4th International Conference on Principles and Practices ... - MADOC

Derivative
Contract
Component
Repository
Removing the constant
lower bound
Silver price as
lower bound
Figure 2: Starting from a simple contract already available in the contract repository, the constant lower
bound is substituted by a protection whose value is the silver market price. Consistent states are indicated
by a green background, whereas transitional states are signaled by a yellow background color.
applicability of hierarchical description techniques. Com-
DeCo uses a domain-specific adaptation that models derivative
contracts as a special variant: Hierarchical Active
Documents (see Figure 2). Being hierarchical, a XML
based representation is easily derived (see Figure 3). Besides
being an alternative to a pure visual composition process,
a XML-based representation allows for further manipulation
operations by third parties (e.g. XSL or XML Schema
tools) and is an excellent foundation for an open, i.e. nonproprietary,
design workflow.
4.1 Building blocks
ComDeCo provides a set of typical financial components
that can be used to create almost arbitrary contracts. The
derivative component is one of those core entities. Having a
sell and an acquire component as its children, the simplest of
all derivative contracts is represented by a virtual sale and a
virtual purchase, whose execution conditions are represented
by appropriate components. By performing composition operations
that are based on the decorator pattern, the user
has the choice to either augment already available contracts
with desired properties or start from scratch. The initial
contract in Figure 3 consists of a derivative component decorated
with an upper bound performance participation limit
property represented by the encapsulating cap component.
The flexibility of an Active Document system stems
from its variable component repository, which is filled according
to specific user requirements. Adding components
to the repository makes all other parts of the system, e.g.
composition and valuation facilities, automatically aware of
the supplemental functionality.
4.2 Separation of concerns
In case of fair price calculations, there is at least one additional
Active Document that is necessary to perform
proper contract valuation: the market specification. Observable
components of the derivative contract express dependencies
to other (potentially external) components refered
to by their model parameter. These hooks 6 are bound
by partially merging the derivative contract and its corre-
6 The concept of a hook resembles similarities to the notions
and techniques of [11].
sponding market specification (see Figure 3). Separation
of these two aspects introduces an additional degree of freedom:
Having the opportunity to choose from a set of market
specifications, the financial engineer is able to run through
several case scenarios just by combining appropriate documents.
After having designed an individual contract (see
Section 6.1), a potential customer is able to get an impression
of a derivative’s performance in different scenarios, e.g.
bullish or bearish markets.
4.3 Component-oriented pricing engine
When determining the fair price of a given derivative contract,
available common mathematical approaches may be
categorised into three groups
Closed-form solutions require limited computational resources,
but the set of available formulae is restricted
and can by no means keep pace with the permanently
growing plethora of derivative contracts.
Monte Carlo simulation provides an almost general-purpose,
but computationally intensive solution. Unfortunately,
pricing american style derivatives is not straightforward.
Tree-based algorithms are able to price european as well
as american style derivatives and usually show up fast
convergence. However, the memory footprint may impose
limitations on usage in multi-dimensional settings.
As the ComDeCo framework allows for the construction of
arbitrary contracts, a categorisation scheme supporting the
determination of the best-fitting approach has to be developed.
None of the above-mentioned standard approaches is
a panacea, as applicability depends on certain properties of
the derivative contract to be valuated. For that reason, the
pricing engine has to obey a strategy that takes closed-form
solutions into account whenever possible, uses tree-based
algorithms as the default approach and offers Monte Carlo
simulation on demand.
Although being a de facto market standard, the Black
& Scholes model [12] reaches its limits in case of complex
derivative contracts. To cope with the flexibility imposed
156