This paper discusses the generalized Black-Scholes-Merton model, where volatility coefficient, drift coefficient of stocks, and interest rate are time-dependent deterministic functions. Together with it, we make assumption that volatility, drift, depend on a gamma or inverse-gamma random variable. model includes models skew Student’s t- variance-gamma-distributed stock log-returns. The price Eu...

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...

The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes price and random deviation describing the risk from the random volatility. By using the ...

An option is a nancial contract whose value depends on that of an underlying asset such as a company stock. The Black-Scholes model for option pricing, published in 1973, revolutionized the nancial industry by introducing a no-arbitrage paradigm for valuing uncertainty and hedging against risk. This simple model assumes that the underlying stock price follows a stochastic Brownian motion proces...

in this paper, heir-equations method is applied to investigate nonclassical symmetries and new solutions of the black-scholes equation. nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

This paper presents an empirical test of Dupire's (1993) option price inversion approach using FT–SE 100 index options. The performance of option deltas determined using the Dupire approach is compared to the performance of a pair of Black-Scholes (1973) based deltas. The study finds that Black-Scholes based deltas out-perform the Dupire-deltas, which is consistent with the results in synthesiz...

This study applies fuzzy set theory to the vulnerable Black-Scholes (1973) or Merton (1973) formula. Expectations of heterogeneity mean option prices are expected to be imprecise, thus making it natural to consider fuzziness to handle this. This article presents a fuzzy approach to value Black-Scholes options subject to non-identical rationality and correlated credit risk. Although no analytica...

Following an approach introduced by Lagnado and Osher (1997), we study Tikhonov regularization applied to an inverse problem important in mathematical finance, that of calibrating, in a generalized Black–Scholes model, a local volatility function from observed vanilla option prices. We first establish W 1,2 p estimates for the Black–Scholes and Dupire equations with measurable ingredients. Appl...