Hedging effectiveness under conditions of asymmetry

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail-specific metrics, for example, value at risk, to compare the hedging effectiveness of short and long hedgers. Comparisons are applied to a number of hedging strategies including OLS and both symmetric and asymmetric generalised autoregressive conditional heteroskedastic models. We apply our analysis to a dataset consisting of S&P500 index cash and futures containing symmetric and asymmetric return distributions chosen ex post. Our findings show that asymmetry reduces out-of-sample hedging performance and that significant differences occur in hedging performance between short and long hedgers.     

Static hedges for reverse barrier options with robustness against skew risk: an empirical analysis

We conduct an empirical evaluation of a static super-replicating hedge of barrier options. The hedge is robust to uncertainty about the future skew. Using almost seven years of current data on the DAX, we evaluate the performance of the hedge and compare it with those of both a dynamic and a static replicating hedge. The main result is that the robustness of the static super-replicating portfolio is also empirically confirmed in practice such that the hedge sets an upper bound for the price of skew risk for barrier options.     

The pricing of basket-spread options

Since the pioneering paper of Black and Scholes was published in 1973, enormous research effort has been spent on finding a multi-asset variant of their closed-form option pricing formula. In this paper, we generalize the Kirk [Managing Energy Price Risk, 1995] approximate formula for pricing a two-asset spread option to the case of a multi-asset basket-spread option. All the advantageous properties of being simple, accurate and efficient are preserved. As the final formula retains the same functional form as the Black–Scholes formula, all the basket-spread option Greeks are also derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark results obtained by numerical integration or Monte Carlo simulation with 10 million paths. An implicit correction method is further applied to reduce the pricing errors by factors of up to 100. The correction is governed by an unknown parameter, whose optimal value is found by solving a non-linear equation. Owing to its simplicity, the computing time for simultaneous pricing and hedging of basket-spread option with 10 underlying assets or less is kept below 1 ms. When compared against the existing approximation methods, the proposed basket-spread option formula coupled with the implicit correction turns out to be one of the most robust and accurate methods.     

The fair value of guaranteed annuity options

We discuss the fair valuation of Guaranteed Annuity Options, i.e. options providing the right to convert deferred survival benefits into annuities at fixed conversion rates. The use of doubly stochastic stopping times and of affine processes provides great computational and analytical tractability, while enabling to set up a very general valuation framework. For example, the valuation of options on traditional, unit-linked or indexed annuities is encompassed. Moreover, security and reference fund prices may feature stochastic volatility or discontinuous dynamics. The longevity risk is also taken into account, by letting the evolution of mortality present stochastic dynamics subject not only to random fluctuations but also to systematic deviations.     

Corporate risk management and firm value: evidence from the UK market

The paper evaluates the effect of corporate risk management activities on firm value, using a sample of large UK non-financial firms. Following recent changes in financial reporting standards, we are able to collect detailed information on risk management activities from audited financial reports. This enables us to gain a better understanding of risk management practices and to investigate value implications of different types of hedging. Overall 86.88% of the firms in the sample use derivatives to manage at least one type of price risk. The hedging premium is statistically and economically significant for foreign currency derivative users, while we provide weak evidence that interest rate hedging increases firm value. The extent of hedging and the hedging horizon have an impact on the hedging premium, whereas operational risk management activities do not significantly influence the market value of the firm.     

The Fundamental Theorem of Derivative Trading - exposition,extensions and experiments

When estimated volatilities are not in perfect agreement with reality, delta-hedged option portfolios will incur a non-zero profit-and-loss over time. However, there is a surprisingly simple formula for the resulting hedge error, which has been known since the late 1990s. We call this The Fundamental Theorem of Derivative Trading. This paper is a survey with twists on that result. We prove a more general version of it and discuss various extensions and applications, from incorporating a multi-dimensional jump framework to deriving the Dupire–Gyöngy–Derman–Kani formula. We also consider its practical consequences, both in simulation experiments and on empirical data, thus demonstrating the benefits of hedging with implied volatility.     

The Optimal Construction of Internationally Diversified Equity Portfolios Hedged Against Exchange Rate Uncertainty

Much of the empirical work on hedging exchange rate exposure in portfolios of financial assets has used a unitary hedge ratio, or a currency overlay. Alternatively, the currencies themselves can be treated as assets and the position in them optimized. This study empirically tests whether the ex post results of recent studies, which conclude that currencies should themselves be optimized, stand up under parameter uncertainty. It may very well be that ex ante, when parameter inputs must be estimated from historical data, the attempt to determine the optimal currency weights results in inferior performance in comparison to using a simple unitary hedging strategy, or even unhedged international investment. The results suggest that a local currency return unitary hedging strategy works best in the presence of parameter uncertainty.     

The generalized value at risk admissible set: constraint consistency and portfolio outcomes

Generalized value at risk (GVaR) adds a conditional value at risk or censored mean lower bound to the standard value at risk and considers portfolio optimization problems in the presence of both constraints. For normal distributions the censored mean is synonymous with the statistical hazard function, but this is not true for fat-tailed distributions. The latter turn out to imply much tighter bounds for the admissible portfolio set and indeed for the logistic, an upper bound for the portfolio variance that yields a simple portfolio choice rule. The choice theory in GVaR is in general not consistent with classic Von Neumann–Morgenstern utility functions for money. A re-specification is suggested to make it so that gives a clearer picture of the economic role of the respective constraints. This can be used analytically to explore the choice of portfolio hedges.     

Hedging Multiperiod Forward Commitments: The Case of Period-by-Period Quantity Uncertainty

This article considers the hedging problem of a producer with along-term forward commitment to deliver a commodity at multiple futurepoints in time. The aggregate quantity to be delivered over time is knownwith certainty; however, the period-by-period quantity is determined bythe customer and is unknown to the producer. A minimum-variancemultiperiod futures position that considers both price uncertainty andperiod-by-period quantity uncertainty is derived. The following resultsare obtained: The individual effects of price uncertainty and quantityuncertainty on the multiperiod minimum-variance are separable. In thetwo-period case, if the spot price is expected to decrease over time, therisk-minimizing hedge considering both price and quantity uncertaintiesis greater than that which considers price uncertainty only. If the spotprice is expected to increase over time, then the hedger would beover-hedged if only price uncertainty were considered. Convenience yieldpromotes a larger risk-minimizing futures position, whereas storage costsand financial costs reduce the size of the risk-minimizing futuresposition. In the multiperiod case, if forward prices are unbiasedestimators of future spot prices, or if spot prices are expected todecrease over time, then quantity uncertainty increases the size of therisk-minimizing hedge. If spot prices are expected to increase, then theeffect of period-by-period quantity uncertainty isindeterminate.     

长寿风险对寿险和年金产品定价的对冲效应研究

作为老龄社会的重要风险,长寿风险专题研究是近20年来公共养老金领域、保险公司关注的热点。长寿风险引发的保险公司寿险产品定价高估和年金产品定价低估之间存在潜在的自然对冲效应。为了量化这种对冲效应的长期影响,本文基于构建的同时涵盖低龄、高龄和超高龄在内的整个生命跨度的全年龄人口动态死亡率模型,采用对冲弹性量化终身寿险与终身年金、两全保险与定期年金、递延寿险与递延年金三类保障型寿险产品和养老型年金产品对冲效应的动态演变,并通过敏感性分析扩展探讨利率变化对对冲效应的长期影响。研究发现,从单位寿险和年金产品组合的净对冲效应来看,由于保险公司的产品定价区分了性别差异,使得女性的对冲效应更明显,因而女性对应的产品组合中的长寿风险对保险公司的影响更不显著。作为系统性风险,利率风险和长寿风险也存在对冲,利率上升能抵消或对冲长寿风险的影响,低利率下长寿风险更显著。     

寿险资金运用的风险限额管理

资金运用风险是寿险公司面临的两大最主要风险之一,加强资金运用风险管理对确保寿险公司持续稳健经营至关重要。风险限额管理作为风险管理的核心内容,是风险管理体系中不可或缺的组成部分。建立一个科学、可操作和有效的风险限额管理体系,为寿险资金运用风险管理提供控制标准,是决定风险管理成效的关键环节。本文借鉴风险限额分配模型,总结寿...     

(Non-)robustness of maximum likelihood estimators for operational risk severity distributions

The quality of operational risk data sets suffers from missing or contaminated data points. This may lead to implausible characteristics of the estimates. Outliers, especially, can make a modeler's task difficult and can result in arbitrarily large capital charges. Robust statistics provides ways to deal with these problems as well as measures for the reliability of estimators. We show that using maximum likelihood estimation can be misleading and unreliable assuming typical operational risk severity distributions. The robustness of the estimators for the Generalized Pareto distribution, and the Weibull and Lognormal distributions is measured considering both global and local reliability, which are represented by the breakdown point and the influence function of the estimate.     

A Critique of Revised Basel II

This paper critiques the revised Basel II capital requirements for banks. To provide a framework for analysis, the XYZ theory of regulatory capital is formulated. Independent of the XYZ theory, we argue that the revised Basel II capital rule for credit risk is not a good approximation to the ideal rule. Based on this, and using the XYZ theory, we argue that: (1) the revised Basel II rules should not replace the existing approaches for determining minimal capital standards, but should be used in conjunction with them, and (2) that calibrating the capital rules to maintain aggregate market capital is a prudent procedure.     

On the economics of the longevity risk transfer market

We present a model of a longevity risk transfer market with different market players (primary insurers, reinsurers, and capital market investors) and investigate how market dynamics and the market players' roles evolve with progressing market saturation. We find that reinsurers' appetite for longevity risk is the key driver in the early stage of market development. Since diversification benefits with other businesses decrease with every transaction, the reinsurance market is intrinsically antimonopolistic. With the increasing saturation of the reinsurance sector as a whole, its competitiveness shrinks leading to rising expected risk-adjusted returns for capital market investors. We show that in a saturated market, reinsurers should assume the entire longevity risk from primary insurers, diversify it within their business mix, and subsequently pass on only specific (nondiversifiable) components of the longevity risk to the capital markets. Our findings provide valuable suggestions on how to make the best use of the market's limited risk absorption capacity.