PRICING PARISIAN-STYLE OPTIONS WITH A LATTICE METHOD

1999 ◽  
Vol 02 (01) ◽  
pp. 1-16 ◽  
Author(s):  
MARCO AVELLANEDA ◽  
LIXIN WU
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Convertible Bonds ◽  
Barrier Option ◽  
Lattice Method ◽  
Underlying Asset

A Parisian-style barrier option expires if the price of the underlying asset remains above or below some level(s) continuously over a specified period of time (the "window"). A trinomial-lattice scheme is developed for calculating the price and the sensitivities of such options. Monte–Carlo simulation of hedging events using the resulting deltas show errors which are of the same magnitude as for hedging vanilla options, confirming the validity of proposed scheme. We use these results to price callable and convertible bonds with this "window" feature.

scholarly journals Exact Monte Carlo simulation of killed diffusions

2008 ◽  
Vol 40 (1) ◽  
pp. 273-291 ◽  
Author(s):  
Bruno Casella ◽  
Gareth O. Roberts
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Barrier Option ◽  
Double Barrier ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Theoretical Predictions ◽  
Efficient Alternative ◽  
Barrier Option Pricing

We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

scholarly journals Exact Monte Carlo simulation of killed diffusions

2008 ◽  
Vol 40 (01) ◽  
pp. 273-291 ◽  
Author(s):  
Bruno Casella ◽  
Gareth O. Roberts
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Barrier Option ◽  
Double Barrier ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Theoretical Predictions ◽  
Efficient Alternative ◽  
Barrier Option Pricing

We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

scholarly journals Valuing Derivatives in Commercial Banks of Emerging Markets - Application to Slovenian Market

Ekonomika ◽  
2005 ◽  
Vol 71 ◽  
Author(s):  
Andraž Grum
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Commercial Banks ◽  
Foreign Currency ◽  
Emerging Market ◽  
Asset Price ◽  
Underlying Asset ◽  
Pricing Options ◽  
Simulation Based ◽  
Derivative Market

In emerging market economies there is usually no institutionalised derivative market. Like in every other market-oriented economy, there exists the need for such instruments, especially in the corporate and financial sectors. In practice, the main market or position risk that a corporate sector is exposed to is the exchange rate or currency risk. The shortage of standardized derivatives is partly covered by unstandardized, tailormade derivatives issued by commercial banks to satisfy the specific needs of clients. Not surprisingly, a large portion of unstandardized derivatives issued by commercial banks comes in the type of forward agreements and I or options, with a foreign currency as the underlying asset. Because those derivatives are “tailormade”, they often have characteristics for which they can be classified as exotic derivatives. To manage efficiently the market risk, the issuer of such derivatives has to address the issue of valuation of those instruments. In practice, the most effective method of valuation of exotic derivatives has been found to be the Monte Carlo simulation based on the parametric model of the underlying asset price dynamics. Using the Monte Carlo simulation for pricing options raises several issues such as measuring the accuracy of simulated prices and determining the number of simulations required for the desired level of accuracy.

scholarly journals Cópulas Dinâmicas de Lévy e suas Aplicações no Apreçamento de Opções Multidimensionais com Dependência na Trajetória

2008 ◽  
Vol 6 (1) ◽  
pp. 69
Author(s):  
Edson Bastos e Santos ◽  
Nelson Ithiro Tanaka
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Asset Pricing ◽  
Lévy Processes ◽  
Levy Processes ◽  
Financial Assets ◽  
Lévy Measure ◽  
Underlying Asset ◽  
Price Process ◽  
Gamma Processes

This article presents an alternative to modeling multidimensional options, where the payoffs depend on the paths of the trajectories of the underlying-asset prices. The proposed technique considers Lévy processes, a very ample class of stochastic processes that allows the existence of jumps (discontinuities) in the price process of financial assets, and as a particular case, comprises the Brownian motion. To describe the dependence among Lévy processes, extending the static concepts of the ordinary copulas to the Lévy processes context, considering the Lévy measure, which characterizes the jumps behavior of these processes. A comparison between the Clayton and the Frank dynamic copulas and their impact in asset pricing of Asian type derivatives contracts is studied, considering gamma processes and Monte Carlo simulation procedures.

An Optimal Selection of the basis Functions for the Valuation of Interest Rate Structured Notes

2014 ◽  
Vol 22 (4) ◽  
pp. 637-674
Author(s):  
Hanki Seong ◽  
Sang Bin Lee
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Interest Rates ◽  
Basis Function ◽  
Basis Functions ◽  
Fixed Rate ◽  
Estimation Errors ◽  
Underlying Asset ◽  
Early Exercise ◽  
Value Estimation

This paper examines which basis functions are efficient to employ a combined method of Hull and White (1990) with the Monte Carlo simulation when we price a callable range note or a callable bond. We use the Huge and Rom-Poulsen (2007) method which has modified the least squared Monte Carlo simulation proposed by Longstaff and Schwartz (2001) to reduce the estimation errors of the continuation value or the underlying assets. To use Monte carlo Simulation for pricing the early exercise premium, it is essential to accurately estimate the continuation value, because the investors will choose the higher value between the exercise and the continuation value at the possible early exercise dates. The main purpose of this paper is to analyze the estimation errors originating from the choice of the basis functions for the underlying asset and the continuation value estimation. We choose the callable bond and the callable range accrual note to show which basis functions are reliable to reduce the estimation errors. For this purpose, we replicate the callable range accrual note with a portfolio of a fixed rate bond and a delayed digital option. We use several basis functions such as a constant, the instantaneous interest rates, and the range in order to see which basis function is efficient for our purpose. We examine several combinations of the basis functions depending on which basis functions will be used for the underlying asset or the continuation value estimation. We show that the range which is an important determinant of the callable range accrual note is an effective basis function to accurately determine the underlying asset and the continuation value for the pricing of the callable range accrual note.

scholarly journals PENENTUAN HARGA JUAL OPSI BARRIER TIPE EROPA DENGAN METODE ANTITHETIC VARIATE PADA SIMULASI MONTE CARLO

2018 ◽  
Vol 7 (2) ◽  
pp. 71
Author(s):  
LUH HENA TERECIA WISMAWAN PUTRI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
Monte Carlo ◽  
Analytic Solution ◽  
Asset Price ◽  
Selling Price ◽  
Barrier Options ◽  
Option Prices ◽  
Barrier Option ◽  
Underlying Asset ◽  
Closing Price ◽  
Path Dependent

The purpose of this research is to compare the selling price of down and out barrier option when the prices are simulated by the Antithetic Variate Monte Carlo and the standar Monte Carlo. Barrier options are path dependent options and the payoff depend on whether the underlying asset price touched the barrier or not during the life of the option. In this research, we conducted simulations against the closing price of the shares of PT Adhi Karya using Standard Monte Carlo simulation and the Monte Carlo-Antithetic Variate simulation. After the simulation, we obtained that the option prices using Antithetic Variate produces a cheaper price than the standar one. We also found that the analytic solution has a smaller error on its confidence interval compare to the Monte Carlo Standar.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

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