why is there excess volatility? an explanation based...
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24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
Why is there excess volatility?An explanation based on stochastic
resonanceby Georges Harras, Claudio Tessone and Didier Sornette
ETH Zürich DMTEC
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
What is excess volatility?
Too big changes in stock prices compared to changes
of their fundamentals like corporate earnings,
dividends, interest rates [1].
First documented by Robert Shiller in 1981 [2], where
he found that the volatility of the S&P 500 is 5-13 times
too high compared to the volatility of information about
future dividends.
[1] David Cutler, James Poterba, and Lawrence Summers. What moves stock prices? Journal of Portfolio Management, 12, 1989.
[2] Robert J. Shiller. Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 71:421—436, 1981.
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
What is excess volatility?
Dividend Discount Model:
pt=∑k=1
∞ d tk1r k
d kr
= dividend at time k
= discount rate
pt = price at time t
Because the future dividends are unknown:
p t∗= ptut
p p∗
pt∗=∑k=1
∞ d t k∗
1r kp t=Et [ p t
∗]
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
What is excess volatility?
Robert J. Shiller. Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 71:421—436, 1981.
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
Basic ideas of the model:
Agent i
private information
“What should I do?”
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
The model:
sit =D k t ∑j=1
N
ij⋅s jt f t i t =a t
log [ price t ]=log [ price t ]r t
return:
imitation term news term idiosyncratic term
Updating:
D(x) = sign(x) orD(x) = x orD(x) = sign(x) Heaviside( |x|thresholdi ).
r t =∑=1
at
=1N
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
The model:
N, the number of agents
f(t) is a Gaussian white noise, with
k(t), dynamic coupling constant
Control parameters:
ij=1
# of neighbors
i t ~N 0,Q2
f t ~N 0,A2
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
Some results: k = constant
increase of volatility by tuning k/Q
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
What is stochastic resonance?R
TSignal
Signal
T
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
Some results: k = constant
increase of volatility decrease of cross-correlation
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
Some results: k = dynamic
clustered volatility
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
Conclusions:
We are able to explain excess volatility, having its origin
in the interaction of the agents with private information
Increase of volatility (stochastic resonance) in an wide
range of parameters and setups
Few assumptions are needed: 1) interacting agents, 2)
distribution of personal information, 3) external
influence
Clustered volatility originates from the dynamics in the
coupling strength
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]
Outlook:
Different network-topologies
Solving for different demand functions D
Endogenize the dynamics of the coupling strength
Dependence of the results with the time window Δ of
returns
...
24.10.2009 Georges Harras/ETH Zürich D-MTEC/[email protected]