A stochastic dynamic programming approach for pricing options on stock-index futures

The aim of this thesis is to price options on equity index futures with an application to standard options on S&P 500 futures traded on the Chicago Mercantile Exchange. Our methodology is based on stochastic dynamic programming, which can accommodate European as well as American options. The model accommodates dividends from the underlying asset. It also captures the optimal exercise strategy and the fair value of the option. This approach is an alternative to available numerical pricing methods such as binomial trees, finite differences, and ad-hoc numerical approximation techniques. Our numerical and empirical investigations demonstrate convergence, robustness, and efficiency. We use this methodology to value exchange-listed options. The European option premiums thus obtained are compared to Black's closed-form formula. They are accurate to four digits. The American option premiums also have a similar level of accuracy compared to premiums obtained using finite differences and binomial trees with a large number of time steps. The proposed model accounts for deterministic, seasonally varying dividend yield. In pricing futures options, we discover that what matters is the sum of the dividend yields over the life of the futures contract and not their distribution.

Can we explain the dynamics of the UK FTSE 100 stock and stock index futures markets?

If stock and stock index futures markets are functioning properly price movements in these markets should best be described by a first order vector error correction model with the error correction term being the price differential between the two markets (the basis). Recent evidence suggests that there are more dynamics present than should be in effectively functioning markets. Using self-exciting threshold autoregressive (SETAR) models, this study analyses whether such dynamics can be related to different regimes within which the basis can fluctuate in a predictable manner without triggering arbitrage. These findings reveal that the basis shows strong evidence of autoregressive behaviour when its value is between the two thresholds but that the extra dynamics disappear once the basis moves above the upper threshold and their persistence is reduced, although not eradicated, once the basis moves below the lower threshold. This suggests that once nonlinearity associated with transactions costs is accounted for, stock and stock index futures markets function more effectively than is suggested by linear models of the pricing relationship.

An alternative approach to investigating lead-lag relationships between stock and stock index futures markets

In the absence of market frictions, the cost-of-carry model of stock index futures pricing predicts that returns on the underlying stock index and the associated stock index futures contract will be perfectly contemporaneously correlated. Evidence suggests, however, that this prediction is violated with clear evidence that the stock index futures market leads the stock market. It is argued that traditional tests, which assume that the underlying data generating process is constant, might be prone to overstate the lead-lag relationship. Using a new test for lead-lag relationships based on cross correlations and cross bicorrelations it is found that, contrary to results from using the traditional methodology, periods where the futures market leads the cash market are few and far between and when any lead-lag relationship is detected, it does not last long. Overall, the results are consistent with the prediction of the standard cost-of-carry model and market efficiency.

A note on execution costs for stock index futures: Information versus liquidity effects

This paper examines execution costs and the impact of trade size for stock index futures using price-volume transaction data from the London International Financial Futures and Options Exchange. Consistent with Subrahmanyam [Rev. Financ. Stud. 4 (1991) 11] we find that effective half spreads in the stock index futures market are small compared to stock markets, and that trades in stock index futures have only a small permanent price impact. This result is important as it helps to better understand the success of equity index products such as index futures and Exchange Traded Funds. We also find that there is no asymmetry in the post-trade price reaction between purchases and sales for stock index futures across various trade sizes. This result is consistent with the conjecture in Chan and Lakonishok [J. Financ. Econ. 33 (1993) 173] that the asymmetry surrounding block trades in stock markets is due to the high cost of short selling and the general reluctance of traders to short sell on stock markets. (C) 2004 Elsevier B.V. All rights reserved.

Price discovery and volatility spillovers in index futures markets: Some evidence from Mexico

This paper investigates the hypotheses that the recently established Mexican stock index futures market effectively serves the price discovery function, and that the introduction of futures trading has provoked volatility in the underlying spot market. We test both hypotheses simultaneously with daily data from Mexico in the context of a modified EGARCH model that also incorporates possible cointegration between the futures and spot markets. The evidence supports both hypotheses, suggesting that the futures market in Mexico is a useful price discovery vehicle, although futures trading has also been a source of instability for the spot market. Several managerial implications are derived and discussed. (C) 2004 Elsevier B.V. All rights reserved.

The relationship between implied and realized volatility : evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

The expiration day effect of indexoptions and index futures on the underlying shares

This paper studies the effect of the expiration day of index options and futures on the trading volume, variance and price of the underlying shares. The data consists of all trades for the underlying shares in the FOX-index for expiration days during the period October 1995 to the mid of yer 1999. The main results seem to support the findings of Kan 2001, i.e. no manipulation on a larger scale. However, some indication of manipulation could be found if certain characteristics are favorable. These characteristics include: a) a large quantity of outstanding futures or at/in the money options contracts, b) there exists shares with high index weight but fairly low trading volume. Lastly, there is some indication that manipulation might be more popular towards the end of the examined time period.

Gauging the Success of Technical Trading Strategies in the S&P 500 Index Futures Market.

Rapport de recherche

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models.

Tests of non-linearity using LIFFE futures transactions price data

This paper presents and implements a number of tests for non-linear dependence and a test for chaos using transactions prices on three LIFFE futures contracts: the Short Sterling interest rate contract, the Long Gilt government bond contract, and the FTSE 100 stock index futures contract. While previous studies of high frequency futures market data use only those transactions which involve a price change, we use all of the transaction prices on these contracts whether they involve a price change or not. Our results indicate irrefutable evidence of non-linearity in two of the three contracts, although we find no evidence of a chaotic process in any of the series. We are also able to provide some indications of the effect of the duration of the trading day on the degree of non-linearity of the underlying contract. The trading day for the Long Gilt contract was extended in August 1994, and prior to this date there is no evidence of any structure in the return series. However, after the extension of the trading day we do find evidence of a non-linear return structure.

Predicting stock index volatility: can market volume help?

This paper explores a number of statistical models for predicting the daily stock return volatility of an aggregate of all stocks traded on the NYSE. An application of linear and non-linear Granger causality tests highlights evidence of bidirectional causality, although the relationship is stronger from volatility to volume than the other way around. The out-of-sample forecasting performance of various linear, GARCH, EGARCH, GJR and neural network models of volatility are evaluated and compared. The models are also augmented by the addition of a measure of lagged volume to form more general ex-ante forecasting models. The results indicate that augmenting models of volatility with measures of lagged volume leads only to very modest improvements, if any, in forecasting performance.

Are price limits on futures markets that cool? evidence from the brazilian merchantile & futures exchange

This paper investigates the impact of price limits on the Brazil- ian future markets using high frequency data. The aim is to identify whether there is a cool-off or a magnet effect. For that purpose, we examine a tick-by-tick data set that includes all contracts on the São Paulo stock index futures traded on the Brazilian Mercantile and Futures Exchange from January 1997 to December 1999. Our main finding is that price limits drive back prices as they approach the lower limit. There is a strong cool-off effect of the lower limit on the conditional mean, whereas the upper limit seems to entail a weak magnet effect on the conditional variance. We then build a trading strategy that accounts for the cool-off effect so as to demonstrate that the latter has not only statistical, but also economic signifi- cance. The resulting Sharpe ratio indeed is way superior to the buy-and-hold benchmarks we consider.

Are price limits on futures markets that cool?: evidence from the Brazilian Mercantile and Futures Exchange

This paper investigates the impact of price limits on the Brazilian futures markets using high frequency data. The aim is to identify whether there is a cool-off or a magnet effect. For that purpose, we examine a tick-by-tick data set that includes all contracts on the S˜ao Paulo stock index futures traded on the Brazilian Mercantile and Futures Exchange from January 1997 to December 1999. The results indicate that the conditional mean features a floor cool-off effect, whereas the conditional variance significantly increases as the price approaches the upper limit. We then build a trading strategy that accounts for the cool-off effect in the conditional mean so as to demonstrate that the latter has not only statistical, but also economic significance. The in-sample Sharpe ratio indeed is way superior to the buy-and-hold benchmarks we consider, whereas out-of-sample results evince similar performances.