590 research outputs found
European Option Pricing with Liquidity Shocks
We study the valuation and hedging problem of European options in a market
subject to liquidity shocks. Working within a Markovian regime-switching
setting, we model illiquidity as the inability to trade. To isolate the impact
of such liquidity constraints, we focus on the case where the market is
completely static in the illiquid regime. We then consider derivative pricing
using either equivalent martingale measures or exponential indifference
mechanisms. Our main results concern the analysis of the semi-linear coupled
HJB equation satisfied by the indifference price, as well as its asymptotics
when the probability of a liquidity shock is small. We then present several
numerical studies of the liquidity risk premia obtained in our models leading
to practical guidelines on how to adjust for liquidity risk in option valuation
and hedging.Comment: 25 pages, 6 figure
On jump-diffusion processes with regime switching: martingale approach
We study jump-diffusion processes with parameters switching at random times.
Being motivated by possible applications, we characterise equivalent martingale
measures for these processes by means of the relative entropy. The minimal
entropy approach is also developed. It is shown that in contrast to the case of
L\'evy processes, for this model an Esscher transformation does not produce the
minimal relative entropy.Comment: 23 pages, 2 figure
Correction to Black-Scholes formula due to fractional stochastic volatility
Empirical studies show that the volatility may exhibit correlations that
decay as a fractional power of the time offset. The paper presents a rigorous
analysis for the case when the stationary stochastic volatility model is
constructed in terms of a fractional Ornstein Uhlenbeck process to have such
correlations. It is shown how the associated implied volatility has a term
structure that is a function of maturity to a fractional power
USLV: Unspanned Stochastic Local Volatility Model
We propose a new framework for modeling stochastic local volatility, with
potential applications to modeling derivatives on interest rates, commodities,
credit, equity, FX etc., as well as hybrid derivatives. Our model extends the
linearity-generating unspanned volatility term structure model by Carr et al.
(2011) by adding a local volatility layer to it. We outline efficient numerical
schemes for pricing derivatives in this framework for a particular four-factor
specification (two "curve" factors plus two "volatility" factors). We show that
the dynamics of such a system can be approximated by a Markov chain on a
two-dimensional space (Z_t,Y_t), where coordinates Z_t and Y_t are given by
direct (Kroneker) products of values of pairs of curve and volatility factors,
respectively. The resulting Markov chain dynamics on such partly "folded" state
space enables fast pricing by the standard backward induction. Using a
nonparametric specification of the Markov chain generator, one can accurately
match arbitrary sets of vanilla option quotes with different strikes and
maturities. Furthermore, we consider an alternative formulation of the model in
terms of an implied time change process. The latter is specified
nonparametrically, again enabling accurate calibration to arbitrary sets of
vanilla option quotes.Comment: Sections 3.2 and 3.3 are re-written, 3 figures adde
Filtering and forecasting commodity futures prices under an HMM framework
We propose a model for the evolution of arbitrage-free futures prices under a regime-switching framework. The estimation of model parameters is carried out using the hidden Markov filtering algorithms. Comprehensive numerical experiments on real financial market data are provided to illustrate the effectiveness of our algorithm. In particular, the model is calibrated with data from heating oil futures and its forecasting performance as well as statistical validity is investigated. The proposed model is parsimonious, self-calibrating and can be very useful in predicting futures prices. © 2013 Elsevier B.V
The History of the Quantitative Methods in Finance Conference Series. 1992-2007
This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.
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