Innovations in Insurance, Risk- and Asset Management

The following sections are included:

• Foreword
• Preface
• About the Editors
• Contents

Behavioral risk affects the pricing of assets and liabilities with embedded pre-payment/extension options whenever the option holder does not act purely on the strength of financial convenience but follows an uncertain and sub-optimal exercise strategy, if seen from the viewpoint of the option seller. Such behavior is particularly relevant for mortgage valuation, since mortgage prepayments are clearly influenced by exogenous and individual factors besides financial reasons. In this paper we apply the general framework, proposed by Bissiri and Cogo, for modeling behavioral risk to the particular case of the valuation of a fixed-rate mortgage portfolio. We also extend the formulas by considering a pool of heterogeneous mortgagors, leading to the introduction of specific behavioral risk adjustments (βVA) in the pricing formulas.

We examine credit value adjustment (CVA) estimation under wrong-way risk (WWR) by computing the expected positive exposure (EPE) under an equivalent measure as suggested in [1], adjusting the drift of the underlying for default risk. We apply this technique to European put and call options and derive the analytic formulas for EPE under WWR obtained with various approximations of the drift adjustment. We give the results of numerical experiments based on 4 parameter sets, and supply figures of the CVA based on both of the suggested proxys, comparing with CVA based on a 2D-Monte Carlo scheme and Gaussian Copula resampling. We also show the CVA obtained by the formulas from Basel III. We observe that the Basel III formula does not account for the credit-market correlation, while the Gaussian Copula resampling method estimates a too large impact of this correlation. The two proxies account for the credit-market correlation, and give results that are mostly similar to the 2D-Monte Carlo results.

A current market-practice to incorporate multivariate defaults in global risk-factor simulations is the iteration of (multiplicative) i.i.d. survival indicator increments along a given time-grid, where the indicator distribution is based on a copula ansatz. The underlying assumption is that the behavior of the resulting iterated default distribution is similar to the one-shot distribution. It is shown that in most cases this assumption is not fulfilled and furthermore numerical analysis is presented that shows sizable differences in probabilities assigned to both “survival-of-all” and “mixed default/survival” events. Moreover, the classes of distributions for which probabilities from the “terminal one-shot” and “terminal iterated” distribution coincide are derived for problems considering “survival-of-all” events as well as “mixed default/survival” events. For the former problem, distributions must fulfill a lack-of-memory type property, which is, e.g., fulfilled by min-stable multivariate exponential distributions. These correspond in a copula-framework to exponential margins coupled via extreme-value copulas. For the latter problem, while looping default inspired multivariate Freund distributions and more generally multivariate phase-type distributions could be a solution, under practically relevant and reasonable additional assumptions on portfolio rebalancing and nested distributions, the unique solution is the Marshall–Olkin class.

When calculating Credit Valuation Adjustment (CVA), the interaction between the portfolio’s exposure and the counterparty’s credit worthiness is referred to as Wrong-Way Risk (WWR). Making the assumption that the Brownian motions driving both the market (exposure) and the (counterparty) credit risk-factors dynamics are correlated represents the simplest way of modeling the dependence structure between these two components. For many practical applications, however, such an approach may fail to account for the right amount of WWR, thus resulting in misestimates of the portfolio’s CVA. We present a modeling framework where a further — and indeed stronger — source of market/credit dependence is introduced through devaluation jumps on the market risk–factors’ dynamics. Such jumps happen upon the counterparty’s default and are a particularly realistic feature to include in case of sovereign or systemically important counterparties. Moreover, we show that, in the special case where the focus is on FX/credit WWR, devaluation jumps provide an effective way of incorporating market information coming from quanto Credit Default Swap (CDS) basis spreads and we derive the corresponding CVA pricing equations as a system of coupled PDEs.

In the 12 months from the middle of June 2016 to the middle of June 2017, a number of events occurred in a relatively short period of time, all of which either had, or had the potential to have, a considerably volatile impact upon financial markets.

The events referred to here are the Brexit referendum (23 June 2016), the US election (8 November 2016), the 2017 French elections (23 April and 7 May 2017) and the surprise 2017 UK parliamentary election (8 June 2017).

All of these events—the Brexit referendum and the Trump election in particular—were notable both for their impact upon financial markets after the event and the degree to which the markets failed to anticipate these events. A natural question to ask is whether these could have been predicted, given information freely available in the financial markets beforehand. In this paper, we focus on market expectations for price action around Brexit and the Trump election, based on information available in the traded foreign exchange options market.

Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [1], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a heavy-tailed context (in particular when our data are described by a Pareto distribution, as is common in much of extreme value theory), the theory of [1] is insufficient, and requires an additional regularization step which we introduce. By asking whether this regularization is possible, we obtain a qualitative requirement for reliable estimation of tail quantities and risk measures, in a Pareto setting.

Monetary risk measures classify a financial position by the minimal amount of external capital that must be added to the position to make it acceptable.

We propose a new concept: intrinsic risk measures. The definition via external capital is avoided and only internal resources appear. An intrinsic risk measure is defined by the smallest percentage of the currently held financial position which has to be sold and reinvested in an eligible asset such that the resulting position becomes acceptable.

We show that this approach requires less nominal investment in the eligible asset to reach acceptability. It provides a more direct path from unacceptable positions towards the acceptance set and implements desired properties such as monotonicity and quasi-convexity solely through the structure of the acceptance set. We derive a representation on cones and a dual representation on convex acceptance sets and we detail the connections of intrinsic risk measures to their monetary counterparts.

Based on the theory of multivariate time changes for Markov processes, we show how to identify affine processes as solutions of certain time change equations. The result is a strong version of a theorem presented by J. Kallsen in [1] which provides a representation in law of an affine process as a time–change transformation of a family of independent Lévy processes. This also leads to a new perspective on strong approximations for affine processes.

The traditional fixed-income asset class has generated very low returns in recent years. Furthermore, due to long-term market trends it is arguably perceived by investors to be riskier and less diversifying than it has ever been. This has led to the emergence of new products that are designed to appeal to institutional investors in their quest for finding complementary return streams, particularly for liability driven investment (LDI). These bond-like products are often augmented with equity-like positions in investors’ portfolios in an attempt to mitigate risk and generate attractive returns. In this paper, we analyze fee structures that have emerged in the hedge fund industry. In particular, we study structures with ‘negative fees,’ which give hedge fund investments risk-return profiles that more closely resemble traditional fixed-income investments. We analyze the value and risk-return profiles of these investments, and study the incentives that the fee structures create for fund managers. In this paper we discuss how the employment of judicious fee structures in combination with suitable trading strategies can assist in accommodating the appetite of a wide range of investors. We will present a spectrum of fee structures where investors can pinpoint a region of interest which fulfills their desired payoff profile.

We consider the optimal solutions to the trade execution problem in the two different classes of i) fully adapted or adaptive and ii) deterministic or static strategies, comparing them. We do this in two different benchmark models. The first model is a discrete time framework with an information flow process, dealing with both permanent and temporary impact, minimizing the expected cost of the trade. The second model is a continuous time framework where the objective function is the sum of the expected cost and a value at risk (or expected shortfall) type risk criterion. Optimal adapted solutions are known in both frameworks from the original works of Bertsimas and Lo (1998) and Gatheral and Schied (2011). In this paper we derive the optimal static strategies for both benchmark models and we study quantitatively the improvement in optimality when moving from static strategies to fully adapted ones. We conclude that, in the benchmark models we study, the difference is not relevant, except for extreme unrealistic cases for the model or impact parameters.

Liability driven investment (LDI) strategies that take stochastic liabilities into account have become increasingly important for insurance companies and pension funds due to market developments such as low interest rates, high volatility and changes in regulatory requirements. We consider stochastic liabilities in a portfolio optimization framework and include aspects from behavioral finance, in particular cumulative prospect theory (CPT). We study LDI strategies with extended preference structures and probability distortion and derive analytical solutions for a CPT portfolio optimization problem in an LDI context. Within a case study, we compare the optimal investment strategies to existing LDI approaches within traditional frameworks such as the partial surplus optimization presented in [1] and the funding ratio optimization in an expected utility framework as introduced in [2].

In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial time series and our model covers both. To illustrate the relevance of our recommended approach, we first compare the proposed model with the well-known hidden Markov model via likelihood ratio tests and a novel goodness-of-fit test on the S&P 500 daily returns. In addition, we present out-of-sample hedging results on S&P 500 vanilla options as well as a trading strategy based on the difference between theoretical and market prices. This strategy is compared to simpler models including the classical Black-Scholes delta-hedging approach.

Following the 2008 financial crisis, the dual curve discounting method became widely used in valuing interest rate swaps denominated in major currencies, which implies the market consensus of accepting Overnight Indexed Swap rates as new proxies of risk-free rates. However, in the Chinese market, the outdated single curve discounting method is still widely used, because there is no consensus on the choice of the risk-free rate proxy. We apply the dual curve discounting method to the Chinese interest rate swap market and recommend using the 7-day fixing repo rate, a benchmark interest rate of the Chinese repo market, as the risk-free rate. Empirically, using the single curve discounting method may significantly undervalue a swap contract to the fixed rate receiver.

Omega ratios have been introduced in [1] as a performance measure to compare the performance of different investment opportunities. It does not have some of the drawbacks of the famous Sharpe ratio. In particular, it is consistent with first order stochastic dominance. Omega ratios also have an interesting relation to expectiles, which found increasing interest recently as risk measures. There is some confusion in the literature about consistency with respect to second order stochastic dominance. In this paper, we clarify this and extend it to a consistency result with respect to stochastic dominance of order 1 + γ recently introduced in [2] and generalizing the classical concepts of stochastic dominance of first and second order. Several examples illustrate the usefulness of this result. Finally, some consistency results for even more general stochastic dominance rules are shown, including the concept of ϵ-almost stochastic dominance introduced in [3].

We survey the underlying scientific concepts and aspects of the implementation of the classification of state-subsidized private German pension products into five different chance-risk classes. The topics range from the choice and calibration of the capital market model via simulation issues of various pension products to specific research topics such as the behavior of chance-risk curves or new valuation algorithms for cliquet-type options.

It is possible to base an equity derivatives pricing model on a stochastic driving process for the share price (spot), or for the equity forward. While the former is the classical approach pioneered by Black and Scholes [9], the latter approach separates the modeling of exogenous random price fluctuations from the cost-of-carry modeling of the stock, probably the first and most prominent example of this technique being the paper by Black [8]. While the Black—Scholes spot price approach and Black’s forward approach are equivalent, the present note demonstrates that the introduction of local volatility and/ or level-dependent default intensity into the stochastic driving process destroys this equivalence, if applied carelessly. The advantages and disadvantages of both approaches are discussed.

In this paper, we first present a review of statistical tools that can be used in asset management either to track financial indexes or to create synthetic ones. More precisely, we look at two important replication methods: the strong replication, where a portfolio of very liquid assets is created and the goal is to track an actual index with the portfolio, and weak replication, where a portfolio of very liquid assets is created and used to either replicate the statistical properties of an existing index, or to replicate the statistical properties of a custom asset. In addition, for weak replication, the target is not an index but a payoff, and the replication amounts to hedge the portfolio so it is as close as possible to the payoff at the end of each month. For strong replication, the main tools are predictive tools, so filtering techniques and regression play an important role. For weak replication, which is the main topic of this paper, in order to determine the target payoff, the investor has to find or choose the distribution function of the target index or custom index, as well as its dependence with other assets, and use a hedging technique. Therefore, the main tools for weak replication are modeling (estimation and goodness-of-fit) and optimal hedging. For example, an investor could wish to obtain Gaussian returns that are independent of some ETFs replicating the Nasdaq and S&P 500 indexes. In order to determine the dependence of the target and a given number of indexes, we introduce a new class of easily constructed models of conditional distributions called B-vines. We also propose to use a exible model to fit the distribution of the assets composing the portfolio and then hedge the portfolio in an optimal way. Examples are given to illustrate all the important steps required for the implementation of this new asset management methodology.