MONTE CARLO EVALUATION OF AMERICAN OPTIONS USING CONSUMPTION PROCESSES

2006 ◽  
Vol 09 (04) ◽  
pp. 455-481 ◽  
Author(s):  
DENIS BELOMESTNY ◽  
GRIGORI N. MILSTEIN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lower Bound ◽  
Upper Bound ◽  
Continuous Time ◽  
Numerical Experiments ◽  
American Options ◽  
Upper And Lower Bounds ◽  
New Approach ◽  
Monte Carlo Evaluation

We develop a new approach for pricing both continuous-time and discrete-time American options which is based on the fact that any American option is equivalent to a European one with a consumption process involved. This approach admits the construction of an upper bound (a lower bound) on the true price using some lower bound (an upper bound) by Monte Carlo simulation. A number of effective estimators of upper and lower bounds with the reduced variance are proposed. The method is supported by numerical experiments which look promising.

A NEW MONTE CARLO METHOD FOR AMERICAN OPTIONS

2004 ◽  
Vol 07 (05) ◽  
pp. 591-614 ◽  
Author(s):  
G. N. MILSTEIN ◽  
O. REIß ◽  
J. SCHOENMAKERS
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Value Problem ◽  
Numerical Experiments ◽  
American Options ◽  
American Option ◽  
Parabolic Boundary ◽  
Black Scholes ◽  
Exercise Boundary

We introduce a new Monte Carlo method for constructing the exercise boundary of an American option in a generalized Black–Scholes framework. Based on a known exercise boundary, it is shown how to price and hedge the American option by Monte Carlo simulation of suitable probabilistic representations in connection with the respective parabolic boundary value problem. The method presented is supported by numerical experiments.

New approach to Monte Carlo simulation of photon transport in the frequency domain

1995 ◽  
Author(s):  
Ilya V. Yaroslavsky ◽  
Anna N. Yaroslavsky ◽  
Hans-Joachim Schwarzmaier ◽  
Garif G. Akchurin ◽  
Valery V. Tuchin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Frequency Domain ◽  
New Approach ◽  
Photon Transport

scholarly journals On the Rank of $p$-Schemes

10.37236/3097 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Fateme Raei Barandagh ◽  
Amir Rahnamai Barghi
Keyword(s):  
Lower Bound ◽  
Prime Number ◽  
Lower Bounds ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Minimum Rank

Let $n>1$ be an integer and $p$ be a prime number. Denote by $\mathfrak{C}_{p^n}$ the class of non-thin association $p$-schemes of degree $p^n$. A sharp upper and lower bounds on the rank of schemes in $\mathfrak{C}_{p^n}$ with a certain order of thin radical are obtained. Moreover, all schemes in this class whose rank are equal to the lower bound are characterized and some schemes in this class whose rank are equal to the upper bound are constructed. Finally, it is shown that the scheme with minimum rank in $\mathfrak{C}_{p^n}$ is unique up to isomorphism, and it is a fusion of any association $p$-schemes with degree $p^n$.

scholarly journals When is non-trivial estimation possible for graphons and stochastic block models?‡

2017 ◽  
Vol 7 (2) ◽  
pp. 169-181
Author(s):  
Audra McMillan ◽  
Adam Smith
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Random Networks ◽  
Block Models

Abstract Block graphons (also called stochastic block models) are an important and widely studied class of models for random networks. We provide a lower bound on the accuracy of estimators for block graphons with a large number of blocks. We show that, given only the number $k$ of blocks and an upper bound $\rho$ on the values (connection probabilities) of the graphon, every estimator incurs error ${\it{\Omega}}\left(\min\left(\rho, \sqrt{\frac{\rho k^2}{n^2}}\right)\right)$ in the $\delta_2$ metric with constant probability for at least some graphons. In particular, our bound rules out any non-trivial estimation (that is, with $\delta_2$ error substantially less than $\rho$) when $k\geq n\sqrt{\rho}$. Combined with previous upper and lower bounds, our results characterize, up to logarithmic terms, the accuracy of graphon estimation in the $\delta_2$ metric. A similar lower bound to ours was obtained independently by Klopp et al.

scholarly journals BÜCHI COMPLEMENTATION MADE TIGHTER

2006 ◽  
Vol 17 (04) ◽  
pp. 851-867 ◽  
Author(s):  
EHUD FRIEDGUT ◽  
ORNA KUPFERMAN ◽  
MOSHE Y. VARDI
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Blow Up ◽  
Careful Analysis ◽  
Point Of View ◽  
Upper And Lower Bounds ◽  
Theoretical Point ◽  
Infinite Words ◽  
Büchi Automata ◽  
Buchi Automata

The complementation problem for nondeterministic word automata has numerous applications in formal verification. In particular, the language-containment problem, to which many verification problems is reduced, involves complementation. For automata on finite words, which correspond to safety properties, complementation involves determinization. The 2n blow-up that is caused by the subset construction is justified by a tight lower bound. For Büchi automata on infinite words, which are required for the modeling of liveness properties, optimal complementation constructions are quite complicated, as the subset construction is not sufficient. From a theoretical point of view, the problem is considered solved since 1988, when Safra came up with a determinization construction for Büchi automata, leading to a 2O(n log n) complementation construction, and Michel came up with a matching lower bound. A careful analysis, however, of the exact blow-up in Safra's and Michel's bounds reveals an exponential gap in the constants hiding in the O( ) notations: while the upper bound on the number of states in Safra's complementary automaton is n2n, Michel's lower bound involves only an n! blow up, which is roughly (n/e)n. The exponential gap exists also in more recent complementation constructions. In particular, the upper bound on the number of states in the complementation construction of Kupferman and Vardi, which avoids determinization, is (6n)n. This is in contrast with the case of automata on finite words, where the upper and lower bounds coincides. In this work we describe an improved complementation construction for nondeterministic Büchi automata and analyze its complexity. We show that the new construction results in an automaton with at most (0.96n)n states. While this leaves the problem about the exact blow up open, the gap is now exponentially smaller. From a practical point of view, our solution enjoys the simplicity of the construction of Kupferman and Vardi, and results in much smaller automata.

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