J. Risk Financial Manag.2015, 8(1), 127-149; doi:10.3390/jrfm8010127 - published 16 February 2015 Show/Hide Abstract
Abstract: It is commonly believed that women are more likely to seek advice than men; for example, on aspects of health or asking for directions when lost. This paper investigates whether women’s relatively greater propensity for advice seeking extends to important business decisions, specifically those involving corporate takeovers. Consistent with the evidence from other contexts, we show that the presence of female directors on target boards is positively and significantly associated with target boards seeking advice from top-ranked financial advisors. In contrast, we do not observe any significant association between the presence of female directors on bidder boards and their engagement of top-ranked financial advisors. We argue that the presence of a gender effect for target boards but not for bidder boards is consistent with less overconfident female versus male directors on bidder boards initiating fewer bids, higher litigation risk facing target boards for accepting too little, and the different type of advice sought by bidders and target firms.
J. Risk Financial Manag.2015, 8(1), 103-126; doi:10.3390/jrfm8010103 - published 13 February 2015 Show/Hide Abstract
Abstract: The statistical distribution of financial returns plays a key role in evaluating Value-at-Risk using parametric methods. Traditionally, when evaluating parametric Value-at-Risk, the statistical distribution of the financial returns is assumed to be normally distributed. However, though simple to implement, the Normal distribution underestimates the kurtosis and skewness of the observed financial returns. This article focuses on the evaluation of the South African equity markets in a Value-at-Risk framework. Value-at-Risk is estimated on four equity stocks listed on the Johannesburg Stock Exchange, including the FTSE/JSE TOP40 index and the S & P 500 index. The statistical distribution of the financial returns is modelled using the Normal Inverse Gaussian and is compared to the financial returns modelled using the Normal, Skew t-distribution and Student t-distribution. We then estimate Value-at-Risk under the assumption that financial returns follow the Normal Inverse Gaussian, Normal, Skew t-distribution and Student t-distribution and backtesting was performed under each distribution assumption. The results of these distributions are compared and discussed.
J. Risk Financial Manag.2015, 8(1), 83-102; doi:10.3390/jrfm8010083 - published 2 February 2015 Show/Hide Abstract
Abstract: This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
J. Risk Financial Manag.2015, 8(1), 43-82; doi:10.3390/jrfm8010043 - published 26 January 2015 Show/Hide Abstract
Abstract: Certain exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Many exotics are priced in a local volatility framework. Pricing under local volatility has become a field of extensive research in finance, and various models are proposed in order to overcome the shortcomings of the Black-Scholes model that assumes a constant volatility. The Johannesburg Stock Exchange (JSE) lists exotic options on its Can-Do platform. Most exotic options listed on the JSE’s derivative exchanges are valued by local volatility models. These models needs a local volatility surface. Dupire derived a mapping from implied volatilities to local volatilities. The JSE uses this mapping in generating the relevant local volatility surfaces and further uses Monte Carlo and Finite Difference methods when pricing exotic options. In this document we discuss various practical issues that influence the successful construction of implied and local volatility surfaces such that pricing engines can be implemented successfully. We focus on arbitrage-free conditions and the choice of calibrating functionals. We illustrate our methodologies by studying the implied and local volatility surfaces of South African equity index and foreign exchange options.
J. Risk Financial Manag.2015, 8(1), 17-42; doi:10.3390/jrfm8010017 - published 26 January 2015 Show/Hide Abstract
Abstract: The 2008 credit crisis changed the manner in which derivative trades are conducted. One of these changes is the posting of collateral in a trade to mitigate the counterparty credit risk. Another is the realization that banks are not risk-free and, as a result, cannot borrow at the risk-free rate any longer. The latter led banks to introduced the controversial adjustment to derivative prices, known as a funding value adjustment (FVA), which is interlinked with the posting of collateral. In this paper, we extend the Cox, Ross and Rubinstein (CRR) discrete-time model to include collateral and FVA. We prove that this derived model is a discrete analogue of Piterbarg’s partial differential equation (PDE), which describes the price of a collateralized derivative. The fact that the two models coincide is also verified by numerical implementation of the results that we obtain.
J. Risk Financial Manag.2015, 8(1), 2-16; doi:10.3390/jrfm8010002 - published 19 January 2015 Show/Hide Abstract
Abstract: It is generally held that derivative prices do not contain useful predictive information, that is, information relating to the distribution of future financial variables under the real-world measure. This is because the market’s implicit forecast of the future becomes entangled with market risk preferences during derivative price formation. A result derived by Ross , however, recovers the real-world distribution of an equity index, requiring only current prices and mild restrictions on risk preferences. In addition to being of great interest to the theorist, the potential practical value of the result is considerable. This paper addresses implementation of the Ross Recovery Theorem. The theorem is formalised, extended, proved and discussed. Obstacles to application are identified and a workable implementation methodology is developed.