Applied Maths Seminar: Schlögl -- Gram/Charlier Series A Expansions for Option Pricing

APPLIED MATHEMATICS SEMINAR AT THE UNIVERSITY OF SYDNEY 

Speaker: Assoc/Prof Erik Schlögl, University of Technology, Sydney 
Title: Gram/Charlier Series A Expansions for Option Pricing 

DATE: Wednesday, May 30 
TIME: 2:00pm 
LOCATION: University of Sydney, Eastern Avenue Lecture Theatre (Level 1) 

Abstract: 

One of the key requirements for a model used to price tailored derivative financial
instruments in practice is that the model fits observed market prices for standard
options, which are typically expressed in the form of an "implied volatility surface".
This can be achieved by extracting an implied probability distribution or stochastic
process for the evolution of the underlying asset(s) from market prices.  One way to go
about this is to approximate the relevant probability densities by Gram/Charlier Series
A expansions.  In option pricing, this has been used previously to fit risk-neutral
asset price distributions to the implied volatility smile, ensuring an arbitrage-free
interpolation of implied volatilities across exercise prices.  However, the existing
literature is restricted to the case of the density of a single asset price, for a
single time horizon, with the series expansion truncated after the fourth moment.  I
present an option pricing formula in terms of the full ( untruncated) series and discuss
a fitting algorithm, which ensures that a series truncated at a moment of arbitrary even
order represents a valid probability density.  The pricing formula is then extended to
options on multiple assets and with multiple event dates.  

http://www.maths.usyd.edu.au/u/AppliedSeminar
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