Abstract
Most models used to fit financial returns and price financial derivatives like options assume
that returns follow a normal distribution, which is unrealistic. Financial returns tend
to have heavy tails with jumps. This research introduces a general class of bilateral
distributions based on mixed Erlang distributions. We call the new class of distribution
bilateral mixed Erlang (BME) or bilateral compound (CB). We first derive the different
statistical properties and characteristics of this new family of compound exponential
bilateral distribution and test its ability to fit financial returns. The BME is dense in
the class of bilateral distributions and stable under convolution. We apply the BME
distribution to price of European options, using closed-form expressions derived through
the application of the Esscher-Transform.
Keywords: Financial returns, Option pricing, Heavy tails, Jumps, Bilateral Mixed
Erlang Distribution, Compound Bilateral Distributions, Statistical properties, Esscher
transform, Financial modelling.