Examples of the analytical approximations are provided in Milevsky and Posner 1998 [3] and [4] who compare the relative accuracy of the lognormal or the inverse gamma distribution for approximating the sum of lognormal distributions. Tree based methods were originally proposed by Cox et al 1979 [2] and adopted in Wan 2002 [5]. Monte Carlo methods were first proposed by Boyle 1977 [1] as an alte...

The primary goal of this paper is to price European options in the Merton’s framework with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes a...

In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an I...

We investigate finite element discretizations using functions that are discontinuous in time and continuous in space for European options with local volatility Black-Scholes models. We present an a posteriori error estimate where a user-specified functional of the error is controlled by the inner product of the finite element residual with the solution of a dual problem that involves the densit...

lance of a few indicators through manual sampling in a limited number of patients (neuromuscular monitoring) and several more by SQL extraction in a sustained and short timeconsuming way through the years for all patients. Manual extraction was time-consuming and necessitated excessive workload and might not be viable in the long run, SQL extraction was very difficult to acquire in the initial ...

The option pricing problem is one of central contents in modern finance. In this paper, European option pricing formula is formulated for fuzzy financial market and some mathematical properties of them are discussed. This formula may be regarded as the fuzzy counterpart of Black-Scholes option pricing formula. In addition, some illustrative examples are also documented with MATLAB codes. c ©200...

In this paper, a modified formula for European options and a set of complete convergence proofs for the solution that cover the entire time horizon of a European option contact are presented under the Heston model with minimal entropy martingale measure. Although He & Zhu [5] worked on this model, they only provided a converged solution with a condition imposed on the time to expiry. The new so...

In this paper, we consider the partial differential equations approach for valuing European and American style options on multiple assets. We use a method of lines finite element implementation available in the software package FEMLAB in order to solve the variational inequality that characterizes the American style option, as well as the partial differential equation that defines the European ...

We consider the Constant Elasticity of Variance (CEV) process, reviewing the relationships between its transition density and that of the non-central chi-squared distribution. When the CEV parameter exceeds one, the forward price process is a strictly local martingale, and the price of a plain vanilla European call option reflects this fact. We develop techniques for Monte Carlo simulation of t...

Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The convergence rate of the COS method is exponential and the computational complexity is linear. It has a wide range of applicability for different underlying dynamics, including Lévy processes and Heston’s stochastic volatility model, and for various types of option co...