana options are emerging on platforms like Zeta Markets and PsyOptions. Understanding pricing models, implied volatility surfaces, and Greeks is essential for hedging, volatility trading, and constructing structured products.

This skill is informational and analytical only. It does not provide financial advice or trading recommendations.

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[STUB] Options pricing models including Black-Scholes, binomial trees, Monte Carlo, implied volatility surfaces, and Greeks for crypto options

Options Pricing

> **Status: STUB** — This skill provides a basic Black-Scholes implementation and an overview of planned capabilities. Full implementation is awaiting community contribution.

Options pricing is the quantitative foundation of derivatives trading. For crypto markets, options on BTC and ETH trade actively on Deribit, Lyra, and Aevo, while Solana options are emerging on platforms like Zeta Markets and PsyOptions. Understanding pricing models, implied volatility surfaces, and Greeks is essential for hedging, volatility trading, and constructing structured products.

This skill is informational and analytical only. It does not provide financial advice or trading recommendations.

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Current Capabilities

This stub includes a working Black-Scholes calculator with Greeks computation and a basic implied volatility solver. See scripts/black_scholes.py for the implementation.

import math
from scipy.stats import norm

def black_scholes_call(S: float, K: float, T: float, r: float, sigma: float) -> float:
    """Price a European call option using Black-Scholes.

    Args:
        S: Current underlying price.
        K: Strike price.
        T: Time to expiration in years.
        r: Risk-free rate (annualized).
        sigma: Volatility (annualized).

    Returns:
        Theoretical call option price.
    """
    d1 = (math.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * math.sqrt(T))
    d2 = d1 - sigma * math.sqrt(T)
    return S * norm.cdf(d1) - K * math.exp(-r * T) * norm.cdf(d2)

Run the demo:

python scripts/black_scholes.py --demo

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Planned Capabilities

When fully implemented, this skill will cover:

### Pricing Models

| Model | Option Style | Use Case |

|-------|-------------|----------|

| Black-Scholes | European | Vanilla calls/puts, quick Greeks |

| Binomial Tree | American | Early exercise, dividend-paying assets |

| Monte Carlo | Exotic | Path-dependent, barrier, Asian options |

| Black-76 | Futures | Futures options on crypto perpetuals |

### Greeks

| Greek | Measures | Formula Basis |

|-------|----------|---------------|

| Delta | Price sensitivity to underlying | dC/dS |

| Gamma | Delta sensitivity to underlying | d²C/dS² |

| Theta | Time decay per day | dC/dT |

| Vega | Sensitivity to volatility | dC/dσ |

| Rho | Sensitivity to interest rates | dC/dr |

### Implied Volatility

• Newton-Raphson and bisection IV solvers
• Volatility smile and skew analysis
• IV surface construction (strike x expiry)
• IV term structure analysis
• Vol-of-vol estimation

### Crypto Options Platforms