The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment methods and discuss applications to exotic volatility derivatives. The method...

The "leverage effect" refers to the well-established relationship between stock returns and both implied and realized volatility: volatility increases when the stock price falls. A standard explanation ties the phenomenon to the effect a change in market valuation of a firm's equity has on the degree of leverage in its capital structure, with an increase in leverage producing an increase in sto...

We examine how price impact in the underlying asset market affects the replication of a European contingent claim. We obtain a generalized Black-Scholes pricing PDE and establish the existence and uniqueness of a classical solution to this PDE. We show that unlike the case with transaction costs, replication in the presence of price impact is always cheaper than superreplication. This model imp...

This paper characterizes the volatility in the Japanese stock market based on a 4-year sample of 5-min Nikkei 225 returns from 1994 through 1997. The intradaily volatility exhibits a doubly U-shaped pattern associated with the opening and closing of the separate morning and afternoon trading sessions on the Tokyo Stock Exchange. This feature is consistent with market microstructure theories tha...

In this paper, we provide an option pricing formula based on an arbitrarily given stock distribution, where the problem of optimally hedging the payoo on a European call option is considered through a self-nancing trading strategy. An optimal hedging problem is solved on a trinomial lattice by assigning suitable probabilities on the lattice, where the underlying stock price distribution is deri...

Nonlinear Black–Scholes equations have been increasingly attracting interest over the last two decades, since they provide more accurate values by taking into account more realistic assumptions, such as transaction costs, risks from an unprotected portfolio, large investor’s preferences or illiquid markets, which may have an impact on the stock price, the volatility, the drift and the option pr...

Internet stock message boards provide individual investors with a new information medium that could have several effects on stock activity. Message boards may provide investors with a new information source on small cap stocks. Message boards may affect the trading and volatility of certain stocks by influencing investors. The impact of message board information may vary according to characteri...

This paper investigates the asymmetry in volatility of returns for the Iranian stock market using the daily closing values of the Tehran exchange price index (TEPIX) covering the period from March 25, 2001 to July 25, 2012, with a total of 2743 observations. To this end, two sets of tests have been employed: the first set is based on the residuals derived from a symmetric GARCH (1,1) model. The...

Volatility is a statistical measure that describes the amount of fluctuation in prices for a given investment; generally, the higher the volatility for an investment, the riskier it is perceived to be. Traders study volatility history so that they can make informed decisions on how to invest capital. The purpose of this article is to analyze implied volatility values, which are derived from the...

The empirical evidence on the effect of options trading on the underlying stocks primarily comes from the United States. The existing literature is surveyed by Damodaran and Subrahmanyam (1992). They find a consistent evidence of positive excess returns with the introduction of call options and negative excess returns with the introduction of put options. They also find strong evidence of a dec...