25,025 research outputs found
Reduced Order Modeling for Heston Stochastic Volatility Model
In this paper we compare two model order reduction techniques, the Proper
Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), for
Heston's option pricing model. The full order model is obtained by
discontinuous Galerkin discretization in space and backward Euler in time.
Numerical results for butterfly spread, European and digital call options
reveal that in general DMD requires more modes than the POD modes as expected
at the same level of accuracy. However, the speed-up factors are much higher
for DMD than POD due to the equation free nature of the DMD.Comment: arXiv admin note: text overlap with arXiv:1606.0838
The Effect of Non-Smooth Payoffs on the Penalty Approximation of American Options
This article combines various methods of analysis to draw a comprehensive
picture of penalty approximations to the value, hedge ratio, and optimal
exercise strategy of American options. While convergence of the penalised
solution for sufficiently smooth obstacles is well established in the
literature, sharp rates of convergence and particularly the effect of gradient
discontinuities (i.e., the omni-present `kinks' in option payoffs) on this rate
have not been fully analysed so far. This effect becomes important not least
when using penalisation as a numerical technique. We use matched asymptotic
expansions to characterise the boundary layers between exercise and hold
regions, and to compute first order corrections for representative payoffs on a
single asset following a diffusion or jump-diffusion model. Furthermore, we
demonstrate how the viscosity theory framework in [Jakobsen, 2006] can be
applied to this setting to derive upper and lower bounds on the value. In a
small extension to [Bensoussan & Lions, 1982], we derive weak convergence rates
also for option sensitivities for convex payoffs under jump-diffusion models.
Finally, we outline applications of the results, including accuracy
improvements by extrapolation.Comment: 34 Pages, 10 Figure
The internal efficiency of Index Option Markets:Tests on the Italian Market
The aim of the present paper is to provide evidence on the internal market efficiency of the Italian index option market. To this end a model-free approach is taken, whereby strategies involving only options are tested by means of a high frequency dataset covering the period 1 September – 31 December 2002. This piece of research thus completes our previous analysis (Brunetti and Torricelli(2003, 2006)), which focused on the cross-market efficiency of the same market. The results obtained further support the efficiency of one of the most important index options markets in Europe.index options;internal market efficiency; no-arbitrage; option spreads
Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements
This paper deals with pricing of European and American options, when the
underlying asset price follows Heston model, via the interior penalty
discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM
space discretization with Rannacher smoothing as time integrator with nonsmooth
initial and boundary conditions are illustrated for European vanilla options,
digital call and American put options. The convection dominated Heston model
for vanishing volatility is efficiently solved utilizing the adaptive dGFEM.
For fast solution of the linear complementary problem of the American options,
a projected successive over relaxation (PSOR) method is developed with the norm
preconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option
pricing by conducting comparison analysis with other methods and numerical
experiments
Pricing Options with Portfolio-based Option Trading Agents in Direct Double Auction
Options constitute integral part of modern financial trades, and are priced according to the risk associated with buying or selling certain asset in future. Financial literature mostly concentrates on risk-neutral methods of pricing options such as Black- Scholes model. However, using trading agents with utility function to determine the option’s potential payoff is an emerging field in option pricing theory. In this paper, we use one of such methodologies developed by Othman and Sandholm to design portfolioholding agents that are endowed with popular option portfolios such as bullish spread, bearish spread, butterfly spread, straddle, etc to price options. Agents use their portfolios to evaluate how buying or selling certain option would change their current payoff structure. We also develop a multi-unit direct double auction which preserves the atomicity of orders at the expense of budget balance. Agents are simulated in this mechanism and the emerging prices are compared to risk-neutral prices under different market conditions. Through an appropriate allocation of option portfolios to trading agents, we can simulate market conditions where the population of agents are bearish, bullish, neutral or non-neutral in their beliefs
Algorithm for payoff calculation for option trading strategies using vector terminology
The aim of this paper is to develop an algorithm for calculating and plotting payoff of option strategies for a portfolio of path independent vanilla and exotic options. A general algorithm for calculating the vector matrix for any arbitrary combination strategy is also developed for some of the commonly option trading strategies.option trading strategies, vector
ALGORITHM FOR PAYOFF CALCULATION FOR OPTION TRADING STRATEGIES USING VECTOR TERMINOLOGY
The aim of this paper is to develop an algorithm for calculating and plotting payoff of option strategies for a portfolio of path independent vanilla and exotic options. A general algorithm for calculating the vector matrix for any arbitrary combination strategy is also developed for some of the commonly option trading strategies.option trading strategy, payoff, vector, vanilla and exotic option
Generalised arbitrage-free SVI volatility surfaces
In this article we propose a generalisation of the recent work of Gatheral
and Jacquier on explicit arbitrage-free parameterisations of implied volatility
surfaces. We also discuss extensively the notion of arbitrage freeness and
Roger Lee's moment formula using the recent analysis by Roper. We further
exhibit an arbitrage-free volatility surface different from Gatheral's SVI
parameterisation.Comment: 20 pages, 4 figures. Corrected some typo
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance
We present a simple and easy to implement method for the numerical solution
of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many
cases, the considered problems have only a viscosity solution, to which,
fortunately, many intuitive (e.g. finite difference based) discretisations can
be shown to converge. However, especially when using fully implicit time
stepping schemes with their desirable stability properties, one is still faced
with the considerable task of solving the resulting nonlinear discrete system.
In this paper, we introduce a penalty method which approximates the nonlinear
discrete system to first order in the penalty parameter, and we show that an
iterative scheme can be used to solve the penalised discrete problem in
finitely many steps. We include a number of examples from mathematical finance
for which the described approach yields a rigorous numerical scheme and present
numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more
detailed introduction. In the current form, the paper will appear in SIAM
Journal on Numerical Analysi
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