Methodologies

Derivatives Methodology

8 min

Derivatives Methodology

Overview

This document outlines the methodology implemented for pricing and risk assessment of derivative instruments in the MantaRisk platform.

Supported Derivative Types

The platform currently supports the following derivative types:

  • Vanilla options (calls and puts)

Exercise Types

The following exercise styles are supported:

  • European Exercise: Can only be exercised at maturity
  • American Exercise: Can be exercised at any time up to maturity

Pricing Methodology

The derivatives module uses the Black-Scholes model for pricing options. The implementation supports European and American options.

Key Parameters for Option Pricing

  • Underlying Price: Current price of the underlying asset
  • Strike Price: The price at which the option holder can buy (call) or sell (put) the underlying asset
  • Maturity Date: The date when the option expires
  • Volatility: The volatility of the underlying asset, used to estimate price fluctuations
  • Risk-Free Rate: The theoretical rate of return of an investment with zero risk

Scenario Generation

The platform generates price scenarios for derivatives based on the underlying asset's price scenarios. This is done through the following process:

  1. For each scenario of the underlying asset price, the corresponding derivative price is calculated using the Black-Scholes model
  2. Returns are calculated based on these price scenarios
  3. Currency conversion is applied if the derivative is denominated in a different currency than the base currency

This approach allows for consistent risk assessment across different types of instruments in a portfolio.

Risk Assessment

Risk metrics for derivatives are calculated based on the generated price scenarios. The platform uses the same risk assessment framework for derivatives as for other instruments, ensuring consistency in risk evaluation across the portfolio.

References

The implementation is based on established financial models and methodologies:

  • Black-Scholes model for option pricing
  • Barone-Adesi and Whaley approximation for American options
  • Scenario-based risk assessment as described in this paper