The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic assumptions including the lognormal distribution of stock market price processes. There, now, subsists abundant empirical evidence that this is not the case. Consequently, several generalisations of the basic model have been ...

The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute numerical results from the formula. The numerical results are...

The payoffs of the barrier options depend on the time path of the underlying price as opposed to just the price at expiry. It implies that both the boundary conditions and the initial condition are imposed on the Black-Scholes partial differential equation. Therefore, the valuation of the barrier options is a boundary value problem. Since the Black-Scholes equation can be converted into a homog...

A super-replication problem with a gamma constraint, introduced in [12], is studied in the context of the one-dimensional Black and Scholes model. Several representations of the minimal super-hedging cost are obtained using the characterization derived in [3]. It is shown that the upper bound constraint on the gamma implies that the optimal strategy consists in hedging a conveniently face-lifte...

This paper studies several aspects of asymptotically hyperbolic Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed con...

We study static brane configurations in the bulk background of the topological black holes in asymptotically flat spacetime. We find that such configurations are possible even for flat black hole horizon, unlike the AdS black hole case. We construct the brane world model with an orbifold structure S/Z2 in such bulk background. We also study massless bulk scalar field.

We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both β parameters equal to 1 and three correlation parameters, which extends the work of Bayer,Friz&Laurence[BFL14] for the multivariate Black-Scholes flat vol model. The result follows from the heat kernel on hyperbolic space for n = 3 combined with the Bellaiche[Bel81] heat kernel expansio...

This paper will derive the Black-Scholes pricing model of a European option by calculating the expected value of the option. We will assume that the stock price is log-normally distributed and that the universe is riskneutral. Then, using Ito’s Lemma, we will justify the use of the risk-neutral rate in these initial calculations. Finally, we will prove put-call parity in order to price European...

We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic–risk minimisation scheme, we obtain a general formula, valid for weakly correlated non–Gaussian processes. We show that for Gaussian price increments, the correlations are irrelevant, and the Black–Scholes formula holds with the volatility of the price increments on the scale of t...

It turns out that a slightly generalised Margrabe formula exhibits symmetry properties leading to semi-static hedges of rather general options in the bivariate Black-Scholes economy. In order to increase the liquidity of the used hedging instruments for currency options, the duality principle can be used to set up the hedges in a foreign market by using only European vanilla options sometimes a...