Derivative Securities Pricing and Modelling: Volume 94

In terms of notional value outstanding, derivatives markets declined in both over-the-counter and exchange-traded transactions during the 2007–2009 global financial crisis (GFC) period, as counterparty and credit concerns became pre-eminent. However, during the 2010–2011 second stage of the GFC, markets rebounded and by June 2011 outstandings reached new levels which highlight the importance these contracts continue to play in the day-to-day risk management and trading activities of corporations and financial intermediaries. The bulk of the contracts traded are interest rate-related instruments and are denominated in either US dollars or Euro. Credit-related instruments remain an important market segment, although outstandings remain at pre-crisis period levels. Of particular concern for regulators is the role of non-bank financial intermediaries, which are the main counterparty to derivatives transactions. While their share of the market remains unchanged over the last decade, outstandings overall have increased more than fourfold. The present volume considers the issues that participants face in today's derivatives markets including the potential impact of derivatives on economic stability, pricing issues, modelling as well as model performance and the application of derivatives for risk management and corporate control.

The purpose of this chapter is to discuss the potential contribution of the option applications to economic instability. To this end, the chapter briefly reviews the extant literature on financial option pricing and its applications to corporate assets and liabilities. It focuses on the direct relationship between the volatility of the underlying asset and the value of the option. It shows that the theory of option applications by its one-sided emphasis on the value-creating role of volatility promotes excessive risk-taking. Then the chapter discusses how the theory of option applications through the educational system encourages economic agents to make excessively risky decisions. Furthermore, the interactions among these risk-welcoming agents lead to an economic system which becomes increasingly risky. This risky economy, combined with the fact that more than half of the value of the option applications is constituted by the highly volatile value of the options embedded in such applications, translates into wide variations in real investments and the economy.

Derivatives market has been epitomized with gross evil in the wake of the global economic crisis that ensued in 2008. This study argues for more extensive understanding of the phenomena as dynamics previously viewed unrelated now exhibit correlation. As empirical reference, this research relies on recent trends in the commodity futures contracts with analytical relation to the currency exchange rate and by extension the financial and real sectors. With varying intensity often speculative sporadic trading in crude oil, coffee, wheat, rice, sugar, and gold benchmark futures may inflict detrimental effects on the global development efforts. The issue is most acute in the emerging markets facing inflation fears, speculative movements of foreign currency-denominated funds, and underlying domestic currency value. This dynamic reasserts the concept of fundamental uncertainty allowing us to connect the typical risk-return stand with a dialectical unity of the financial, real sector, and social costs. Ultimately, issues raised in this study relate to the problems of social stability and sustained economic development in the postcrisis environment given high frequency and volatility of capital flows. As such, this chapter contributes to the literature that bridges financial empirical analysis with modern socially responsible economic development.

We describe some recent contingent capital securities (CoCos) and explore the issues that confront their development. We take the view that bank CoCos should be designed to maintain confidence in a bank before a crisis begins because once a crisis commences it is difficult to see how a bank can assure the capital market without the support of state aid. With this overriding objective in mind we find that, in at least some respects, existing examples of bank CoCos have got the ‘right’ design. Existing bank CoCos are unfunded as they should be as there is no need to structure these securities to provide additional liquidity. If funding turns out to be necessary then a liquidity crisis is already underway and the CoCo has already failed in its attempt to maintain confidence in the bank. Moreover, existing CoCos use the simpler single trigger that we favour rather than dual trigger structure recommended by some.

In this chapter, we propose a nonconventional methodology, the graph theory, which is especially relevant for the study of high-dimensional financial data. We illustrate the advantages of this method in the context of systemic risk in derivative markets, a main subject nowadays in finance. A key issue is that this methodology can be used in various areas. Numerous applications have now to face the challenge of analyzing gigantic financial data sets, which are more and more frequent. We offer a pedagogical introduction to the use of the graph theory in finance and to some tools provided by this method. As we focus on systemic risk, we first examine correlation-based graphs in order to investigate markets integration and inter/cross-market linkages. We then restrain the analysis to a subset of these graphs, the so-called “minimum spanning trees.” We study their topological and dynamic properties and discuss the relevance of these tools as well as the robustness of the empirical results relying on them.

How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.

Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.

The pricing kernel puzzle of Jackwerth (2000) concerns the fact that the empirical pricing kernel implied in S&P 500 index options and index returns is not monotonically decreasing in wealth as standard economic theory would suggest. Thus, those options are currently priced in a way such that any risk-averse investor would increase his/her utility by trading in them. We provide a representative agent model where volatility is a function of a second momentum state variable. This model is capable of generating the empirical patterns in the pricing kernel, albeit only for parameter constellations that are not typically observed in the real world.

In this research, we analyze the impact of catastrophe events on risk-neutral densities which can be implied from European option markets. As catastrophe events we consider the destruction of the nuclear power plant at Fukushima and the downgrading of U.S. sovereign debt in 2011. In an event study, we analyze the impact on European blue chip index options traded at EUREX. We find that after a short adaption period, probability mass of especially risk-neutral density functions derived from long-term options is shifted toward the right side. Thus, very good states of the economy become more expensive indicating higher prices for deep out-of-the-money options. This signifies that there has been speculation on a recovery of the German stock market after the shocks.

It is well known that the probability distribution of stock returns is non-Gaussian. The tails of the distribution are too “fat,” meaning that extreme price movements, such as stock market crashes, occur more often than predicted given a Gaussian model. Numerous studies have attempted to characterize and explain the fat-tailed property of returns. This is because understanding the probability of extreme price movements is important for risk management and option pricing. In spite of this work, there is still no accepted theoretical explanation. In this chapter, we use a large collection of data from three different stock markets to show that slow fluctuations in the volatility (i.e., the size of return increments), coupled with a Gaussian random process, produce the non-Gaussian and stable shape of the return distribution. Furthermore, because the statistical features of volatility are similar across stocks, we show that their return distributions collapse onto one universal curve. Volatility fluctuations influence the pricing of derivative instruments, and we discuss the implications of our findings for the pricing of options.

This chapter analyzes the empirical performance of alternative option pricing models using Black and Scholes (1973) as a benchmark. Specifically, we consider the Heston (1993) and Corrado and Su (1996) models and price call options on the S&P 500 index over the period from November 2010 to April 2011, evaluating each model by computing in- and out-of-sample pricing errors. We find that the two proposed models reduce both types of errors and mitigate the smile effect with respect to the benchmark. Moreover, in most of the cases, the model in Corrado and Su (1996) beats that in Heston (1993). Then, we conclude that skewness and kurtosis matter for option pricing purposes.

We examine whether the hedging effectiveness of crude oil futures is affected by asymmetry in the return distribution by applying tail-specific metrics to compare the hedging effectiveness of both short and long hedgers. The hedging effectiveness metrics we use are based on lower partial moments (LPM), value at risk (VaR) and conditional value at risk (CVaR). Comparisons are applied to a number of hedging strategies including ordinary least square (OLS), and both symmetric and asymmetric GARCH models. We find that OLS provides consistently better performance across different measures of hedging effectiveness as compared with GARCH models, irrespective of the characteristics of the underlying distribution.

In this chapter we concentrate at the most popular model for convertible bond (CB) valuation in a one-factor, stochastic underlying stock price setting. Through the last decade, the Tsiveriotis–Fernandes model (1998) has become a widely commented model that involves the state of default of the issuer of the CB. A routine approach to the solution of this model is the usage of methods of finite difference schemes (FDS). However, for many people trained in finance these methods are not very intuitive and they tend to ignore them and prefer to use binomial-tree approach as more intuitive technique. For that reason, our primary focus is to highlight the answer of the so far unanswered question: Does the binomial-tree approach to CBs provide accurate pricing, hedging, and risk assessment? We show on a set of representative examples that by using binomial-tree methodology one is unable to provide a consistent analysis of the pricing, hedging, and risk assessment. We start the chapter with the basics of CBs and CB market. We then explain the implementation of TF model within binary-tree approach. We conclude the chapter with performance valuation of binomial-tree approach showing unexpected behavior in practice areas such as pricing (profile of CB's price versus underlying stock price), hedging (performance of CB's delta, gamma, and convertible arbitrage strategy versus underlying stock), and risk assessment (Monte Carlo VaR with respect to the underlying).

In this chapter, we define the “inflation forward rates” based on arbitrage arguments and develop a dynamic model for the term structure of inflation forward rates. This new model can serve as a framework for specific no-arbitrage models, including the popular practitioners’ market model and all models based on “foreign currency analogy.” With our rebuilt market model, we can price inflation caplets, floorlets, and swaptions with the Black formula for displaced-diffusion processes, and thus can quote these derivatives using “implied Black's volatilities.” The rebuilt market model also serves as a proper platform for developing models to manage volatility smile risks.

Through this chapter, we hope to correct two major flaws in existing models or with the current practices. First, a consumer price index has no volatility, so models based on the diffusion of the index are essentially wrong. Second, the differentiation of models based on zero-coupon inflation-indexed swaps and models based on year-on-year inflation-indexed swaps is unnecessary, and the use of “convexity adjustment,” a common practice to bridge models that are based on the two kinds of swaps, is redundant.

Compensation of funds managers increasingly involves elements of profit sharing that entitle managers to option-like payoffs. An important example is the compensation of private equity fund managers. Compensation of private equity fund managers typically consists of a fixed management fee and a performance-related carried interest. The fixed management fee resembles common compensation terms of mutual funds and hedge funds, while the performance-related carried interest is uncommon among most mutual funds. Moreover, the performance-related carried interest typically differs from variable hedge fund fees. In this chapter, we derive the value of the variable components of private equity fund managers’ compensation based on a risk-neutral option-pricing approach.

This chapter presents a structural model à la Leland (1994) that is, at the same time, novel, simple, and able to explain the quotes of credit default swaps (CDS), equity, and equity options. The model gives a closed-form formula for the term structure of default probabilities and can be calibrated to fit the CDS spreads. It also offers closed-form formulas for equity, equity volatility, and equity options. Differently from other structural models, debt has been modeled as a perpetual fixed-rate bond, instead of a zero-coupon bond with finite maturity. Therefore, default can happen at any time, and not only at the bond's maturity. The model (which belongs to the class of first-passage models) specifies default as the first time the firm's asset value hits a lower barrier. The barrier is endogenously determined as a solution of an optimal stopping problem (stockholders’ equity maximization). Equity is seen as a portfolio that contains a perpetual American option to default and can be valuated by using the results of Rubinstein-Reiner (1991) for barrier options. Equity options are valued by a closed-form formula that requires only an extra parameter (leverage) with respect to the standard input list of Black–Scholes–Merton equation. The formula is consistent with the volatility skew that is generally observed in the equity options markets and can be used to estimate the firms’ implied leverage, as it is perceived by traders. The chapter concludes with an application of the model to the case of Goldman Sachs.

This study examines the response of Australian interest rate swap spreads to the arrival of macroeconomic news information during the economic expansion and contraction periods. We find that the impact of news announcements on swap spread change differs and largely depends on the state of the economy. The unexpected inflation rate is the only news released that has significant impact on swap spreads across all maturities during contractions and remains the important news announcement throughout the business cycles, while the unanticipated unemployment rate tends to be more relevant to 10-year swap and the unanticipated change in money supply tends to be more relevant to 4- and 7-year swaps during expansions. We also find shocks from these news surprises appear to have significant impact on the conditional volatility of the swap spread change during both economic phases. The macroeconomic shocks in general are negatively related to the conditional volatility of the swap spread change, suggesting that the newsworthy announcements tend to reduce uncertainty on the news announcement days in the swap market during expansion and contraction periods.

We investigate the evolution of corporate risk management practices in Slovenian non-financial firms in the period 2004–2009 and compare the findings several surveys conducted for other countries. We mail questionaires to non-financial companies, where the target group included non-financial companies listed on Ljubljana Stock Exchange and the largest exporting companies in Slovenia. We find that the current use of derivatives for hedging purposes is still at a lower level than in the majority of developed countries. The great expansion of Slovenian economy in the period 2004–2008, the development of Slovenian financial system, the convergence of Slovenian and EU accounting standards and recent financial crisis did not sufficiently induce Slovenian firms to adopt risk management practices. The most often stated reasons for the low use of derivatives are (1) insufficient risk exposure, (2) problems with the evaluation and monitoring of derivatives and (3) the costs associated with the implementation of derivatives programme. In our opinion, the institutional environment in Slovenia does not induce managers to undertake proper risk management activities. We argue that not only managers, but also owners and creditors should be more accountable for the decisions they take (or do not take).