Comparison of Path Generation Methods for Monte Carlo Valuation of Single Underlying Derivative Securities

1996 ◽  
Author(s):  
Leonard Berman
Keyword(s):  
Monte Carlo ◽  
Path Generation ◽  
Derivative Securities

RATE OF CONVERGENCE OF MONTE CARLO SIMULATIONS FOR THE HOBSON–ROGERS MODEL

2008 ◽  
Vol 11 (08) ◽  
pp. 889-904 ◽  
Author(s):  
FABIO ANTONELLI ◽  
VALENTINA PREZIOSO
Keyword(s):  
Monte Carlo ◽  
Rate Of Convergence ◽  
Asset Price ◽  
Approximation Error ◽  
Derivative Securities ◽  
Step Size ◽  
Time Step ◽  
No Arbitrage ◽  
Time Step Size ◽  
Theoretical Results

The Hobson–Rogers model is used to price derivative securities under the no-arbitrage condition in a stochastic volatility setting, preserving the completeness of the market. Here we are studying the rate of convergence of the Euler/Monte Carlo approximations, when pricing European, Asian and digital type options. The aim of the present work is to express the approximation error in terms of the time step size, denoted by h, used for the Euler scheme. We recover an already known result, obtained by other authors using PDE approximations, for European options. Namely we show that for a Lipschitz coefficient of the driving equations for the asset price and Lipschitz payoffs, we obtain an error of the order of [Formula: see text]. Moreover, using Malliavin Calculus techniques, we show that with a regular coefficient we may attain an error of the order of h for regular payoffs and of the order of [Formula: see text] for non Lipschitz payoffs. Finally we show some numerical simulations supporting our theoretical results.

scholarly journals MCPath: Monte Carlo path generation approach to predict likely allosteric pathways and functional residues

2013 ◽  
Vol 41 (W1) ◽  
pp. W249-W255 ◽  
Author(s):  
Cihan Kaya ◽  
Andac Armutlulu ◽  
Solen Ekesan ◽  
Turkan Haliloglu
Keyword(s):  
Monte Carlo ◽  
Path Generation

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

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