45,499 research outputs found
Pricing Step Options under the CEV and other Solvable Diffusion Models
We consider a special family of occupation-time derivatives, namely
proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96
(1999)]. We develop new closed-form spectral expansions for pricing such
options under a class of nonlinear volatility diffusion processes which
includes the constant-elasticity-of-variance (CEV) model as an example. In
particular, we derive a general analytically exact expression for the resolvent
kernel (i.e. Green's function) of such processes with killing at an exponential
stopping time (independent of the process) of occupation above or below a fixed
level. Moreover, we succeed in Laplace inverting the resolvent kernel and
thereby derive newly closed-form spectral expansion formulae for the transition
probability density of such processes with killing. The spectral expansion
formulae are rapidly convergent and easy-to-implement as they are based simply
on knowledge of a pair of fundamental solutions for an underlying solvable
diffusion process. We apply the spectral expansion formulae to the pricing of
proportional step options for four specific families of solvable nonlinear
diffusion asset price models that include the CEV diffusion model and three
other multi-parameter state-dependent local volatility confluent hypergeometric
diffusion processes.Comment: 30 pages, 16 figures, submitted to IJTA
Some numerical methods for solving stochastic impulse control in natural gas storage facilities
The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP
Pricing options and computing implied volatilities using neural networks
This paper proposes a data-driven approach, by means of an Artificial Neural
Network (ANN), to value financial options and to calculate implied volatilities
with the aim of accelerating the corresponding numerical methods. With ANNs
being universal function approximators, this method trains an optimized ANN on
a data set generated by a sophisticated financial model, and runs the trained
ANN as an agent of the original solver in a fast and efficient way. We test
this approach on three different types of solvers, including the analytic
solution for the Black-Scholes equation, the COS method for the Heston
stochastic volatility model and Brent's iterative root-finding method for the
calculation of implied volatilities. The numerical results show that the ANN
solver can reduce the computing time significantly
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