scholarly journals Nonparametric Malliavin–Monte Carlo Computation of Hedging Greeks

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 120
Author(s):  
Maria Elvira Mancino ◽  
Simona Sanfelici
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Finite Difference ◽  
Finite Difference Method ◽  
The Other ◽  
Monte Carlo Computation ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Discontinuous Payoffs ◽  
Weight Method

We propose a way to compute the hedging Delta using the Malliavin weight method. Our approach, which we name the λ-method, generally outperforms the standard Monte Carlo finite difference method, especially for discontinuous payoffs. Furthermore, our approach is nonparametric, as we only assume a general local volatility model and we substitute the volatility and the other processes involved in the Greek formula with quantities that can be nonparametrically estimated from a given time series of observed prices.

Analytical approximation for spread option pricing in local volatility model

2017 ◽  
Vol 04 (04) ◽  
pp. 1750022
Author(s):  
Ying Yang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Analytical Approximation ◽  
Second Order ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Spread Option

This paper introduces a methodology of analytical approximation in general European option-pricing case based on local volatility model and then apply it to price a European Spread Option. The approximation procedure is flexible in pricing financial derivatives with any form of volatility, drift rate, risk-free rate and payoff function. We also work out the explicit pricing formula up to the second-order approximation of spread option which is good-fitting compared with finite difference method and Monte Carlo simulation. The relative error compared to finite difference method is no more than 5%, which attests to the accuracy of our second-order closed-form formulas.

scholarly journals A note on stochastic volatility model estimation

2019 ◽  
Vol 17 (4) ◽  
pp. 22
Author(s):  
Omar Abbara ◽  
Mauricio Zevallos
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Parameter Estimates ◽  
Model Estimation ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Monte Carlo Evaluation

<p>The paper assesses the method proposed by Shumway and Stoffer (2006, Chapter 6, Section 10) to estimate the parameters and volatility of stochastic volatility models. First, the paper presents a Monte Carlo evaluation of the parameter estimates considering several distributions for the perturbations in the observation equation. Second, the method is assessed empirically, through backtesting evaluation of VaR forecasts of the S&amp;P 500 time series returns. In both analyses, the paper also evaluates the convenience of using the Fuller transformation.</p>

scholarly journals BAYESIAN INFERENCE OF STOCHASTIC VOLATILITY MODEL BY HYBRID MONTE CARLO

2009 ◽  
Vol 18 (08) ◽  
pp. 1381-1396 ◽  
Author(s):  
TETSUYA TAKAISHI
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Stochastic Volatility ◽  
Metropolis Algorithm ◽  
Stochastic Volatility Model ◽  
Financial Data ◽  
Stock Index ◽  
Hybrid Monte Carlo ◽  
Volatility Model

The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we compute parameters of the SV model by using the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC algorithm decorrelates the volatility variables faster than the Metropolis algorithm. Second we make an empirical study for the time series of the Nikkei 225 stock index by the HMC algorithm. We find the similar correlation behavior for the sampled data to the results from the artificial financial data and obtain a ϕ value close to one (ϕ ≈ 0.977), which means that the time series has the strong persistency of the volatility shock.

Boundary-layer flow between nodal and saddle points of attachment

1970 ◽  
Vol 41 (4) ◽  
pp. 823-835 ◽  
Author(s):  
J. C. Cooke ◽  
A. J. Robins
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Saddle Point ◽  
Difference Method ◽  
Series Solution ◽  
Nodal Point ◽  
Saddle Points ◽  
The Other ◽  
The Finite Difference Method ◽  
Layer Flow

A simplified example of this type of flow was examined in detail by developing two series, eventually matched, one about the nodal point and the other about the saddle point, and also by finite differences, marching from the nodal point to the saddle point. It was found that the results of marching the two series were in agreement with the finite difference method. The series solution near the saddle point is not unique, but numerical evidence indicates that the correct solution is that which has ‘exponential decay’ at infinity, and that this type of solution, if such exists, automatically emerges when the finite difference method is used.

scholarly journals CAM Stochastic Volatility Model for Option Pricing

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Wanwan Huang ◽  
Brian Ewald ◽  
Giray Ökten
Keyword(s):  
Monte Carlo ◽  
Characteristic Function ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
The Other ◽  
Stochastic Volatility Models ◽  
Control Variate ◽  
Volatility Models ◽  
Volatility Model ◽  
Cam Model

The coupled additive and multiplicative (CAM) noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks) of the model. We also derive an approximation for the characteristic function of the model.

Influence of Rotational Speed on Thermal Performance of Tri-Sector Rotary Regenerative Air Preheater

2016 ◽  
Author(s):  
Xun Chen ◽  
Xue-nong Duan ◽  
Li-min Wang ◽  
Yi Yang ◽  
Dun-dun Wang ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Rotational Speed ◽  
The Other ◽  
Heating Period ◽  
Height Range ◽  
Rotational Angle ◽  
Air Preheater ◽  
Deposition Area

This paper provides a detailed analysis of how a rotary regenerative air preheater’s performance parameters such as effectiveness, fluid and metal temperature fields, and ammonium bisulfate (ABS) deposition area vary with rotor rotational speed. A tri-sector rotary regenerative air preheater for a 600MW unit was studied as an example by use of effectiveness–modified number of transfer units (ε-NTU0) method and a finite difference method. The findings of the research are as follows: (1) There is a nonlinear relationship between matrix temperature distribution and rotational angle, and the degree of nonlinearity, represented by unsteady heat transfer correction factor Π, increases with decreasing rotational speed and varies between sectors; (2) There exist two equilibrium positions around the intersection points of matrix temperature curves for different rotational speeds, one occurring in the heating period and the other in the cooling period; (3) The act of reducing the rotor speed has two effects on ABS deposition. On the one hand, the height range of possible ABS deposition area will expand as the matrix temperature within the first third of gas sector’s angle range further decreases with decreasing rotational speed. On the other hand, after the rotational speed falls below a certain level, the hot-end matrix temperature climbs above the ABS formation temperature during part of the heating period, resulting in gasification and decomposition of the condensed product. The combined effect is yet to be examined through further theoretical and empirical analyses. (4) The trends of average outlet temperatures of primary and secondary air depend on rotor rotation direction and angles of sectors. (5) The effectiveness values calculated by ε-NTU0 method are greater than those acquired by the finite difference method, especially at low rotor rotational speeds.

scholarly journals Numerical analyses of embankment dams containing plastic concrete cut-off walls using finite difference method (A case study: The Karkheh Embankment Dam)

2021 ◽  
Vol 9 (3) ◽  
pp. 143-153
Author(s):  
Yadolah Pashang Pisheh ◽  
Seyd Majdeddin Mir Mohammad Hosseini
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
The Other ◽  
Numerical Analyses ◽  
Maximum Magnitude ◽  
Embankment Dam ◽  
Plastic Concrete ◽  
Clay Core

In this paper, numerical analyses have been performed on the Karkheh embankment dam with a clayey core and plastic concrete cut-off wall during construction, impounding, and permanent seepage stages. The dam has 127 meters height and is located in a high seismic hazard zone in Iran. Different stages of construction, water impounding, and steady state seepage were modelled and analyzed using the hyperbolic and Mohr-Coulomb models with the two dimensional finite difference method (FDM). So, nonlinear analyses were performed using FLAC 2D to investigate the settlements and the pore water pressure changes in different zones of the dam during above-mentioned stages and the results were compared to those of the other studies. The results show that at the end of the construction stage, the maximum settlement equal to 1.45m occurs inside the clay core at the height of 65m. Then, after impounding of the reservoir and steady state stage, the maximum magnitude of the horizontal deformations occurs in the downstream of the dam equal to 0.55m; however, these magnitudes reach to 0.17m at the crest of the dam. Moreover, it was shown that the maximum horizontal displacement of the plastic concrete cut-off wall has happened at the top of the wall in the clay core which is in a good agreement with the other studies’ result.

Influence of Deformations Prior to Instability on the Dynamic Instability of Conical Shells Under Periodic Axial Load

1976 ◽  
Vol 43 (1) ◽  
pp. 87-91 ◽  
Author(s):  
J. Tani
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Axial Load ◽  
Basic Equation ◽  
Natural Frequencies ◽  
Dynamic Instability ◽  
Forced Vibrations ◽  
The Other ◽  
Conical Shells ◽  
Instability Regions

The dynamic instability of clamped, truncated conical shells under periodic axial load is studied using the Donnell-type basic equation and considering the effect of bending deformations before instability. Two principal instability regions are determined by combining Bolotin’s method and a finite-difference method. One of these belongs to double the natural frequencies of asymmetrical vibration; the other corresponds to the resonance of symmetrically forced vibrations. The effects of static axial load and end-plate mass on the principal instability regions are also investigated.

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