Derivative Pricing – an Overview
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The Nematrian website provides users with a range of
algorithms that they can use to price and hedge derivative instruments.
There are, of course, many different types of derivative,
many different types of instruments that might be used for hedging purposes,
many different pricing models and many different ways of implementing such
models in a timely and efficient manner.
Moreover, as is explained in Kemp (2009), it is
well known by most practitioners in these markets that formulae typically used
to derive pricing and hedging parameters (such as the BlackScholes formulae)
generally rely on a number of unrealistic assumptions that do not represent
market reality. Despite this, such models are still widely used, principally as
a price quotation convention rather than because market practitioners believe
that they closely approximate reality. By this we mean that the relevant
formulae are being used to derive from the observed market prices of one or
more instruments some market implied values for one or more input parameters to
our pricing models, which we then use to price ‘similar’ instrument for which
no directly observable market price is available. Thus practical derivative
pricing also involves calibration of the model, i.e. identifying
value(s) that these input parameter(s) need to take for the derivative prices
to match actual observed market price(s).
We are therefore expecting this part of the Nematrian
website to grow significantly through time as instrument, model and calibration
approach and other algorithm coverage is developed.
Examples of material already covered in the Nematrian
website include:

Option
pricing ‘greeks’ for some instrument types in a BlackScholes world

Derivation
of the BlackScholes Option Pricing Formulae using the limit of a suitably
constructed lattice

Derivation
of the BlackScholes Option Pricing Formulae using Ito (stochastic) calculus
and partial differential equations

Material
describing SemiAnalytic Lattice Integrator Approaches to derivative pricing

Nematrian
derivative pricing web functions
If you spot any errors in this material please contact us to advise us of
the error.