20,438 research outputs found
Coupling Index and Stocks
In this paper, we are interested in continuous time models in which the index
level induces some feedback on the dynamics of its composing stocks. More
precisely, we propose a model in which the log-returns of each stock may be
decomposed into a systemic part proportional to the log-returns of the index
plus an idiosyncratic part. We show that, when the number of stocks in the
index is large, this model may be approximated by a local volatility model for
the index and a stochastic volatility model for each stock with volatility
driven by the index. This result is useful in a calibration perspective : it
suggests that one should first calibrate the local volatility of the index and
then calibrate the dynamics of each stock. We explain how to do so in the
limiting simplified model and in the original model
A selective overview of nonparametric methods in financial econometrics
This paper gives a brief overview on the nonparametric techniques that are
useful for financial econometric problems. The problems include estimation and
inferences of instantaneous returns and volatility functions of
time-homogeneous and time-dependent diffusion processes, and estimation of
transition densities and state price densities. We first briefly describe the
problems and then outline main techniques and main results. Some useful
probabilistic aspects of diffusion processes are also briefly summarized to
facilitate our presentation and applications.Comment: 32 pages include 7 figure
Stock Price Dynamics and Option Valuations under Volatility Feedback Effect
According to the volatility feedback effect, an unexpected increase in
squared volatility leads to an immediate decline in the price-dividend ratio.
In this paper, we consider the properties of stock price dynamics and option
valuations under the volatility feedback effect by modeling the joint dynamics
of stock price, dividends, and volatility in continuous time. Most importantly,
our model predicts the negative effect of an increase in squared return
volatility on the value of deep-in-the-money call options and, furthermore,
attempts to explain the volatility puzzle. We theoretically demonstrate a
mechanism by which the market price of diffusion return risk, or an equity
risk-premium, affects option prices and empirically illustrate how to identify
that mechanism using forward-looking information on option contracts. Our
theoretical and empirical results support the relevance of the volatility
feedback effect. Overall, the results indicate that the prevailing practice of
ignoring the time-varying dividend yield in option pricing can lead to
oversimplification of the stock market dynamics.Comment: 23 pages, 7 figures, 2 table
Modelling FX smile : from stochastic volatility to skewness
Imperial Users onl
Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility
This paper develops a two-step estimation methodology, which allows us to
apply catastrophe theory to stock market returns with time-varying volatility
and model stock market crashes. Utilizing high frequency data, we estimate the
daily realized volatility from the returns in the first step and use stochastic
cusp catastrophe on data normalized by the estimated volatility in the second
step to study possible discontinuities in markets. We support our methodology
by simulations where we also discuss the importance of stochastic noise and
volatility in deterministic cusp catastrophe model. The methodology is
empirically tested on almost 27 years of U.S. stock market evolution covering
several important recessions and crisis periods. Due to the very long sample
period we also develop a rolling estimation approach and we find that while in
the first half of the period stock markets showed marks of bifurcations, in the
second half catastrophe theory was not able to confirm this behavior. Results
suggest that the proposed methodology provides an important shift in
application of catastrophe theory to stock markets
Option pricing with non-Gaussian scaling and infinite-state switching volatility
Volatility clustering, long-range dependence, and non-Gaussian scaling are
stylized facts of financial assets dynamics. They are ignored in the Black &
Scholes framework, but have a relevant impact on the pricing of options written
on financial assets. Using a recent model for market dynamics which adequately
captures the above stylized facts, we derive closed form equations for option
pricing, obtaining the Black & Scholes as a special case. By applying our
pricing equations to a major equity index option dataset, we show that
inclusion of stylized features in financial modeling moves derivative prices
about 30% closer to the market values without the need of calibrating models
parameters on available derivative prices.Comment: Revised version. 31 pages, 4 figure
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