This paper examines the behaviour of European option price (Duan (1995)) and the Black-Scholes model bias when stock returns follow a GARCH (1,1) process. The GARCH option price is not preferenceneutral and depends on the unit risk premium (λ) as well as the two GARCH (1,1) process parameters (α1 , β1). In general, the GARCH option price does not seem overly sensitive to these parameters. Deep-...

This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined Black-Scholes closed form solution modified (MBS) partial differential equation using Crank-Nicolson finite difference method. These equations were approximated to obtain Call Put prices. The explicit price both options found accordingly. solutions c...

Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized simultaneously. In this paper, the authors have solved the Black-Scholes equation by employing a reasonably accurate implicit method. Options with known analytic...

Abstract In option pricing, it is customary to first specify a stochastic underlying model and then extract valuation equations from it. However, possible reverse this paradigm: starting an arbitrage-free formula, one could derive family of risk-neutral probabilities corresponding asset process. paper, we start two simple equations, inspired by the log-sum-exponential function $\ell ^{p}$ <mml:...

European options can be priced using the analytical solution of the Black-Scholes-Merton differential equation with the appropriate boundary conditions. A different approach and the one commonly used in situations where no analytical solution is available is the Monte Carlo Simulation. We present the results of Monte Carlo simulations for pricing European options and we compare with the analyti...

“Normality” of Stock Prices Bo Shi Abstract. The Black-Scholes Model, often simply called Black-Scholes, models the varying price of financial instruments over time: stocks in particular. This model assumes that returns on the underlying stock are lognormally distributed, which can be reasonable for many assets that offer options. However, from a selection of 100 stock histories, I found that a...

In this paper we analyze a nonlinear generalization of the Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We propose a novel method of pricing American style call options by means of transformation of the free boundary problem for a nonlinear Black-Scholes equation into the so-called Gam...

In this paper, Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method, is employed to obtain a quick and accurate solution to the fractional Black Scholes equation with boundary condition for a European option pricing problem. The Black-Scholes formula is used as a model for valuing European or American call and put options on ...

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at ha...