Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement

@article{Hong2017KernelSF,
  title={Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement},
  author={L. Jeff Hong and Sandeep Juneja and Guangwu Liu},
  journal={Oper. Res.},
  year={2017},
  volume={65},
  pages={657-673}
}
Nested estimation involves estimating an expectation of a function of a conditional expectation via simulation. This problem has of late received increasing attention amongst researchers due to its broad applicability particularly in portfolio risk measurement and in pricing complex derivatives. In this paper, we study a kernel smoothing approach. We analyze its asymptotic properties, and present efficient algorithms for practical implementation. While asymptotic results suggest that the kernel… 
View via Publisher
personal.cb.cityu.edu.hk
29 Citations
Highly Influential Citations
2
Background Citations
10
Methods Citations
14
Results Citations
2

Figures and Tables from this paper

29 Citations

Portfolio risk measurement via stochastic mesh
TLDR
It is established that the stochastic mesh estimator is asymptotically unbiased and consistent, and its mean squared error (MSE) converges to zero in a rate of Γ−1, where Γ is the effort required to simulate the sample paths.
Sample Recycling for Nested Simulation with Application in Portfolio Risk Measurement
Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level…
Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions
TLDR
A new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable is proposed and can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases.
A least-squares Monte Carlo approach to the estimation of enterprise risk
The estimation of enterprise risk for financial institutions entails a reevaluation of the company’s assets and liabilities at some future point in time for a (large) number of stochastic forecasts…
EFFICIENT NESTED SIMULATION OF TAIL RISK MEASURES
TLDR
The numerical results show that IANS can be an order of magnitude more accurate that a standard nested simulation procedure, called Importance-Allocated Nested Simulation (IANS), for tail risk estimation.
A NESTED SIMULATION OPTIMIZATION APPROACH FOR PORTFOLIO SELECTION
TLDR
A nested simulation optimization approach to solve the problem of portfolio selection with risk factors, where the goal is to select the portfolio position that minimizes the value at risk (VaR) of the expected portfolio loss.
A Nested Simulation Optimization Approach for Portfolio Selection
TLDR
A nested simulation optimization approach to solve the problem of portfolio selection with risk factors, where the goal is to select the portfolio position that minimizes the value at risk (VaR) of the expected portfolio loss.
ONLINE RISK MEASURE ESTIMATION VIA NATURAL GRADIENT BOOSTING
TLDR
A natural gradient boosting (NGBoost) approach is proposed to use to estimate the conditional probability density function of the loss (or the value) of the portfolio under the framework of offline simulation online application, and then estimate the real-time risk measures based on the conditional probabilities density function.
Online Risk Measure Estimation VIA Natural Gradient Boosting
TLDR
A natural gradient boosting (NGBoost) approach is proposed to use to estimate the conditional probability density function of the loss (or the value) of the portfolio under the framework of offline simulation online application, and then estimate the real-time risk measures based on the conditional probabilities density function.
An efficient estimation of nested expectations without conditional sampling
TLDR
This paper proposes a new Monte Carlo method using post-stratification to estimate nested expectations efficiently without taking samples of the inner random variable from the conditional distribution given the outer random variable.
...
...

References

SHOWING 1-10 OF 52 REFERENCES
Nested Simulation in Portfolio Risk Measurement
TLDR
It is shown that a relatively small number of trials in the inner step can yield accurate estimates, and how a fixed computational budget may be allocated to the inner and the outer step to minimize the mean square error of the resultant estimator is analyzed.
Risk Estimation via Regression
TLDR
A regression-based nested Monte Carlo simulation method is introduced for the estimation of financial risk and combines information from different risk factor realizations to provide a better estimate of the portfolio loss function.
Efficient Risk Estimation via Nested Sequential Simulation
TLDR
A new algorithm is proposed to estimate one risk measure, the probability of a large loss, and it is proposed that the risk estimator has a faster convergence order compared to the conventional uniform inner sampling approach.
Efficient Simulation for Risk Measurement in Portfolio of CDOs
TLDR
It is shown that a relatively small number of trials in the inner step can yield accurate estimates, and how a fixed computational budget may be allocated to the inner and the outer step to minimize the mean square error of the resultant estimator is analyzed.
Estimating the mean of a non-linear function of conditional expectation
TLDR
A nested simulation strategy to estimate the expectation of a non linear function of a conditional expectation via simulation and identify bias and optimized mean square error allocation is developed.
Variance reduction techniques for pricing American options using function approximations
Monte Carlo simulation techniques that use function approximations have been successfully applied to approximately price multi-dimensional American options. However, for many pricing problems the…
Stochastic Kriging for Efficient Nested Simulation of Expected Shortfall
TLDR
Stochastic kriging, a metamodeling technique, is used to speed up nested simulation of expected shortfall, a portfolio risk measure, and adaptively allocates more computational effort to inner-level simulation of those scenarios, which improves computational efficiency.
Regression methods for pricing complex American-style options
TLDR
A simulation-based approximate dynamic programming method for pricing complex American-style options, with a possibly high-dimensional underlying state space, and a related method which uses a single (parameterized) value function, which is a function of the time-state pair.
A Comparison of Higher-Order Bias Kernel Density Estimators
Abstract We consider many kernel-based density estimators, all theoretically improving bias from O(h 2), as the smoothing parameter h → 0, to O(h 4). Examples include higher-order kernels, variable…
Regression Methods for Stochastic Control Problems and Their Convergence Analysis
TLDR
The main idea behind the algorithms is to simulate a set of trajectories under some reference measure and to use the Bellman principle combined with fast methods for approximating conditional expectations and functional optimization.
...
...