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Showing papers in "The Journal of Risk Finance in 2005"


Journal ArticleDOI
Joshua Abor1
TL;DR: In this article, the relationship between capital structure and profitability of listed firms on the Ghana Stock Exchange (GSE) during a five-year period was investigated, which revealed a significantly positive relation between the ratio of short-term debt to total assets and ROE.
Abstract: Purpose – This paper seeks to investigate the relationship between capital structure and profitability of listed firms on the Ghana Stock Exchange (GSE) during a five‐year period.Design/methodology/approach – Regression analysis is used in the estimation of functions relating the return on equity (ROE) with measures of capital structure.Findings – The results reveal a significantly positive relation between the ratio of short‐term debt to total assets and ROE. However, a negative relationship between the ratio of long‐term debt to total assets and ROE was found. With regard to the relationship between total debt and return rates, the results show a significantly positive association between the ratio of total debt to total assets and return on equity.Originality/value – The research suggests that profitable firms depend more on debt as their main financing option. In the Ghanaian case, a high proportion (85 percent) of the debt is represented in short‐term debt.

871 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined risk information disclosed by UK public companies within their annual reports and examined whether a relationship exists between company size or level of risk and risk disclosure totals, finding that the principal driver affecting levels of risk disclosure is company size and not company risk level.
Abstract: Purpose – This paper examines risk information disclosed by UK public companies within their annual reports. The types of risk information disclosed are analyzed and the authors examine whether a relationship exists between company size or level of risk and risk disclosure totals.Design/methodology/approach – No prior empirical studies of the risk information content of annual reports have been undertaken. To analyze the risk disclosures, a sentence‐based approach was used.Findings – Overall the results indicate that the companies sampled are not providing a complete picture of the risks they face. There is minimal disclosure of quantified risk information and a significant proportion of risk disclosures consist of generalized statements of risk policy. More usefully directors are releasing forward‐looking risk information. The principal driver affecting levels of risk disclosure is company size and not company risk level.Research limitations/implications – Further risk disclosure research is possible in ...

139 citations


Journal ArticleDOI
TL;DR: In this article, the authors compared the different factors that can determine the level of debt of firms by means of panel data methodology and concluded that the stated variables, other than reputation, can be considered to be explanatory variables of firm debt level.
Abstract: Purpose – To contrast the different factors that can determine the level of debt of firms by means of panel data methodology.Design/methodology/approach – The variables used in the study are: size, generated resources, level of warrants, debt cost, growth opportunities, and reputation. Six hypotheses are considered.Findings – The results obtained suggest that the stated variables, other than reputation, can be considered to be explanatory variables of firm debt level. Using within‐groups estimation and generalized least squares, the results suggest that the behavior of the sample throughout the study period is consistent with the fixed effects approach, in which the specific characteristics of each firm remain constant throughout time. Moreover, with respect to the six considered hypotheses, the analysis shows the influence of all stated variables except reputation on the leverage.Originality/value – Adds to the body of research that has focused on the analysis of the financial decisions of the firm, with...

68 citations


Journal ArticleDOI
Joshua Abor1
TL;DR: In this paper, the authors report on the foreign exchange risk management practices among Ghanaian firms involved in international trade and find that close to one half of the firms do not have any wellfunctioning risk management system.
Abstract: Purpose – This paper reports on the foreign exchange risk‐management practices among Ghanaian firms involved in international trade. The study focuses on how Ghanaian firms manage their foreign exchange risk and the problems involved in managing exchange rate exposure. It also seeks to ascertain the extent to which these firms use foreign exchange risk management techniques.Design/methodology/approach – Descriptive statistics were used in the presentation and analysis of empirical results.Findings – The results indicate that close to one‐half of the firms do not have any well‐functioning risk‐management system. Foreign exchange risk is mainly managed by adjusting prices to reflect changes in import prices resulting from currency fluctuation, and also by buying and saving foreign currency in advance. The main problems the firms face are the frequent appreciation of foreign currencies against the local currency and the difficulty in retaining local customers because of the high prices of imported inputs, wh...

66 citations


Journal ArticleDOI
TL;DR: In this article, a multi-objective decision problem aimed to reach goals such as maximization of liquidity, revenue, capital adequacy, and market share subject to financial, legal requirements and institutional policies.
Abstract: Purpose – An efficient asset‐liability management requires maximizing banks' profit as well as controlling and lowering various risks. This multi‐objective decision problem aims to reach goals such as maximization of liquidity, revenue, capital adequacy, and market share subject to financial, legal requirements and institutional policies. This paper models asset and liability management (ALM) in order to show how different managerial strategies affect the financial wellbeing of banks during crisis.Design/methodology/approach – A goal programming model is developed and applied to two medium‐scale Turkish commercial banks with distinct risk‐taking behavior. This article brings new evidence on the performance of emerging market banks with different managerial philosophies by comparing asset‐liability management in crisis.Findings – The study has shown how shifts in market perceptions can create trouble during crisis, even if objective conditions have not changed.Originality/value – The proposed model can pro...

59 citations


Journal ArticleDOI
TL;DR: Analyzes the shortcomings of various measures of risk, and group decision making, which was not addressed in developing Prospect Theory and Cumulative Prospect Theory, and develops a mew model for decision making and risk named “belief systems”, which differentiates it from belief networks.
Abstract: Purpose – To: evaluate Prospect Theory and Cumulative Prospect Theory as functional models of decision making and risk within various contexts; compare and analyze risk models and decision‐making models; evaluate models of stock risk developed by Robert Engle and related models; establish whether the models are related and have the same foundations; relate risk, decision making and options theory; and develop the foundations for a new model of decision making and risk named “belief systems”.Design/methodology/approach – Critiques existing academic work in different contexts. Analyzes the shortcomings of various measures of risk, and group decision making, which was not addressed in developing Prospect Theory and Cumulative Prospect Theory. Develops the characteristics of a mew model for decision making and risk named “belief systems”, and then differentiates it from belief networks.Findings – Decision making is a multi‐factor, multi‐dimensional process that often requires the processing of information, an...

45 citations


Journal ArticleDOI
TL;DR: In this article, a generalization of the familiar two-sample t-test for equality of means to the case where the sample values are to be given unequal weights is presented, where some samples are considered more reliable than others in predicting a common mean.
Abstract: Purpose – The purpose of this paper is to describe a generalization of the familiar two‐sample t‐test for equality of means to the case where the sample values are to be given unequal weights. This is a natural situation in financial risk modeling when some samples are considered more reliable than others in predicting a common mean. We also describe an example with real credit data showing that ignoring this modification of the two‐sample test can lead to the wrong statistical conclusion.Design/methodology/approach – We follow the analysis of the classical two‐sample tests in the more general situation of weighted means. We also test our methods against some market data to assess the importance of the findings.Findings – We formulate some explicit test statistics that should be used when the sample values are to be assigned differing known weights. Different cases are presented depending on how much is known about the variances. In the most typical case (the unpooled two‐sample test), we approximate the ...

44 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of Knightian uncertainty in the evaluation of value-at-risk (VaR) of financial investments is studied. And the authors develop methods for augmenting existing VaR estimates to account for the uncertainty of the future size and shape of the lower tail of the PDF.
Abstract: Purpose – To study the effect of Knightian uncertainty – as opposed to statistical estimation error – in the evaluation of value‐at‐risk (VaR) of financial investments. To develop methods for augmenting existing VaR estimates to account for Knightian uncertainty.Design/methodology/approach – The value at risk of a financial investment is assessed as the quantile of an estimated probability distribution of the returns. Estimating a VaR from historical data entails two distinct sorts of uncertainty: probabilistic uncertainty in the estimation of a probability density function (PDF) from historical data, and non‐probabilistic Knightian info‐gaps in the future size and shape of the lower tail of the PDF. A PDF is estimated from historical data, while a VaR is used to predict future risk. Knightian uncertainty arises from the structural changes, surprises, etc., which occur in the future and therefore are not manifested in historical data. This paper concentrates entirely on Knightian uncertainty and does not ...

40 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigate the accuracy of parametric, nonparametric, and semiparametric methods in predicting the one-day-ahead value-at-risk (VaR) measure in three types of markets (stock exchanges, commodities, and exchange rates), both for long and short trading positions.
Abstract: Purpose – Aims to investigate the accuracy of parametric, nonparametric, and semiparametric methods in predicting the one‐day‐ahead value‐at‐risk (VaR) measure in three types of markets (stock exchanges, commodities, and exchange rates), both for long and short trading positions.Design/methodology/approach – The risk management techniques are designed to capture the main characteristics of asset returns, such as leptokurtosis and asymmetric distribution, volatility clustering, asymmetric relationship between stock returns and conditional variance, and power transformation of conditional variance.Findings – Based on back‐testing measures and a loss function evaluation method, finds that the modeling of the main characteristics of asset returns produces the most accurate VaR forecasts. Especially for the high confidence levels, a risk manager must employ different volatility techniques in order to forecast accurately the VaR for the two trading positions.Practical implications – Different models achieve acc...

33 citations


Journal ArticleDOI
TL;DR: In this paper, a multi-criteria model is proposed to determine an appropriate equity risk premium, and thereby, a cost of capital for small businesses, which is an alternative to traditional proxy approaches.
Abstract: Purpose – For publicly traded firms, calculating the cost of capital is predicated typically on information from the financial markets. Small businesses do not have the necessary market‐based information. As an alternative to traditional proxy approaches, this paper argues for a multi‐criteria model to determine an appropriate equity risk premium, and thereby, a cost of capital.Design/methodology/approach – The study proposes a multi‐criteria model – an analytical hierarchy process (AHP) – to determine the cost of capital for small businesses.Findings – Since the three proxy methods are shown to have numerous shortcomings, the use of the AHP model is clearly a method to determine the equity risk premium and the cost of capital for small businesses.Research limitations/implications – The model requires small business managers to identify all information sources for the required input data.Originality/value – The article offers practical help to lenders and small businesses wishing to invest in new capital ...

24 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the roles of the number of trades, size of trades and share volume in explaining the volatility volume relation in the Shanghai Stock Exchange with high frequency trade data used.
Abstract: Purpose – The Chinese stock market is a typical emerging market with special features that are very different from those of mature markets. The objective of this study is to investigate whether and how these features affect the volatility‐volume relation for Chinese stocks.Design/methodology/approach – This paper examines the roles of the number of trades, size of trades, and share volume in explaining the volatility‐volume relation in the Shanghai Stock Exchange with high frequency trade data used.Findings – The results confirm that the volatility‐volume relation is driven mainly by the number of trades on the Chinese stock market. The number of trades explains the volatility‐volume relation better than the size of trades. Furthermore, some results are obtained that differ from those of mature markets, such as the US market. The results show that the second largest sized trades affect the volatility more than other trades on the Chinese market.Originality/value – The results show that, in the Shanghai St...

Journal ArticleDOI
TL;DR: In this paper, a "collective risk" model that models the credit risk of a portfolio, an approach typical of insurance mathematics, is presented, which offers a good representation of cascading phenomena due to bankruptcies.
Abstract: Purpose – This paper seeks to discuss a modeling tool for explaining credit‐risk contagion in credit portfolios.Design/methodology/approach – Presents a “collective risk” model that models the credit risk of a portfolio, an approach typical of insurance mathematics.Findings – ACD models are self‐exciting point processes that offer a good representation of cascading phenomena due to bankruptcies. In other words, they model how a credit event might trigger other credit events. The model herein discussed is proposed as a robust global model of the aggregate loss of a credit portfolio; only a small number of parameters are required to estimate aggregate loss.Originality/value – Discusses a modeling tool for explaining credit‐risk contagion in credit portfolios.

Journal ArticleDOI
TL;DR: In this article, the authors developed a new theory of portfolio and risk based on incremental entropy and Markowitz's theory, which emphasizes that there is an objectively optimal portfolio for given probability of returns.
Abstract: Purpose – To develop a new theory of portfolio and risk based on incremental entropy and Markowitz's theory.Design/methodology/approach – Replacing arithmetic, the mean return adopted by M.H. Markowitz, with geometric mean return as a criterion for assessing a portfolio, one gets incremental entropy: one of the generalized entropies. It indicates that the incremental speed of capital is a more objective and testable criterion.Findings – The difference between the new theory based on incremental entropy and Markowitz's theory is that the new theory emphasizes that there is an objectively optimal portfolio for given probability of returns.Originality/value – This paper provides some formulas for optimizing portfolio allocations. Based on the new portfolio theory, this paper also presents a new measure of information value, analyzes the differences and similarities between this measure and K.J. Arrow's measure of information value, and discusses how to optimize forecasts with the new measure.

Journal ArticleDOI
TL;DR: In this paper, an empirical study has been conducted on the US Treasury bonds market by means of the formation of different portfolios among a selected set of bonds with different maturities and structures.
Abstract: Purpose – Interest rate risk immunization is one of the key concerns for fixed income portfolio management. In recent years, the affluence of new risk measures has emphasized the importance of comparing them with the classic approaches. As a result, one question arises: what is the relation among classic risk measures (e.g. Macaulay duration, convexity, and dispersion) and other more recent risk measures (e.g. value‐at‐risk and conditional value‐at‐risk) as tools for the formation of an optimum investment portfolio? This article aims to discuss this issue.Design/methodology/approach – To enhance objectivity, an empirical study has been conducted on the US Treasury bonds market by means of the formation of different portfolios among a selected set of bonds with different maturities and structures. In addition, information about yields from the mid‐1990s and early 2000s has been used to find the optimum portfolio compositions based on each alternative risk measure.Findings – The main finding of the study is...

Journal ArticleDOI
TL;DR: In this article, the authors presented a multi-criteria model to determine an appropriate equity risk premium, and thereby, a cost of capital for a small business in South Africa, based on the analytical hierarchy process (AHP).
Abstract: Purpose – For publicly traded firms, calculating the cost of capital is predicated typically on information from the financial markets. Small businesses do not have the necessary market‐based information. As an alternative to traditional proxy approaches, this paper presents a multi‐criteria model to determine an appropriate equity risk premium, and thereby, a cost of capital.Design/methodology/approach – The study applies a multi‐criteria model – an analytical hierarchy process (AHP) – to determine the cost of capital for small businesses. It is a useful tool for the complex world in which small businesses function. Arbitrary and capricious ways of allocating resources is a luxury that small businesses can ill afford. The application of the model to a small business in South Africa is shown in this study.Findings – The use of the AHP model is clearly a method to determine the equity risk premium and the cost of capital for small businesses.Research limitations/implications – The model requires small busi...

Journal ArticleDOI
Mayank Raturi1
TL;DR: In this paper, the authors investigated the use of derivatives in the life insurance industry and found that derivatives are used by large companies, especially in the US life insurance market. But, the lack of knowledge and publication about the recent use of derivative by insurers is a major barrier to their use in risk management.
Abstract: Purpose – Derivatives are important risk management tools widely used by financial institutions, including insurers. Insurers rely on derivatives for managing actuarial, market, credit as well as liquidity risks. There is lack of knowledge and publication about the recent use of derivatives by insurers. This paper attempts to fill the gap in the literature.Design/methodology/approach – The paper analyses data based on statutory company filings with state regulators in the USA.Findings – The analysis suggests that derivatives are used by larger companies, especially in the life insurance industry. This could be explained by the significant economies of scale that are possible when using derivatives. Smaller firms do not have the resources to invest in the latest risk management technologies, and management may be uncomfortable using such new tools. Surveys and anecdotal evidence also suggest that, for insurance companies, the lack of familiarity with the regulatory and accounting treatment of derivatives i...

Journal ArticleDOI
TL;DR: In this paper, the optimal number of reinsurers in a market is given asymptotically by the square root of the total number of primary insurers, and the empirical results are consistent with the square-root rule.
Abstract: Purpose – Using a game‐theoretic model of insurance markets, Powers and Shubik in 2001 derived a mathematical expression for the optimal number of reinsurers for a given number of primary insurers. Subsequently in 2005, Powers and Shubik showed analytically that, for large numbers of primary insurers, this expression is effectively a “square‐root rule”, i.e. the optimal number of reinsurers in a market is given asymptotically by the square root of the total number of primary insurers. In this paper, we test the accuracy of the square‐root rule empirically.Design/methodology/approach – The numbers of primary insurers and reinsurers existing in a range of 18‐20 different national insurance markets over a period of 11 years are used.Findings – The empirical results are consistent with the square‐root rule. In addition, we find that the number of reinsurers may also be associated with the market's willingness to pay for risk. When the market's perception of risk is high, there is a greater supply of reinsuran...

Journal ArticleDOI
TL;DR: In this paper, the authors present a real-world model that optimizes index-based reinsurance instruments using the genetic algorithm, and demonstrate that the combined effect of these factors frequently allows the construction of an index•based hedging program that is more efficient than a traditional excess-of-loss reinsurance contract.
Abstract: Purpose – Demonstrates the feasibility of, and introduces a practical approach to enhancing, reinsurance efficiency using index‐based instruments.Design/methodology/approach – First reviews the general mathematical framework of reinsurance optimization. Next, illustrates how index‐based instruments can potentially enhance reinsurance efficiency through a simple yet self‐contained example. The simplicity allows the analytical examination of the cost and benefits of an index‐based contract. Finally, introduces a real‐world model that optimizes index‐based reinsurance instruments using the genetic algorithm.Findings – Identifies the key factors that determine the efficiency of index‐based reinsurance contracts and demonstrates that, in the property catastrophe reinsurance market, the combined effect of these factors frequently allows the construction of an index‐based hedging program that is more efficient than a traditional excess‐of‐loss reinsurance contract. A robust optimization model based on the geneti...

Journal ArticleDOI
TL;DR: In this article, the authors propose a new method for credit risk allocation among economic agents by decomposing the credit risk into idiosyncratic and systematic components, which accounts for the aggregate statistical difference between credit defaults in a given period and the long run average of these defaults.
Abstract: Purpose – This paper aims to propose a new method for credit risk allocation among economic agentsDesign/methodology/approach – The paper considers a pool of bank loans subject to a credit risk and develops a method for decomposing the credit risk into idiosyncratic and systematic components The systematic component accounts for the aggregate statistical difference between credit defaults in a given period and the long‐run average of these defaultsFindings – The paper shows how financial contracts might be redesigned to allow for banks to manage the idiosyncratic component for their own accounts, while allowing the systematic component to be handled separately The systematic component can be retained, passed off to the capital markets, or shared with the borrower In the latter case, the paper introduces a type of floating interest rate, in which the rate is set in arrears, based on a composite index for the systematic risk This increases the efficiency of risk sharing between borrowers, lenders and

Journal ArticleDOI
TL;DR: In this article, the risk inherent in the insurance of the aviation industry, to take an outsider's look at those risks and to develop certain "capital market" pricing rules, is examined.
Abstract: Purpose – This article aims to examine the risk inherent in the insurance of the aviation industry, to take an outsider's look at those risks and to develop certain “capital market” pricing rules.Design/methodology/approach – The aviation industry presents a classic low‐frequency/high‐limit insurance problem. Pricing such exposures is difficult because of the high degree of uncertainty involved. After a review of the considerations that an insurance underwriter traditionally brings to the problem, the author applies a simple pricing rule incorporating current thinking on risk evaluation.Findings – The results of the author's approach are compared with the results of traditional pricing rules, generating interesting insights. The application of the new methodology to the analysis of current pricing and of alternative proposals is suggested.Originality/value – The article will be of value to those interested in the aviation industry and in the pricing of insurance and reinsurance.

Journal ArticleDOI
TL;DR: In this paper, a multi-period model of the insurance market equilibrium is proposed to solve for the insureds' optimal demand for insurance, as well as insurers' optimal supply.
Abstract: Purpose – This article aims to apply a multi‐period model of insurance market equilibrium to solve for the insureds' optimal demand for insurance, as well as insurers' optimal supply.Design/methodology/approach – Most approaches to competitive equilibrium in the insurance market involve the construction of demand and supply curves based on maximizing the insureds' and insurers' expected utility for a single time period. However, it is important to recongnize that, for a given utility function, the demand (supply) decisions of insureds (insurers) in a single‐period model may differ substantially from those under a multi‐period formulation. In this article, first, separate multi‐period models of demand and supply are constructed, and then a dynamic solution for equilibrium price and quantity is provided.Findings – Although a single‐period model generally requires the assumption of an exact loss distribution to compute expected utilities, the multi‐period model requires only the expected loss and its associa...

Journal ArticleDOI
TL;DR: In this paper, a multi-dimensional diffusion model is proposed to describe the operations of an insurance company and the Laplace transform of the desired first-passage time (to ruin) distribution can be stated analytically.
Abstract: Purpose – The paper aims to develop a realistic, yet flexible model of insurer net worth.Design/methodology/approach – Inspired by and as an improvement to Powers, the paper develops a multi‐dimensional diffusion model to describe the operations of an insurance company. The paper then explores whether or not this multi‐dimensional model can be approximated conservatively by a homogeneous one‐dimensional diffusion.Findings – The multi‐dimensional model that is proposed can be approximated conservatively by a homogeneous one‐dimensional diffusion, which is clearly much easier to solve analytically or numerically than a multi‐dimensional system. Also, the Laplace transform of the desired first‐passage time (to ruin) distribution can be stated analytically.Practical implications – The analysis provides a theoretical model of the relationship between the insurer's ruin‐time distribution and many aspects of the insurer's operations, including loss‐payout patterns, premium‐earning patterns, and investment strate...



Journal ArticleDOI
TL;DR: In this paper, the problem is formulated as a two-person, non-cooperative Bayesian game with the decision maker and one expert as players, and perfect Bayesian equilibrium solutions are identified.
Abstract: Purpose – In forecasting unknown quantities, risk and finance decision makers often rely on one or more biased experts, statistical specialists representing parties with an interest in the decision maker's final forecast. This problem arises in a variety of contexts, and the decision maker may represent a corporate enterprise, rating agency, government regulator, etc. The purpose of the paper is to assist decision makers, experts, and others to have a better understanding of the dynamics of the problem, and to adopt strategies and practices that enhance efficiency.Design/methodology/approach – The problem is formulated as a two‐person, non‐cooperative Bayesian game with the decision maker and one expert as players, and perfect Bayesian equilibrium solutions are identified. Then the analysis is extended to variations of the game in which the expert's loss function is not common knowledge, and in which there are multiple experts.Findings – In the struggle for information between the decision maker and the e...

Journal ArticleDOI
Stephen Miller1
TL;DR: In this article, country alpha swaps are proposed to facilitate emerging market risk-sharing, even during global financial crises, by subtracting the product of average world index returns and the country's beta, measuring its contribution to global systematic risk, from average country index returns.
Abstract: Purpose – Country alpha swaps are proposed to facilitate emerging market risk‐sharing, even during global financial crises. Country alphas measure risk‐adjusted performance by subtracting the product of average world index returns and the country's beta, measuring its contribution to global systematic risk, from average country index returns. It has been proposed that emerging market country betas rose during the Asian crisis, and that country beta call options pay out for large increases in risk. Swaps on the difference between country and world index returns have also been proposed. Country alpha swaps combine elements of Merton's and Miller's proposals.Design/methodology/approach – Daily, rolling, synchronous country alphas are estimated from the subset of assets available to all investors in 13 emerging markets between 1995 and 2003, using Scholes and Williams' method.Findings – Country alphas become increasingly negative during the Asian crisis, and typically rise thereafter, eventually becoming posi...

Journal ArticleDOI
TL;DR: The main value is to demonstrate in rather large detail how a somewhat complicated model can be developed and used in an organization, which, originally, was not well aligned with the ideas of the modellers.
Abstract: Purpose – Discusses why it is necessary to align a mathematical model with the organization in order to achieve the desired results. The structure of a model's input must fit with the structure of data collection in the firm, and the output must be consistent with the decision structure. Otherwise, data collection will not be properly taken care of and the results of a model will not find their way to where decisions are made. Five years passed from the cooperation first started with the university until the model came on‐line.Design/methodology/approach – Parts 1 and 2 of this series of papers discussed the stochastic programming model itself and the relationship between the model and the organization. The results are now reported.Findings – Reports on both organizational and financial results.Practical implications – Shows that, although a lot of work is needed to implement a complicated stochastic programming model within an organization, it can be done and can lead to good results. However, it takes t...


Journal ArticleDOI
TL;DR: In this paper, a closed form option pricing formula is used for valuation and future price movements are modeled by an empirical distribution in conjunction with a semi-parametrically estimated tail.
Abstract: Purpose – It is the purpose of this article to improve existing methods for risk management, in particular stress testing, for derivative portfolios. The method is explained and compared with other methods, using hypothetical portfolios.Design/methodology/approach – Closed form option pricing formulas are used for valuation. To assess the risk, future price movements are modeled by an empirical distribution in conjunction with a semi‐parametrically estimated tail. This approach captures the non‐linearity of the portfolio risk and it is possible to estimate the extreme risk adequately.Findings – It is found that this method gives excellent results and that it clearly outperforms the standard approach based on a quadratic approximation and the normal distribution. Especially for very high confidence levels, the improvement is dramatic.Practical implications – In applications of this type the present method is highly preferable to the classical Delta‐Gamma cum normal distribution approach.Originality/value –...