The pricing of dividend futures in the European market: A first empirical analysis

Pengelly, M. (2008) Gambling on dividends. Risk 21 (December): 21–23. Blees, W. (2008) Dividend option market tipped for growth. Risk News, 30 April. Eurex (2008) Eurex Dow Jones Euro Stoxx 50 Index Dividend Futures – Pricing & Applications for the Institutional Investor. Frankfurt/Main, Germany. See Barclays Capital (2008) Dividend Swap Indices: Access to Equity Income Streams Made Easy. Research Report, April; and Eurex (2008) Eurex Dow Jones Euro Stoxx 50 Index Dividend futures – Pricing & Applications for the Institutional Investor. Frankfurt/Main, Germany for more details and examples on dividend derivatives. For a comprehensive review of markets for dividends and problems of trading dividends confer Manley, R. and Mueller-Glissmann, C. (2008) The market for dividends and related investment strategies. Financial Analysts Journal 64(May/June): 17–29. A general discussion on designated dividend claims for equity indices is provided by Brennan M.J. (1998) Stripping the S&P 500 index. Financial Analysts Journal 54(January/February): 12–22. For example, in products such as reverse convertibles investors implicitly sell (out-of-the-money) put options to the issuing institution, creating a long dividend position for the latter – that increases in case stock prices fall. See Pengelly, M. (2008) Sunk by correlation risk. Risk 21 (July): 20–24, and Pengelly M. (2008) Gambling on dividends. Risk 21(December): 21–23 for details. Barclays Capital (2008) Dividend Swap Indices: Access to Equity Income Streams Made Easy. Research Report, April. Ferry, J. (2007) An unusual existence. Risk South Africa 20 (October): 77–78. Dividends are much more volatile in the South African market than in other market places. Missing standardized rules on how corporate actions are to be treated caused a special dividend uncertainty in the South African equity market. See Ferry, J. (2007) An unusual existence. Risk South Africa 20 (October): 77–78, for more background information. The Eurex has encouraged this development by waiving the trading fees in these contracts until the end of 2008. See Eurex (2008) Eurex Dow Jones Euro Stoxx 50 Index Dividend Futures – Pricing & Applications for the Institutional Investor. Frankfurt/Main, Germany. Brooks, R. (1994) Dividend predicting using put-call parity. International Review of Economics and Finance 3 (4): 373–392. Chance, D., Kumar, R. and Rich, D. (2000) Dividend forecast biases in index option valuation. Review of Derivatives Research 4: 285–303. For an overview of deterministic and stochastic equity dividend models used in the pricing and hedging of derivative contracts see Bakstein, D. and Wilmott, P. (2006) Equity Dividend Models. University of Oxford. Working Paper, October. Eurex (2008) Products. Frankfurt/Main, Germany. Note that (1) and (2) are expressed with discretely instead of continuously compounded interest rates, with the latter being the usual text book notation aligned with option pricing formulas. The approach chosen here follows suggestions from the Eurex based on their settlement procedure for option prices and conventions in the OTC dividend derivatives market. We are thankful to Byron Baldwin from Eurex for advice on this point. It turns out in the later analysis that results are not affected qualitatively by the choice of the compounding frequency. The DVP represents the ordinary unadjusted gross cash dividends declared and paid by the individual components of the Euro Stoxx 50, covering a 1-year period from the third Friday in December of the previous year and including the third Friday in December of the current year; see Stoxx (2008) Dow Jones Euro Stoxx 50 Dividend Points Calculation Guide, October for details. The ongoing value of the index is the summation of dividend points up to that point in time, that is, the index represents the cumulative dividends and is therefore non-decreasing by construction. The DVP can essentially be considered the underlying of the Eurex dividend futures. In the following, Act/360 is employed as a day count convention, in accordance with a proposal in Eurex. (2008) Eurex Dow Jones Euro Stoxx 50 Index Dividend Futures – Pricing & Applications for the Institutional Investor. Frankfurt/Main, Germany. It turns out that this fit is very tight, with the standard deviations across the daily implied values of PV t(Div t, T) generally not exceeding 0.05% of the average. While two daily pairs of calls and puts would theoretically be sufficient to estimate the tuple (PV t(Div t, T),r t, T), at least 10 pairs were employed in order to reduce potential noise in the data. The option pairs for each contract maturity were chosen across a fixed set of strikes at the beginning of the investigation period. As a means of increasing liquidity the Eurex supports designated market making for selected futures contracts. The Eurex member(s) agree(s) to quote prices within a certain response time and at least for a minimum contract size and within a maximum spread. In exchange, at least parts of the trading and clearing fees for the traded contracts are refunded to the market maker. For the dividend futures contracts a period with designated market making has been granted until end of 2012, but no Eurex member has accepted this role so far. Since market participants are charged margins based on the daily closing prices, any material deviation from prevailing market rates would likely be challenged by either the long or the short parties. Note that the procedure to derive closing prices is essential to the study provided here. An immediate speculation consists in the observed pricing imbalances being driven to a large extent – if not exclusively – by potential differences in ways the Eurex settles index options on the one side and dividend futures on the other side. Insightful discussions with Byron Baldwin from Eurex helped abandon this theory. It should be borne in mind that the replication approach is static in nature, that is, no dynamic rebalancing is required. Direct trading costs thus only occur at inception of the arbitrage portfolio. Exceptions might result, for example, from changes in the index composition over time if S t is replicated by positions in the actual index members. In this context, no statistically significant relationship between the price difference and the average size of the bid-ask spread on each trading day could be detected. Such as funding needs for margin requirements and exchange/clearing fees, which should be of minor importance, especially for active market participants. Manley, R. and Mueller-Glissmann, C. (2008) The market for dividends and related investment strategies. Financial Analysts Journal 64 (May/June): 17–29.