A Technical Note, Looback Options: a comparison between Monte Carlo Techniques

Looback options are path dependent contingent claims whose payoffs depend on the extrema of the underlying asset price over a certain time interval. In this note we compare the performance of two Monte Carlo techniques to price lookback options, a crude Monte Carlo estimator and Antithetic variate estimator. We find that the Antithetic estimator performs better under a variety of performance measures.

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

E-Jurnal Matematika ◽

10.24843/mtk.2018.v07.i02.p187 ◽

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.

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PENENTUAN HARGA OPSI BELI TIPE ASIA DENGAN METODE MONTE CARLO-CONTROL VARIATE

E-Jurnal Matematika ◽

10.24843/mtk.2017.v06.i01.p145 ◽

2017 ◽

Vol 6 (1) ◽

pp. 29

Author(s):

NI NYOMAN AYU ARTANADI ◽

KOMANG DHARMAWAN ◽

KETUT JAYANEGARA

Keyword(s):

Monte Carlo ◽

Standard Error ◽

Asset Price ◽

Option Price ◽

Asian Option ◽

Underlying Asset ◽

Average Value ◽

Control Variate ◽

Exercise Price ◽

Maturity Date

Option is a contract between the writer and the holder which entitles the holder to buy or sell an underlying asset at the maturity date for a specified price known as an exercise price. Asian option is a type of financial derivatives which the payoff taking the average value over the time series of the asset price. The aim of the study is to present the Monte Carlo-Control Variate as an extension of Standard Monte Carlo applied on the calculation of the Asian option price. Standard Monte Carlo simulations 10.000.000 generate standard error 0.06 and the option price convergent at Rp.160.00 while Monte Carlo-Control Variate simulations 100.000 generate standard error 0.01 and the option price convergent at Rp.152.00. This shows the Monte Carlo-Control Variate achieve faster option price toward convergent of the Monte Carlo Standar.

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Option Pricing for Path-Dependent Options with Assets Exposed to Multiple Defaults Risk

Discrete Dynamics in Nature and Society ◽

10.1155/2020/2418620 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Taoshun He

Keyword(s):

Option Pricing ◽

Default Risk ◽

Asset Price ◽

Default Time ◽

Original Technique ◽

Endogenous Default ◽

Lookback Options ◽

Option Model ◽

Analytical Formulas ◽

Path Dependent

In the present paper, we derive analytical formulas for barrier and lookback options with underlying assets exposed to multiple defaults risks which include exogenous counterparty default risk and endogenous default risk. The endogenous default risk leads the asset price drop to zero and the exogenous counterparty default risk induces a drop in the asset price, but the asset can still be traded after this default time. An original technique is developed to valuate the barrier and lookback options by first conditioning on the predefault and the afterdefault time and then obtaining the unconditional analytic formulas for their price. We also compare the pricing results of our model with the default-free option model and exogenous counterparty default risk option model.

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

Ekonomika ◽

10.15388/ekon.2005.17522 ◽

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.

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Bayesian Estimation of DSGE Models

10.23943/princeton/9780691161082.001.0001 ◽

2015 ◽

Cited By ~ 45

Author(s):

Edward P. Herbst ◽

Frank Schorfheide

Keyword(s):

Monte Carlo ◽

Sequential Monte Carlo ◽

Likelihood Function ◽

Academic Research ◽

Dynamic Stochastic General Equilibrium ◽

Computational Techniques ◽

Dsge Models ◽

Monte Carlo Techniques ◽

Dynamic Stochastic ◽

Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

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Neutron dose evaluation of Elekta Linac at two energies (10 & 18 MV) by MCNP code and comparison with experimental measurements

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v6i1.1820 ◽

2014 ◽

Vol 6 (1) ◽

pp. 1006-1015

Author(s):

Negin Shagholi ◽

Hassan Ali ◽

Mahdi Sadeghi ◽

Arjang Shahvar ◽

Hoda Darestani ◽

...

Keyword(s):

Monte Carlo ◽

Measurement Data ◽

Calculated Data ◽

High Energy ◽

Neutron Dose ◽

Dose Assessment ◽

Photon Flux ◽

Dose Equivalent ◽

Monte Carlo Techniques ◽

Neutron Dose Equivalent

Medical linear accelerators, besides the clinically high energy electron and photon beams, produce other secondary particles such as neutrons which escalate the delivered dose. In this study the neutron dose at 10 and 18MV Elekta linac was obtained by using TLD600 and TLD700 as well as Monte Carlo simulation. For neutron dose assessment in 2020 cm2 field, TLDs were calibrated at first. Gamma calibration was performed with 10 and 18 MV linac and neutron calibration was done with 241Am-Be neutron source. For simulation, MCNPX code was used then calculated neutron dose equivalent was compared with measurement data. Neutron dose equivalent at 18 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 3.3, 4, 5 and 6 cm. Neutron dose at depths of less than 3.3cm was zero and maximized at the depth of 4 cm (44.39 mSvGy-1), whereas calculation resultedÂ in the maximum of 2.32 mSvGy-1 at the same depth. Neutron dose at 10 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 2.5, 3.3, 4 and 5 cm. No photoneutron dose was observed at depths of less than 3.3cm and the maximum was at 4cm equal to 5.44mSvGy-1, however, the calculated data showed the maximum of 0.077mSvGy-1 at the same depth. The comparison between measured photo neutron dose and calculated data along the beam axis in different depths, shows that the measurement data were much more than the calculated data, so it seems that TLD600 and TLD700 pairs are not suitable dosimeters for neutron dosimetry in linac central axis due to high photon flux, whereas MCNPX Monte Carlo techniques still remain a valuable tool for photonuclear dose studies.

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Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽

10.3390/e23060662 ◽

2021 ◽

Vol 23 (6) ◽

pp. 662

Author(s):

Mateu Sbert ◽

Jordi Poch ◽

Shuning Chen ◽

Víctor Elvira

Keyword(s):

Monte Carlo ◽

Probability Distributions ◽

Stochastic Order ◽

Arithmetic Mean ◽

Stochastic Orders ◽

Arithmetic Means ◽

Increasing Convex Order ◽

Monte Carlo Techniques ◽

Multiple Importance Sampling ◽

Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

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Random Sampling Many-Dimensional Sets Arising in Control

Mathematics ◽

10.3390/math9050580 ◽

2021 ◽

Vol 9 (5) ◽

pp. 580

Author(s):

Pavel Shcherbakov ◽

Mingyue Ding ◽

Ming Yuchi

Keyword(s):

Monte Carlo ◽

Random Sampling ◽

Linear Matrix ◽

Matrix Inequalities ◽

Computational Mathematics ◽

Closed Form Solutions ◽

Monte Carlo Techniques ◽

Control Optimization ◽

Point Representation ◽

Hit And Run

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

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