GARCH option pricing

The theory of european option pricing in the GARCH framework has been developed in recent years by the work of

Duan (The GARCH option pricing model)
Heston/Nandi (A closed-form GARCH option valuation model).

The work of Heston/Nandi includes a closed-form option pricing formula for a spot asset whose variance follows a GARCH process.

Unfortunately, an efficient method for computing option prices in this Heston/Nandi framework was lacking, since the price calculation was executed by using methods of numerical integration for evaluation of integrals.

The paper Fast analytic option valuation with GARCH proposes an option price calculation based on cumulants.

This project implements both methods (numerical integration and cumulants) in C++.

Three model parameter sets are available

Alpha Stress Test Szenario (ASTS)
omega = 0.00025, alpha = 0.001, beta = 0.4, gamma* = 10, r = 0.0002
High Volatility Persistence Szenario (HVPS)
omega = 0.00000025, alpha = 0.000001, beta = 0.5, gamma* = 700, r = 0.0002
Maximum Likelihood Estimation Szenario (MLES)
omega = 0.000000451, alpha = 0.00000124, beta = 0.73, gamma* = 445.93, r = 0.05/365

Usage:

garch.exe <T> <scenario>

where T is days until expiry and scenario is one of ASTS, HVPS or MLES.

Default is 100 days and ASTS.

For example, printing speed and accuracy for 250 days and MLES:

garch.exe 250 MLES

Download executable and source code
Browse source code