789,825 research outputs found
Hedging Greeks for a portfolio of options using linear and quadratic programming
The aim of this paper is to develop a hedging methodology for making a portfolio of options delta, vega and gamma neutral by taking positions in other available options, and simultaneously minimizing the net premium to be paid for the hedging. A quadratic programming solution for the problem is formulated, and then it is approximated to a linear programming solution. A prototype for the linear programming solution has been developed in MS Excel using VBA.Hedging, Greeks, portfolio of options
Bounding Option Prices Using SDP With Change Of Numeraire
Recently, given the first few moments, tight upper and lower bounds of the no arbitrage prices can be obtained by solving semidefinite programming (SDP) or linear programming (LP) problems. In this paper, we compare SDP and LP formulations of the European-style options pricing problem and prefer SDP formulations due to the simplicity of moments constraints. We propose to employ the technique of change of numeraire when using SDP to bound the European type of options. In fact, this problem can then be cast as a truncated Hausdorff moment problem which has necessary and sufficient moment conditions expressed by positive semidefinite moment and localizing matrices. With four moments information we show stable numerical results for bounding European call options and exchange options. Moreover, A hedging strategy is also identified by the dual formulation.moments of measures, semidefinite programming, linear programming, options pricing, change of numeraire
Short-time asymptotics for marginal distributions of semimartingales
We study the short-time asymptotics of conditional expectations of smooth and
non-smooth functions of a (discontinuous) Ito semimartingale; we compute the
leading term in the asymptotics in terms of the local characteristics of the
semimartingale. We derive in particular the asymptotic behavior of call options
with short maturity in a semimartingale model: whereas the behavior of
\textit{out-of-the-money} options is found to be linear in time, the short time
asymptotics of \textit{at-the-money} options is shown to depend on the fine
structure of the semimartingale
A method for pricing American options using semi-infinite linear programming
We introduce a new approach for the numerical pricing of American options.
The main idea is to choose a finite number of suitable excessive functions
(randomly) and to find the smallest majorant of the gain function in the span
of these functions. The resulting problem is a linear semi-infinite programming
problem, that can be solved using standard algorithms. This leads to good upper
bounds for the original problem. For our algorithms no discretization of space
and time and no simulation is necessary. Furthermore it is applicable even for
high-dimensional problems. The algorithm provides an approximation of the value
not only for one starting point, but for the complete value function on the
continuation set, so that the optimal exercise region and e.g. the Greeks can
be calculated. We apply the algorithm to (one- and) multidimensional diffusions
and to L\'evy processes, and show it to be fast and accurate
Derivatives pricing in energy markets: an infinite dimensional approach
Based on forward curves modelled as Hilbert-space valued processes, we
analyse the pricing of various options relevant in energy markets. In
particular, we connect empirical evidence about energy forward prices known
from the literature to propose stochastic models. Forward prices can be
represented as linear functions on a Hilbert space, and options can thus be
viewed as derivatives on the whole curve. The value of these options are
computed under various specifications, in addition to their deltas. In a second
part, cross-commodity models are investigated, leading to a study of square
integrable random variables with values in a "two-dimensional" Hilbert space.
We analyse the covariance operator and representations of such variables, as
well as presenting applications to pricing of spread and energy quanto options
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