In this paper, we investigate model-independent bounds for option prices given market instruments.This super-replication problem can be written as a semi-infinite linear programming problem. As these super-replication prices can be large and the densities Q which achieve the upper bounds quite...

In this work, we analyse the Galerkin Infinite Element method for option pricing. The Infinite Element method is a very simple and efficient modifcation of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy,...

In this paper we investigate the use of finite difference and finite element schemes when applied to the valuation of exotic options characterized by discontinuities in the payoff function. In particular, we will conduct a numerical analysis of several common schemes in order to give a better...

Under the local volatility model, the convergence of Monte-Carlo with Milstein discretization and Euler discretization are compared for the pricing of Vanilla, Digital, discrete Barrier options as well as a more exotic variety of option, the Accumulator. A finite difference approach is also...

In this essay, we empirically test the Constant-Elasticity-of-Variance (CEV) option pricing model by Cox (1975, 1996 [note: A revised version of the paper was published by the Journal of Portfolio Management (1996).]) and Cox and Ross (1976), and compare the performances of the CEV and...

Pricing different types of derivative contracts to minimize risk is a significant step for business sustainability. Whaley (2006) refers that for the European Puts and Calls, known as vanilla options, there is a closed form solution that delivers the 'fair' price of the option with respect to...

This manuscript gives introduction to parabolic Partial Differential Equations (PDE) in one-dimensional case. It recalls the notion and main limitations of Black-Scholes model and establishes the Black-Scholes formula. It recalls the standard machinery of solving the parabolic PDE which is...

The majority of quasi-analytic pricing methods for American options are efficient near-maturity but are prone to larger errors when time-to-maturity increases. A new methodology, called the "extension"-method, is introduced to increase the accuracy of almost any existing quasi-analytic approach...

Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial variables. In most cases, analytically closed form solutions for pricing such payoffs are not available, and the application of numerical pricing methods turns out to be non-trivial. We...