4,160 research outputs found
Option Pricing with Orthogonal Polynomial Expansions
We derive analytic series representations for European option prices in
polynomial stochastic volatility models. This includes the Jacobi, Heston,
Stein-Stein, and Hull-White models, for which we provide numerical case
studies. We find that our polynomial option price series expansion performs as
efficiently and accurately as the Fourier transform based method in the nested
affine cases. We also derive and numerically validate series representations
for option Greeks. We depict an extension of our approach to exotic options
whose payoffs depend on a finite number of prices.Comment: forthcoming in Mathematical Finance, 38 pages, 3 tables, 7 figure
A Moment-Matching Method for Approximating Vector Autoregressive Processes by Finite-State Markov Chains
This paper proposes a moment-matching method for approximating vector autoregressions by finite-state Markov chains. The Markov chain is constructed by targeting the conditional moments of the underlying continuous process. The proposed method is more robust to the number of discrete values and tends to outperform the existing methods for approximating multivariate processes over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle.Markov Chain, Vector Autoregressive Processes, Functional Equation, Numerical Methods, Moment Matching
Bayesian Inference for Latent Biologic Structure with Determinantal Point Processes (DPP)
We discuss the use of the determinantal point process (DPP) as a prior for
latent structure in biomedical applications, where inference often centers on
the interpretation of latent features as biologically or clinically meaningful
structure. Typical examples include mixture models, when the terms of the
mixture are meant to represent clinically meaningful subpopulations (of
patients, genes, etc.). Another class of examples are feature allocation
models. We propose the DPP prior as a repulsive prior on latent mixture
components in the first example, and as prior on feature-specific parameters in
the second case. We argue that the DPP is in general an attractive prior model
for latent structure when biologically relevant interpretation of such
structure is desired. We illustrate the advantages of DPP prior in three case
studies, including inference in mixture models for magnetic resonance images
(MRI) and for protein expression, and a feature allocation model for gene
expression using data from The Cancer Genome Atlas. An important part of our
argument are efficient and straightforward posterior simulation methods. We
implement a variation of reversible jump Markov chain Monte Carlo simulation
for inference under the DPP prior, using a density with respect to the unit
rate Poisson process
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