Intraday volatility spillovers between spot and futures indices: Evidence from the Korean stock market

This study provides empirical evidence of the relationship between spot and futures markets in Korea. In particular, the study focuses on the volatility spillover relationship between spot and futures markets by using three high-frequency (10 min, 30 min, and 1 h time-scales) intraday data sets of KOSPI 200 spot and futures contracts. The results indicate a strong bi-directional causal relationship between futures and spot markets, suggesting that return volatility in the spot market can influence that in the futures market and vice versa. Thus, the results indicate that new information is reflected in futures and spot markets simultaneously. This bi-directional causal relationship provides market participants with important guidance on understanding the intraday information transmission between the two markets. Thus, on a given trading day, there may be sudden and sharp increases or decreases in return volatility in the Korean stock market as a result of positive feedback and synchronization of spot and futures markets.     

Volatility skews and extensions of the Libor market model

The paper considers extensions of the Libor market model to markets with volatility skews in observable option prices. The family of forward rate processes is expanded to include diffusions with non-linear forward rate dependence, and efficient techniques for calibration to quoted prices of caps and swaptions are discussed. Special emphasis is put on generalized CEV processes for which closed-form expressions for cap and swaption prices are derived. Modifications of the CEV process which exhibit more appealing growth and boundary characteristics are also discussed. The proposed models are investigated numerically through Crank–Nicholson finite difference schemes and Monte Carlo simulations.     

The role of index bonds in universal currency hedging

This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values.     

The pricing of derivatives on assets with quadratic volatility

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model guarantees positive asset prices. In this paper, it is shown that the pricing partial differential equation can be solved for level-dependent volatility which is a quadratic polynomial. If zero is attainable, both absorption and negative asset values are possible. Explicit formulae are derived for the call option: a generalization of the Black-Scholes formula for an asset whose volatiliy is affine, the formula for the Bachelier model with constant volatility, and new formulae in the case of quadratic volatility. The implied Black-Scholes volatilities of the Bachelier and the affine model are frowns, the quadratic specifications imply smiles.     

Multigrid for American option pricing with stochastic volatility

The paper describes an implicit finite difference approach to the pricing of American options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices and adaptive time-stepping.     

A study of the interplay between the structure variation and fluctuations of the Shanghai stock market

The intricate interplay between the variation of the stock network structure and fluctuations of that stock market is increasingly becoming a hot topic. In this work, employing a moving window to scan through every stock price time series over a period from 2 January 2001 to 7 December 2010, we use mutual information to measure the statistical interdependence between stock prices, and we construct a corresponding network for 501 Shanghai stocks in every given window. Then we address the time-varying relationships between the structure variation and fluctuations for the Shanghai stock market. All the results obtained here indicate that at turning points the growing independence of stocks causes the scalefreeness of the degree distribution to be disrupted, and that the Shanghai stock index has little volatility clustering. In contrast, under normality of the market, the stock networks have characteristics of scalefree degree distribution. Furthermore, the degree of volatility clustering is a little higher.     

Waiting time distributions of the volatility in the Italian MIB30 index: Clustering or Poisson functions?

We investigate the time behaviour of the Italian MIB30 stock index collected every minute during two months in the period from May 17, 2006, up to July 24, 2006. We find short-range correlations in the price returns and, on the contrary, a long persistent time lag and slow decay in the autocorrelation functions of volatility. Besides, we find that the probability density functions (PDFs) of returns show fat tails, which are well fit by the log-normal model of Castaing [B. Castaing, Y. Gagne, E.J. Hopfinger, Physica D 46 (1990) 177], and a convergence toward a normal distribution for large time scales; we also find that the PDFs of volatility, for short time horizons, fit better with a log-normal distribution than with a Gaussian. Most of these features characterize the indexes and stocks of the largest American, European and Asian markets.We also investigate the distribution of stochastic separation between isolated strong events in the volatility signal. This is interesting because this gives us a deeper understanding about the price formation process. By using a test for the occurrence of local Poisson hypothesis, we show that the process we examined strongly departs from a Poisson statistics, the origin of this failure stemming from the presence of temporal clustering and of a certain amount of memory.     

The impact of futures trading on volatility of the underlying asset in the Turkish stock market

This paper examines the impact of the introduction of stock index futures on the volatility of the Istanbul Stock Exchange (ISE), using asymmetric GARCH model, for the period July 2002-October 2007. The results from EGARCH model indicate that the introduction of futures trading reduced the conditional volatility of ISE-30 index. Results further indicate that there is a long-run relationship between spot and future prices. The results also suggest that the direction of both long- and short-run causality is from spot prices to future prices. These findings are consistent with those theories stating that futures markets enhance the efficiency of the corresponding spot markets.     

The day-of-the-week effects on the volatility: The role of the asymmetry

In this paper, we propose to evaluate whether asymmetry influences the day-of-the-week effects on volatility. We also investigate empirically the impact of the day-of-the-week effect in major international stock markets using GARCH family models from a forecast framework. Indeed the existence of calendar effects might be interesting only if their incorporation in a model results in better volatility forecasts.     

Robust option pricing

In this paper, we combine robust optimization and the idea of ?$?$-arbitrage to propose a tractable approach to price a wide variety of options. Rather than assuming a probabilistic model for the stock price dynamics, we assume that the conclusions of probability theory, such as the central limit theorem, hold deterministically on the underlying returns. This gives rise to an uncertainty set that the underlying asset returns satisfy. We then formulate the option pricing problem as a robust optimization problem that identifies the portfolio which minimizes the worst case replication error for a given uncertainty set defined on the underlying asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-asset, American and Asian options using linear optimization; and thus the computational complexity of our approach scales polynomially with the number of assets and with time to expiry and (b) modeling flexibility illustrated by our ability to model different kinds of options, various levels of risk aversion among investors, transaction costs, shorting constraints and replication via option portfolios.