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This chapter aims to find an optimal way to hedge foreign exchange exposures on three main currency pairs being the EURUSD, EURGBP and EURJPY. Furthermore, it analyses the risk level of each portfolio together with its kurtosis level. This chapter also looks into the relationship between the EURUSD portfolios and the VIX level.

This study is based on a back-testing analysis over a period of seven years starting in January 2007 and ending in December 2014. Two main Foreign Exchange Premium-Free strategies were structured using the Bloomberg Terminal. These were the ‘At-Expiry Forward Extra’ and the ‘Window Forward Extra’. Portfolios were created using FX options strategies, FX spot and FX forwards. The EURUSD portfolios were also analysed and compared with the VIX level in order to see whether volatility has a direct effect on the outcome of the strategies. The statistical significance of the difference between returns of portfolios was analysed using a paired sample t-test. Finally, the histogram and distribution curve of each portfolio were created and plotted in order to provide a more visual analysis of returns.

It was found that the optimal strategies in all cases were the FX option strategies. The portfolios’ risk was analysed and indicated that optimal portfolios do not necessarily derive the lowest risk. It was also found that with a high VIX level, the forward contract was the most beneficial whilst the option strategy benefited from a low VIX level. When testing for statistical significance between returns of different portfolios, in most cases, the difference in returns between portfolios resulted to be statistically insignificant. Although some similarities were noticed in distribution curves, these differed from the normal distribution. When analysing the kurtosis levels, it is found that such levels differed from that of a normal distribution which has a kurtosis level of 3. Interpretation of such histograms, distribution curves and the kurtosis analysis was explained.

The premise of this discussion is that private equity players intend to create real options that maximize the value derived from potential movement in the worth of the underlying business platform. This intended maximization occurs when the current value of the exercise instrument equals the current value of the underlying asset (so the option is at the money). It is also clear that when the time horizons of different arrangements tend to be consistent (as tends to happen in private equity arrangements) the attraction will be for higher volatility. The actions often criticized in the media are readily understandable in this context. For example, private equity partnerships are criticized for “borrowing heavily to buy companies, breaking them up, and selling off the pieces at huge profits.” Even before exiting, the private equity players separate the acquisitions into business units and asset pools. This changes an option on a portfolio into a portfolio of options, and we know from option pricing theory that the resulting position is worth more than the starting point.

Private equity partnerships also have been criticized for putting acquisitions into debt to receive dividends. Upon acquisition of a new business platform (perhaps composed of multiple business units) the private equity firm has paid a substantial premium for an option on a portfolio. After separating it into multiple options on different business units, the private equity firm might understandably want to sell assets that do not need to be owned (but could be leased instead), thereby reducing their equity investment and bringing the options closer to the money. Then additional borrowing (and withdrawal of dividends) again brings the options closer to the money.

In order to illustrate the nuances of private equity as real options, we include discussion of three recent cases, each illustrating one of the common paths followed in private equity.

This research applies a static hedging portfolio method derived from Derman, Ergener, and Kani (1995) (henceforth Derman's SHP method) and a new SHP method with European cash-or-nothing binary options developed by Chung, Shih, and Tsai (2013) to price European continuous double barrier (ECDB) options and the rebates of the ECDB options. Our numerical results indicate that the new SHP method outperforms Derman's SHP method in terms of efficiency and effectiveness under all circumstances.

Empirical evidence of the hedging pressure risk premium exists only in the futures contracts with delivery-related options. Since hedging pressure is supposed to exist for all futures contracts, the empirical evidence raises an interesting empirical question: whether the hedging pressure risk premium is in fact the risk premium associated with the delivery-related options. This chapter contains an empirical test of the non-redundancy between the two related but alternative sources of non-market risks. For the test, we employs a futures risk premia model in which the expected futures returns contain the market risk premium (proxied by the equity market risk premium) and two non-market risk premia (proxied by the hedging pressure effect and by the delivery risk premium reflected in the returns of futures options, respectively). Our main finding is that both the hedging pressure and the delivery risk premia are non-redundant and statistically significant for futures contracts with delivery-related options. This finding implies a substantial degree of segmentations between these futures markets and the underlying asset markets.