Using the Laplace transform approach, we compute the expected value and the variance of the error of a hedging strategy for a contingent claim when trading in discrete time. The method applies to a fairly general class of models, including Black-Scholes, Merton’s jump-diffusion and Normal Inverse Gaussian, and to several interesting strategies, as the Black-Scholes delta, the Wilmott’s improved...

An adjusted Black-Scholes pricing formula is derived in this paper. By separating risk and uncertainty through the robust control technique, we find that uncertainty as well as risk raises the management’s subjective evaluation of real options. We suggest a simple method to filter the risk of the project and to acquire a more reliable value of real options without the influence of uncertainty. ...

We prove a Donsker type approximation theorem for the fractional Brownian motion in the case H > 1/2. Using this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black–Scholes model. We show that there exist arbitrage opportunities in this model. One such opportunity is constructed explicitly.

This article studies the pricing of options in an extended Black Scholes economy in which the underlying asset is not perfectly liquid. The resulting liquidity risk is modeled as a stochastic supply curve, with the transaction price being a function of the trade size. Consistent with the market microstructure literature, the supply curve is upward sloping with purchases executed at higher price...

A string theory description of near extremal black rings is proposed. The entropy is computed and the thermodynamic properties are derived for a large family of black rings that have not yet been constructed in supergravity. It is also argued that the most general black ring in N = 8 supergravity has 21 parameters up to duality.

Volatility modeling and analysis are traditionally based on either historical price data or option data. Finance theory shows that option prices heavily depend on the underlying stocks’ prices, thus the two kinds of data are related. This paper explores the approach that combines both stock price data and option data to perform the statistical analysis of volatility. We investigate the Black-Sc...

Markets liquidity is an issue of very high concern in financial risk management. In a perfect liquid market the option pricing model becomes the well-known linear Black-Scholes problem. Nonlinear models appear when transaction costs or illiquid markets effects are taken into account. This paper deals with the numerical analysis of nonlinear Black-Scholes equations modeling illiquid markets when...

In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black-Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are respectively first, second and third order approximations w.r.t. th...