991 research outputs found
Thermodynamics of regular black holes with cosmic strings
In this article, the thermodynamics of regular black holes with a cosmic
string passing through it is studied. We will observe that the string has no
effect on the temperature as well as the relation between entropy S and horizon
area A.Comment: Accepted for publication in EPJ Plus, 6 page
Consistency Problems For Jump-Diffusion Models
In this paper we examine a consistency problem for a multi-factor jump diffusion model. First we bridge a gap between a jump-diffusion model and a generalized Heath-Jarrow-Morton (HJM) model, and bring a multi- factor jump-diffusion model into the HJM framework. By applying the drift condition for a generalized arbitrage-free HJM model, we derive the general consistency condition for a jump-diffusion model. Then we consider the case that the forward rate function has a separable structure, and obtain a specific version of the general consistency condition. In particular, we provide the necessary and sufficient condition for a jump-diffusion model to be affine, which generalizes the result in Duffie and Kan (1996). Finally we discuss the Nelson-Siegel type of forward curve structure, and give the necessary and sufficient condition for the consistency of this class of models in the jump- diffusion case.Arbitrage-free Condition, HJM Models, Jump-Diffusion Models
Consistency Problems for Jump-Diffusion Models
In this paper consistency problems for multi-factor jump-diffusion models,
where the jump parts follow multivariate point processes are examined. First
the gap between jump-diffusion models and generalized Heath-Jarrow-Morton (HJM)
models is bridged. By applying the drift condition for a generalized
arbitrage-free HJM model, the consistency condition for jump-diffusion models
is derived. Then we consider a case in which the forward rate curve has a
separable structure, and obtain a specific version of the general consistency
condition. In particular, a necessary and sufficient condition for a
jump-diffusion model to be affine is provided. Finally the Nelson-Siegel type
of forward curve structures is discussed. It is demonstrated that under
regularity condition, there exists no jump-diffusion model consistent with the
Nelson-Siegel curves.Comment: To appear in Applied Mathematical Financ
Projecting the Forward Rate Flow on a Finite Dimensional Manifold
Given an Heath-Jarrow-Morton (HJM) interest rate model and a parametrized family of finite dimensional forward rate curves, this paper provides us a way to project this infinite dimensional HJM forward rate curve to the finite dimensional manifold. This projection characterizes banks' behavior of calibrating forward curves by applying a certain family of curves (e.g., Nelson-Seigel family). Moreover, we derive the Stratonovich dynamics of the projected finite dimensional forward curve. This leads an implicit algorithm for parametric estimation of the original HJM model. We have demonstrated the feasibility of this method by applying generalized method of moments and methods of simulated moments.HJM Model, Finite-dimensional Manifolds, Nelson_Siegel Family
Pluripotential theory and convex bodies: large deviation principle
We continue the study in [2] in the setting of weighted pluripotential theory arising from polynomials associated to a convex body P in (R^+)^d. Our goal is to establish a large deviation principle in this setting specifying the rate function in terms of P-pluripotential-theoretic notions. As an important preliminary step, we first give an existence proof for the solution of a Monge-Amp\`ere equation in an appropriate finite energy class. This is achieved using a variational approach
Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio
We use a continuous version of the standard deviation premium principle for
pricing in incomplete equity markets by assuming that the investor issuing an
unhedgeable derivative security requires compensation for this risk in the form
of a pre-specified instantaneous Sharpe ratio. First, we apply our method to
price options on non-traded assets for which there is a traded asset that is
correlated to the non-traded asset. Our main contribution to this particular
problem is to show that our seller/buyer prices are the upper/lower good deal
bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko
(2006) and to determine the analytical properties of these prices. Second, we
apply our method to price options in the presence of stochastic volatility. Our
main contribution to this problem is to show that the instantaneous Sharpe
ratio, an integral ingredient in our methodology, is the negative of the market
price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar
(2000).Comment: Keywords: Pricing derivative securities, incomplete markets, Sharpe
ratio, correlated assets, stochastic volatility, non-linear partial
differential equations, good deal bound
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