113 research outputs found
An SFPâFCC method for pricing and hedging early-exercise options under LĂ©vy processes
This paper extends the singular FourierâPadĂ© (SFP) method proposed by Chan [Singular FourierâPadĂ© series expansion of European option prices. Quant. Finance, 2018, 18, 1149â1171] for pricing/hedging early-exercise optionsâBermudan, American and discrete-monitored barrier optionsâunder a LĂ©vy process. The current SFP method is incorporated with the FilonâClenshawâCurtis (FCC) rules invented by DomĂnguez et al. [Stability and error estimates for FilonâClenshawâCurtis rules for highly oscillatory integrals. IMA J. Numer. Anal., 2011, 31, 1253â1280], and we call the new method SFPâFCC. The main purpose of using the SFPâFCC method is to require a small number of terms to yield fast error convergence and to formulate option pricing and option Greek curves rather than individual prices/Greek values. We also numerically show that the SFPâFCC method can retain a global spectral convergence rate in option pricing and hedging when the risk-free probability density function is piecewise smooth. Moreover, the computational complexity of the method is O((Lâ1)(N+1)( Ă log Ă)) with N, a (small) number of complex Fourier series terms, Ă, a number of Chebyshev series terms and L, the number of early-exercise/monitoring dates. Finally, we compare the accuracy and computational time of our method with those of existing techniques in numerical experiments
Singular Fourier-Padé Series Expansion of European Option Prices
We apply a new numerical method, the singular Fourier-Pad Ìe (SFP) method invented by Driscoll and
Fornberg (2001, 2011), to price European-type options in L Ìevy and affine processes. The motivation
behind this application is to reduce the inefficiency of current Fourier techniques when they are used to
approximate piecewise continuous (non-smooth) probability density functions. When techniques such as
fast Fourier transforms and Fourier series are applied to price and hedge options with non-smooth prob-
ability density functions, they cause the Gibbs phenomenon; accordingly, the techniques converge slowly
for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and
accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the
SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. More-
over, we show that our method requires a small number of terms to yield fast error convergence, and it
is able to accurately price any European-type option deep in/out of the money and with very long/short
maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This
new method performs favourably in numerical experiments compared with existing techniques
Isospectrality in Chaotic Billiards
We consider a modification of isospectral cavities whereby the classical
dynamics changes from pseudointegrable to chaotic. We construct an example
where we can prove that isospectrality is retained. We then demonstrate this
explicitly in microwave resonators.Comment: 5 pages, 7 figure
On surface states and star-subalgebras in string field theory
We elaborate on the relations between surface states and squeezed states.
First, we investigate two different criteria for determining whether a matter
sector squeezed state is also a surface state and show that the two criteria
are equivalent. Then, we derive similar criteria for the ghost sector. Next, we
refine the criterion for determining whether a surface state is in
H_{\kappa^2}, the subalgebra of squeezed states obeying [S,K_1^2]=0. This
enables us to find all the surface states of the H_{\kappa^2} subalgebra, and
show that it consists only of wedge states and (hybrid) butterflies. Finally,
we investigate generalizations of this criterion and find an infinite family of
surface states subalgebras, whose surfaces are described using a "generalized
Schwarz-Christoffel" mapping.Comment: 38 pages, 6 figures, JHEP style; typos corrected, ref. adde
CDMS, Supersymmetry and Extra Dimensions
The CDMS experiment aims to directly detect massive, cold dark matter
particles originating from the Milky Way halo. Charge and lattice excitations
are detected after a particle scatters in a Ge or Si crystal kept at ~30 mK,
allowing to separate nuclear recoils from the dominating electromagnetic
background. The operation of 12 detectors in the Soudan mine for 75 live days
in 2004 delivered no evidence for a signal, yielding stringent limits on dark
matter candidates from supersymmetry and universal extra dimensions. Thirty Ge
and Si detectors are presently installed in the Soudan cryostat, and operating
at base temperature. The run scheduled to start in 2006 is expected to yield a
one order of magnitude increase in dark matter sensitivity.Comment: To be published in the proceedings of the 7th UCLA symposium on
sources and detection of dark matter and dark energy in the universe, Marina
del Rey, Feb 22-24, 200
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