Wyniki wyszukiwania - Biblioteka Nauki

Ten serwis zostanie wyłączony 2025-02-11.

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 6

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: American option

Sortuj według:

Ogranicz wyniki do:

On Backward Stochastic Differential Equations Approach to Valuation of American Options

100%

Klimsiak T. , Rozkosz A.

2011

tom Vol. 59, no 3

275--288

We consider the problem of valuation of American (call and put) options written on a dividend paying stock governed by the geometric Brownian motion. We show that the value function has two different but related representations: by means of a solution of some nonlinear backward stochastic differential equation, and by a weak solution to some semilinear partial differential equation.

Hedging in the CRR model under concave transaction costs

100%

Kociński M.

2001

tom Vol. 34, nr 2

497-512

In the paper hedging a contingent claim in the Cox-Ross-Rubinstein model under concave transaction costs is studied. Sufficient conditions for the optimality of the replicating strategy for the European option are given. The problem of describing of portfolios which allow, starting from a given moment to hedge a contingent claim is considered for both the European and American options.

Reflected BSDE with superlinear quadratic coefficient

100%

Kobylański M. , Lepeltier J. P. , Quenez M. C. , Torres S.

2002

tom Vol. 22, Fasc. 1

51--83

In this paper, we provide existence of a reflected solution of the one-dimensional backward stochastic differential equation when the coefficient is continuous, has a superlinear growth in y and quadratic growth in z. We also give a characterization of the solution as the value function of an optimal stopping time problem. We also study the links between the solution of the quadratic RBSDE and the corresponding obstacle problem. Then we give an application of quadratic RBSDE’s to the pricing of American contingent claims in an incomplete market.

Optimality of the replicating strategy for American options

100%

Kociński M.

Applicationes Mathematicae

1999

tom 26

nr 1

93-105

The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.

Supervised Machine Learning with Control Variates for American Option Pricing

63%

Mu G. , Godina T. , Maffia A. , Sun Y. C.

Foundations of Computing and Decision Sciences

2018

tom Vol. 43, No. 3

207--217

In this paper, we make use of a Bayesian (supervised learning) approach in pricing American options via Monte Carlo simulations. We first present Gaussian process regression (Kriging) approach for American options pricing and compare its performance in estimating the continuation value with the Longstaff and Schwartz algorithm. Secondly, we explore the control variates technique in combination with Kriging to further improve the estimation of the continuation value. This method allows to reduce dramatically the standard errors and to improve the stability of the Kriging approach. For illustrative purposes, we use American put options on a stock whose dynamics is given by Heston model, and use European options on the same stock as control variates.

Selected applications of differential equations in Vanilla Options valuation

51%

Krzyżanowski G.

tom Vol. 46, no. 2

273--291

The purpose of this paper is to present the applications of differential equations in Vanilla Options pricing. At the beginning we introduce main assumptions of the Black-Scholes Model with necessary comments, which as a norm can not be easily found in literature. In section 2, we show what the diffusion equation and the fair price of the European option have in common. Please note that these considerations were originally presented as proof of the Black-Scholes Formula. In sections 3 and 4 we explain why valuation of the American option can be coming down to Free Boundary Problem. Note: It is very interesting that the same mathematical model is well known as Stefan Problem describing temperature distribution in a homogeneous medium undergoing a phase change. At the end, we introduce the Finite Difference Method which will be used to solve problem numerically. We will describe the main features of the method and highlight situations in which the method might fail. At the end we make a comparison with other, widely used methods. The contribution of this paper is in an empirical analysis of effectiveness of the Finite Difference Method applied to the considered problem. Beyond this, the article has a review character.

Celem niniejszego artykułu jest przedstawienie zastosowań równań różniczkowych w wycenie opcji waniliowych. Na początku przedstawiamy główne założenia modelu Blacka-Scholesa z niezbędnymi komentarzami, których jako normę nie można łatwo znaleźć w literaturze. Następnie pokazujemy, co wspólnego ma równanie dyfuzji ze sprawiedliwą ceną opcji europejskiej. Należy pamiętać, że te rozważania zostały pierwotnie przedstawione jako dowód wzoru Blacka-Scholesa. Kolejno wyjaśniamy, dlaczego wycena opcji amerykańskiej może zostać sprowadzona do problemu ze swobodnym brzegiem, znanym jako problem Stefana opisującym propagacje temperatury w niejednorodnym ośrodku ulegającym przemianom fazowym. W końcowej części pracy wprowadzamy metodę różnic skończonych, która posłuży do numerycznego rozwiązania problemu. Opisujemy główne cechy metody pokazując potencjalne zagrożenia, które mogą pojawić się w wyniku zastosowania tej metody bez dokładnego zrozumienia jej struktury. Dokonujemy również porównania z innymi, szeroko stosowanymi metodami.