scholarly journals Change of Measure in Midcurve Pricing

Wilmott ◽  
2020 ◽  
Vol 2020 (106) ◽  
pp. 76-81 ◽  
Author(s):  
Konstantin Feldman
Keyword(s):  
Change Of Measure

scholarly journals Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting

1999 ◽  
Vol 29 (2) ◽  
pp. 197-214 ◽  
Author(s):  
Rudolf Grübel ◽  
Renate Hermesmeier
Keyword(s):  
Numerical Evaluation ◽  
Change Of Measure ◽  
Exponential Tilting ◽  
Transform Methods ◽  
Compound Distributions ◽  
Heavy Tailed Distributions ◽  
Panjer Recursion ◽  
Heavy Tailed ◽  
Suitable Change

AbstractNumerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy-tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.

Computing Risk Measures of Life Insurance Policies through the Cox–Ross–Rubinstein Model

2018 ◽  
Keyword(s):  
Monte Carlo ◽  
Life Insurance ◽  
Risk Measures ◽  
Probability Measures ◽  
Time Interval ◽  
Change Of Measure ◽  
Insurance Policies ◽  
Straightforward Application ◽  
The Monte Carlo Method ◽  
Remaining Time

The problem of computing risk measures of life insurance policies is complicated by the fact that two different probability measures, the real-world probability measure along the risk horizon and the risk-neutral one along the remaining time interval, have to be used. This implies that a straightforward application of the Monte Carlo method is not available and the need arises to resort to time consuming nested simulations or to the least squares Monte Carlo approach. We propose to compute common risk measures by using the celebrated binomial model of Cox, Ross, and Rubinstein (1979) (CRR). The main advantage of this approach is that the usual construction of the CRR model is not influenced by the change of measure and a unique lattice can be used along the whole policy duration. Numerical results highlight that the proposed algorithm computes highly accurate values.

scholarly journals Evaluating Scale Functions of Spectrally Negative Lévy Processes

2008 ◽  
Vol 45 (01) ◽  
pp. 135-149 ◽  
Author(s):  
B. A. Surya
Keyword(s):  
Numerical Method ◽  
Numerical Computation ◽  
Numerical Algorithm ◽  
Levy Process ◽  
Scale Function ◽  
Esscher Transform ◽  
Change Of Measure ◽  
Scale Functions ◽  
Spectrally Negative Lévy Process ◽  
Spectrally Negative Lévy Processes

In this paper we present a robust numerical method to compute the scale function W (q)(x) of a general spectrally negative Lévy process (X, P). The method is based on the Esscher transform of measure Pν under which X is taken and the scale function is determined. This change of measure makes it possible for the scale function to be bounded and, hence, makes numerical computation easy, fast, and stable. Working under the new measure Pν and using the method of Abate and Whitt (1992) and Choudhury, Lucantoni, and Whitt (1994), we give a fast stable numerical algorithm for the computation of W (q)(x).

scholarly journals A Change of Measure Formula for Recursive Conditional Expectations

2021 ◽  
Author(s):  
Luca di Persio ◽  
Alessandro Gnoatto ◽  
Marco Patacca
Keyword(s):  
Change Of Measure ◽  
Conditional Expectations
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