Chapter 18. Portfolio Valuation

Price is what you pay. Value is what you get.

— Warren Buffet

By now, the whole approach for building the DX derivatives analytics library — and its

associated benefits — should be rather clear. By strictly relying on Monte Carlo

simulation as the only numerical method, we accomplish an almost complete

modularization of the analytics library:

Discounting

The relevant risk-neutral discounting is taken care of by an instance of the

constant_short_rate class.

Relevant data

Relevant data, parameters, and other input are stored in (several) instances of the

market_environment class.

Simulation objects

Relevant risk factors (underlyings) are modeled as instances of one of three

simulation classes:

geometric_brownian_motion

jump_diffusion

square_root_diffusion

Valuation objects

Options and derivatives to be valued are modeled as instances of one of two

valuation classes:

valuation_mcs_european

valuation_mcs_american

One last step is missing: the valuation of possibly complex portfolios of options and

derivatives. To this end, we require the following:

Nonredundancy

Every risk factor (underlying) is modeled only once and potentially used by multiple

valuation objects.

Correlations

Correlations between risk factors have to be accounted for.

Positions

An options position, for example, can consist of certain multiples of an options

contract.