scholarly journals Exotic Option Prices Simulated by Monte Carlo Method on Market Driven by Diffusion with Poisson Jumps and Stochastic Volatility

2005 ◽  
pp. 1112-1115
Author(s):  
Magdalena Broszkiewicz ◽  
Aleksander Janicki
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stochastic Volatility ◽  
Option Prices ◽  
Poisson Jumps ◽  
Exotic Option ◽  
Market Driven

scholarly journals USING MODEL-INDEPENDENT LOWER BOUNDS TO IMPROVE PRICING OF ASIAN STYLE OPTIONS IN LÉVY MARKETS

2014 ◽  
Vol 44 (2) ◽  
pp. 237-276 ◽  
Author(s):  
Griselda Deelstra ◽  
Grégory Rayée ◽  
Steven Vanduffel ◽  
Jing Yao
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Lower Bounds ◽  
Mathematical Finance ◽  
Asian Option ◽  
Asian Options ◽  
Option Prices ◽  
Control Variates ◽  
Proposed Model ◽  
Model Independent

AbstractAlbrecheret al. (Albrecher, H., Mayer Ph., Schoutens, W. (2008) General lower bounds for arithmetic Asian option prices.Applied Mathematical Finance,15, 123–149) have proposed model-independent lower bounds for arithmetic Asian options. In this paper we provide an alternative and more elementary derivation of their results. We use the bounds as control variates to develop a simple Monte Carlo method for pricing contracts with Asian-style features. The conditioning idea that is inherent in our approach also inspires us to propose a new semi-analytic pricing approach. We compare both approaches and conclude that these both have their merits and are useful in practice. In particular, we point out that our newly proposed Monte Carlo method allows to deal with Asian-style products that appear in insurance (e.g., unit-linked contracts) in a very efficient way, and outperforms other known Monte Carlo methods that are based on control variates.

THE PRICING OF EXOTIC OPTIONS BY MONTE–CARLO SIMULATIONS IN A LÉVY MARKET WITH STOCHASTIC VOLATILITY

2003 ◽  
Vol 06 (08) ◽  
pp. 839-864 ◽  
Author(s):  
WIM SCHOUTENS ◽  
STIJN SYMENS
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stock Price ◽  
Poisson Approximation ◽  
Exotic Options ◽  
Option Prices ◽  
Compound Poisson Approximation ◽  
Black Scholes ◽  
Cliquet Options

Recently, stock price models based on Lévy processes with stochastic volatility were introduced. The resulting vanilla option prices can be calibrated almost perfectly to empirical prices. Under this model, we will price exotic options, like barrier, lookback and cliquet options, by Monte–Carlo simulation. The sampling of paths is based on a compound Poisson approximation of the Lévy process involved. The precise choice of the terms in the approximation is crucial and investigated in detail. In order to reduce the standard error of the Monte–Carlo simulation, we make use of the technique of control variates. It turns out that there are significant differences with the classical Black–Scholes prices.

scholarly journals Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xuemei Gao ◽  
Dongya Deng ◽  
Yue Shan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stochastic Volatility ◽  
Least Square ◽  
Two Dimensional ◽  
Stochastic Volatility Models ◽  
Lattice Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Volatility Models

The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999) for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.

scholarly journals STRONG CONVERGENCE FOR EULER–MARUYAMA AND MILSTEIN SCHEMES WITH ASYMPTOTIC METHOD

2014 ◽  
Vol 17 (02) ◽  
pp. 1450014 ◽  
Author(s):  
HIDEYUKI TANAKA ◽  
TOSHIHIRO YAMADA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Strong Convergence ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Convergence Results ◽  
Multi Level ◽  
Alpha Beta ◽  
Sabr Model ◽  
Theoretical Results

Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results can be applied to analyze the multi-level Monte Carlo method originally developed by M.B. Giles. Several numerical experiments for the stochastic alpha-beta-rho (SABR) model of stochastic volatility are presented in order to confirm the efficiency of the schemes.

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