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Topic
: Jump Starting GARCH: Pricing and Hedging
Options
with Jumps in Returns and Volatilities Speaker
:
Professor Jin-Chuan
Duan
(Rotman School of Management,
University of Toronto, Canada)
Time
: May 12 (Wednesday) 10:30 - 11:30 am Abstract:
This paper considers the pricing of
options when there are jumps in the
pricing kernel and correlated jumps in asset returns and
volatilities. Limiting cases of our GARCH processes consist of
models where both asset returns and local volatility follow jump
diffusion processes with correlated jump sizes. Convergence of the
GARCH models to their continuous time limits is extremely fast.
Empirical analysis on the S&P 500
index reveals that the incorporation of jumps in returns and
volatilities adds significantly to the description of the time series
process. Since the state variables are fully determined by the path of
prices, once the parameters have been estimated, option prices can
readily be computed. We find that option prices, even 50 weeks after the
parameters are estimated are fairly precise. In addition to pricing
tests, we examine hedging effectiveness, and provide evidence that the
hedges can be maintained very well over time.
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