Nonzero transaction costs invalidate the Black-Scholes (1973) arbitrage argument based on continuous trading. Leland (1985) developed a hedging strategy which modifies the Black-Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Leland claimed that the exact hedge could be achieved in the limit as the le...

A digital option is a special type of financial derivative with a non-linear discontinuous payoff function. In spite of this, the payoff is simple enough to allow (relatively) easy valuation of these contracts. It is the reason why digital options can be (and regularly are) applied to decompose and hedge statically the positions in many options with more complicated and usually discontinuous pa...

We present an asymptotic solution for call options on zero-coupon bonds, assuming a stochastic process the price of bond, rather than interest rates in general. The bond incorporates dampening return volatility based maturity bond. derive PDE similar way to Black and Scholes. Using perturbation approach, we value option. result is interesting, as leading order terms are equivalent Black–Scholes...

This paper presents everything you need to know about Merton jump diffusion (we call it MJD) model. MJD model is one of the first beyond Black-Scholes model in the sense that it tries to capture the negative skewness and excess kurtosis of the log stock price density ( ) 0 ln( / ) T S S P by a simple addition of a compound Possion jump process. Introduction of this jump process adds three extra...

Numerical Approximation of the Black-Scholes Equations: A Practical Experience By Dylan Connor Black and Scholes equations for pricing of derivatives are an interesting and up-to-date topic of research, where both backgrounds in math and finance are fundamentals. In this work we aim at experiencing the mathematical approach and the numerical approximation of this differential problem. We will a...

Abstract. The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of generalized Black-Scholes equations. We analyze qualitatively and quantitatively the early exercise boundary for a linear as well as a class of nonline...

In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we first establish, under easy-to-check conditions, tail asymptoics on logarithmic scale as soft applications of st...

The story of this theorem started like most of modern Mathematical Finance with the work of F. Black, M. Scholes [3] and R. Merton [25]. These authors consider a model S = (St)0≤t≤T of geometric Brownian motion proposed by P. Samuelson [30], which today is widely known under the name of Black–Scholes model. Presumably every reader of this article is familiar with the by now wellknown technique ...

We consider a pure endowment contract whose life contingent payout is linked to the performance of a risky stock or index. Because of the additional mortality risk, the market is incomplete; thus, a fundamental assumption of the Black-Scholes theory is violated. We price this contract via the principle of equivalent utility and demonstrate that, under the assumption of exponential utility, the ...

In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively...