# Implied Volatility Calculator AI Agent Connect

> Deterministic engine for calculating implied volatility via Newton-Raphson iteration.

## Overview
- **Category:** finance
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_18Sl7GkhAkt4nPkwLvoXovlmCsQrnscu7xj1l3ox/ai-agent-connect
- **Tags:** options, black-scholes, volatility, quantitative-finance, newton-raphson

## Description

This MCP server provides high-precision tools for quantitative finance. It uses the Newton-Raphson method to solve for implied volatility by iteratively adjusting estimates based on the Black-Scholes model and Vega. Users can calculate the implied volatility for a single option using `calculate_single_iv`, map the volatility smile across multiple strikes with `calculate_volatility_smile`, or analyze the volatility term structure across different expirations using `calculate_volatility_term_structure`.

## Tools

### calculate_single_iv
Calculates the implied volatility for a single European option using the Newton-Raphson method

### calculate_volatility_smile
Generates a set of implied volatilities across multiple strike prices to visualize the volatility smile

### calculate_volatility_term_structure
Generates a set of implied volatilities across different expiration dates to visualize the volatility term structure

## Prompt Examples

**Prompt:** 
```
What is the implied volatility for a call option with a market price of 5.0, underlying price of 100.0, strike of 105.0, 0.5 years to expiration, and a 5% risk-free rate?
```

**Response:** 
```
The implied volatility for this option is 0.2456.
```

**Prompt:** 
```
Calculate the volatility smile for an underlying price of 100.0, 1 year to expiration, 5% risk-free rate, for call options with strikes [90, 100, 110] and market prices [15.0, 7.0, 3.0].
```

**Response:** 
```
The volatility smile is: strike 90: 0.285, strike 100: 0.221, strike 110: 0.184.
```

**Prompt:** 
```
Show me the volatility term structure for a strike of 100.0, underlying price 100.0, 5% risk-free rate, for expirations of 0.2, 0.5, and 1.0 years with market prices [4.5, 6.0, 8.5].
```

**Response:** 
```
The volatility term structure is: 0.2 years: 0.21, 0.5 years: 0.23, 1.0 years: 0.25.
```

## Frequently Asked Questions

**What method is used to find implied volatility?**
The engine uses the Newton-Raphson iteration method, which utilizes Vega to converge on the volatility that matches the observed market price.

**Can I visualize the volatility smile?**
Yes, you can use the `calculate_volatility_smile` tool to generate a set of implied volatilities across various strike prices.

**What happens if the calculation does not converge?**
If the Newton-Raphson algorithm fails to reach the required precision within 100 iterations, the tool will flag a non-convergence error.