Replicating Portfolio Approach to Capital Calculation

Cambou, Mathieu; Filipović, Damir

doi:10.2139/ssrn.2763733

Cited by 8 publications

(9 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, motivated by the Solvency II requirements, there has been active recent research in the area of replicating portfolios offering new approaches to link assets and liabilities (see e.g. Cambou and Filipovic, 2017a, Natolski and Werner, 2014, or Pelsser and Schweizer, 2015. Here, replication is considered in the sense of mimicking the dynamic behaviour of the liabilities as well as possible, since it is clear that there cannot be a complete replication of the liabilities by market assets.…”

Section: Illiquid Assetsmentioning

confidence: 99%

Asset-liability management for long-term insurance business

et al. 2018

View full text Add to dashboard Cite

This is a summary of the main topics and findings from the Swiss Risk and Insurance Forum 2017. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss past and current developments as well as future perspectives in dealing with asset-liability management for long-term insurance business. Topics include valuation, innovations in insurance products, investment, and modelling aspects.

show abstract

Section: Illiquid Assetsmentioning

confidence: 99%

Asset-liability management for long-term insurance business

et al. 2018

View full text Add to dashboard Cite

show abstract

“…They analyze the asymptotic behaviour of matching the terminal value of liabilities (instead of matching cash flows; see below for more details) as the number of scenarios and the number of replicating assets grows at specific relative speeds. Recently, Cambou and Filipovic [16] proved that the matching of terminal values indeed has a mathematical foundation in the sense that a good match of the terminal values is strongly intertwined with a good approximation of the risk measure of the future MCEV (i.e., the resulting risk capital). Simultaneously, Natolski and Werner [17] demonstrated that this foundation holds for any form of matching problem in Natolski and Werner [18] (and many more), especially including all cash flow matching and all terminal value matching problems considered here.…”

Section: Real World Risk Neutralmentioning

confidence: 99%

“…Simultaneously, Natolski and Werner [17] demonstrated that this foundation holds for any form of matching problem in Natolski and Werner [18] (and many more), especially including all cash flow matching and all terminal value matching problems considered here. In both Cambou and Filipovic [16] and Natolski and Werner [18], it is shown that it is possible to change from the real world measure in the first period to the risk neutral measure while maintaining the strong link between objective function and error in risk capital. These results provide the basis for the practically most relevant replication setup 1 where only the risk neutral measure is considered (see Section 2 for the mathematical setup).…”

Section: Real World Risk Neutralmentioning

confidence: 99%

Mathematical Analysis of Replication by Cash Flow Matching

Natolski

Werner

2017

Risks

View full text Add to dashboard Cite

Abstract:The replicating portfolio approach is a well-established approach carried out by many life insurance companies within their Solvency II framework for the computation of risk capital. In this note, we elaborate on one specific formulation of a replicating portfolio problem. In contrast to the two most popular replication approaches, it does not yield an analytic solution (if, at all, a solution exists and is unique). Further, although convex, the objective function seems to be non-smooth, and hence a numerical solution might thus be much more demanding than for the two most popular formulations. Especially for the second reason, this formulation did not (yet) receive much attention in practical applications, in contrast to the other two formulations. In the following, we will demonstrate that the (potential) non-smoothness can be avoided due to an equivalent reformulation as a linear second order cone program (SOCP). This allows for a numerical solution by efficient second order methods like interior point methods or similar. We also show that-under weak assumptions-existence and uniqueness of the optimal solution can be guaranteed. We additionally prove that-under a further similarly weak condition-the fair value of the replicating portfolio equals the fair value of liabilities. Based on these insights, we argue that this unloved stepmother child within the replication problem family indeed represents an equally good formulation for practical purposes.

show abstract

“…If first and second derivatives of the portfolio with respect to the underlying risk factors are accessible, the method is computationally efficient, but its accuracy depends on how well the second order Taylor polynomial approximates the true portfolio loss. Similarly, the replicating portfolio approach approximates future cashflows with a portfolio of liquid instruments that can be priced efficiently; see e.g., Wüthrich (2016), Pelsser and Schweizer (2016), Natolski and Werner (2017) or Cambou and Filipović (2018). Building on work on American option valuation (see e.g., Carriere, 1996;Longstaff and Schwartz, 2001;Tsitsiklis and Van Roy, 2001), Broadie et al (2015) as well as Ha and Bauer (2019) have proposed to regress future cash flows on finitely many basis functions depending on state variables known at the risk horizon.…”

Section: Introductionmentioning

confidence: 99%

Assessing Asset-Liability Risk with Neural Networks

Cheridito

Ery

Wüthrich

2020

Risks

View full text Add to dashboard Cite

We introduce a neural network approach for assessing the risk of a portfolio of assets and liabilities over a given time period. This requires a conditional valuation of the portfolio given the state of the world at a later time, a problem that is particularly challenging if the portfolio contains structured products or complex insurance contracts which do not admit closed form valuation formulas. We illustrate the method on different examples from banking and insurance. We focus on value-at-risk and expected shortfall, but the approach also works for other risk measures.

show abstract

Replicating Portfolio Approach to Capital Calculation

Cited by 8 publications

References 22 publications

Asset-liability management for long-term insurance business

Asset-liability management for long-term insurance business

Mathematical Analysis of Replication by Cash Flow Matching

Assessing Asset-Liability Risk with Neural Networks

Contact Info

Product

Resources

About