CLOSED FORM PRICING FORMULAS FOR DISCRETELY SAMPLED GENERALIZED VARIANCE SWAPS

Most of the existing pricing models of variance derivative products assume continuous sampling of the realized variance processes, though actual contractual specifications compute the realized variance based on sampling at discrete times. We present a general analytic approach for pricing discretely sampled generalized variance swaps under the stochastic volatility models with simultaneous jumps in the asset price and variance processes. The resulting pricing formula of the gamma swap is in closed form while those of the corridor variance swaps and conditional variance swaps take the form of one‐dimensional Fourier integrals. We also verify through analytic calculations the convergence of the asymptotic limit of the pricing formulas of the discretely sampled generalized variance swaps under vanishing sampling interval to the analytic pricing formulas of the continuously sampled counterparts. The proposed methodology can be applied to any affine model and other higher moments swaps as well. We examine the exposure to convexity (volatility of variance) and skew (correlation between the equity returns and variance process) of these discretely sampled generalized variance swaps. We explore the impact on the fair strike prices of these exotic variance swaps with respect to different sets of parameter values, like varying sampling frequencies, jump intensity, and width of the monitoring corridor.     

ALLOWING FOR JUMP MEASUREMENTS IN VOLATILITY: A HIGH‐FREQUENCY FINANCIAL DATA ANALYSIS OF INDIVIDUAL STOCKS

Following recent advances in the non‐parametric realized volatility approach, we separately measure the discontinuous jump part of the quadratic variation process for individual stocks and incorporate it into heterogeneous autoregressive volatility models. We analyse the distributional properties of the jump measures vis‐à‐vis the corresponding realized volatility ones, and compare them to those of aggregate US market index series. We also demonstrate important gains in the forecasting accuracy of high‐frequency volatility models.     

Liquidity,information, strategic trading in an electronic order book: New insights from the European carbon markets

The electronic limit order book (LOB hereafter) has rapidly become the primary way of trading European carbon assets over the 4 years of the EU ETS programme (2008–2012). In this first attempt of examining the informational content of an electronic order book, we evidence that order flow imbalances have a moderate capacity to predict short term price changes. However, we find that both LOB slope and immediacy costs help to forecast quote improvements and volatility in the next 30 min. Further, we explain why informed trading is highly influential and show that it consists in mixing order splitting strategies and posting fleeting orders once the asymmetric information is reduced (Rosu, 2009). Overall, the consolidated status of the order book mirrors a high level of market uncertainty and a low degree of informational efficiency. In this way, strategic trading can in itself explain some of order book properties, independently of the degree of traders’ sophistication and market competition.     

Contractual signaling,relationship-specific investment and exclusive agreements

I analyze a model of hold-up with asymmetric information at the contracting stage. The asymmetry of information concerns the value of trade with external parties. I show that contractual signaling and efficiency of investment can conflict if only quantity is contractible. This conflict generates inefficient equilibria in terms of investment. Contracting on exclusivity in addition to quantity resolves the conflict and consequently eliminates the inefficiency of investment.     

The impact of FIFA’s official announcements on the stock market of Qatar: The case of the 2022 World Cup

This study examines the impact of the FIFA’s official announcements on Doha Stock Exchange (DSE) of Qatar with respect to the 2022 World Cup. Using the abnormal unsystematic volatility method of Hilliard and Savickas (2002), our empirical findings reveal that the DSE market is sensitive to FIFA’s announcements about the 2022 World Cup. We find that four out of six FIFA announcements act as primary drivers to the DSE market volatility. The significant reactions of the DSE market to these announcements unveil the investors’ sentiments about the fate of the governmental and private expenditures on medium- and long-term projects undertaken in anticipation of hosting the 2022 World Cup. The results have some implications to investors in this newly emerging market related to this global sporting event. Any future announcements, good or bad, are likely to impact share prices in DSE market and trigger portfolio reallocation by local and international investors, leading to increased volatility.     

Foreign banks,financial crises and macroeconomic fluctuations

Understanding the implications of increased foreign bank presence is especially compelling in periods of financial crisis. In this paper, we explore this issue by examining the relationship between the involvement of foreign banks in the banking systems and the volatility of key macroeconomic variables in normal and crisis periods. Using a sample of 20 Emerging European countries from 1998 to 2013, we find that an increase in the assets of foreign banks in the banking system reduces output and consumption growth volatility in general but does not significantly affect the volatility of investments. However, these banks were found to play a significant role in increasing output, consumption and investment volatility in 2009. Our findings suggest that foreign banks’ harmful impact during the global crisis was only temporary and that they seem to help Emerging European countries stabilize macroeconomic volatility in normal times and after the global crisis.     

Modelling the implied volatility surface based on Shanghai 50ETF options

We develop a dynamic factor model to forecast the implied volatility surface (IVS) of Shanghai Stock Exchange 50ETF options. Based on the assumption that dynamic change in IVS is mean-reverting and Markovian, we use a state space model to capture the dynamics of IVS, and set the latent factors to be the Ornstein–Uhlenbeck processes. We obtain the optimal estimations of parameters using the Kalman filter algorithm. Empirical results show that our model performs better than the traditional IVS model in terms of fitting ability and prediction performance.     

Political uncertainty and a firm's credit risk: Evidence from the international CDS market

Using a large sample of firms with single-name credit default swap (CDS) contracts in 30 countries, we document the evidence that political uncertainty, proxied by national election dummy, is positively related to firm-level credit risk. Specifically, this positive relation is more pronounced for the firms that have no political connection or poor international diversification, and in the countries with higher political uncertainty and lower investor protections. Further, by using a difference-in-differences approach, we find evidence to support idiosyncratic volatility and debt rollover channels through which political uncertainty affects the credit risk of individual firm.     

Short-time at-the-money skew and rough fractional volatility

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.     

Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model

The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. This paper investigates whether the use of models which allow for negative interest rates can improve option pricing and implied volatility forecasting. This is done with special attention to foreign exchange and index options. To this end, we carried out an empirical analysis on the prices of call and put options on the US S&P 500 index and Eurodollar futures using a generalization of the Heston model in the stochastic interest rate framework. Specifically, the dynamics of the option’s underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. Explicit formulas for the transition probability density function and moments are derived. These formulas are used to estimate the model parameters efficiently. Three empirical analyses are illustrated. The first two show that the use of models which allow for negative interest rates can efficiently reproduce implied volatility and forecast option prices (i.e. S&P index and foreign exchange options). The last studies how the US three-month government bond yield affects the US S&P 500 index.