scholarly journals A EUROPEAN OPTION GENERAL FIRST-ORDER ERROR FORMULA

2013 ◽  
Vol 54 (4) ◽  
pp. 248-272 ◽  
Author(s):  
GUILLAUME LEDUC
Keyword(s):  
Random Walks ◽  
European Security ◽  
European Option ◽  
Order Error ◽  
First Order ◽  
Error Formula ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Values ◽  
Payoff Functions

AbstractWe study the value of European security derivatives in the Black–Scholes model when the underlying asset $\xi $ is approximated by random walks ${\xi }^{(n)} $. We obtain an explicit error formula, up to a term of order $ \mathcal{O} ({n}^{- 3/ 2} )$, which is valid for general approximating schemes and general payoff functions. We show how this error formula can be used to find random walks ${\xi }^{(n)} $ for which option values converge at a speed of $ \mathcal{O} ({n}^{- 3/ 2} )$.

A Binary Option Pricing Based on Fuzziness

2014 ◽  
Vol 13 (06) ◽  
pp. 1211-1227 ◽  
Author(s):  
Masatoshi Miyake ◽  
Hiroshi Inoue ◽  
Jianming Shi ◽  
Tetsuya Shimokawa
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Primary Role ◽  
Pricing Model ◽  
European Option ◽  
Over The Counter ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Fuzzy Boundary

In pricing for European option Black–Scholes model has been widely used in various fields in which the model can be applied under appropriate conditions. In this paper, we discuss a binary option, which is popular in OTC (Over the Counter) market for hedging and speculation. In particular, asset-or-nothing option is basic for any other options but gives essential implications for constructing more complex option products. In addition to the primary role of the asset-or-nothing option, another availability of the option is considered by introducing fuzzy concept. Therefore, the uncertainty which an investor and intermediary usually have in their minds is incorporated in the pricing model. Thus, the model is described with fuzzy boundary conditions and applied to the conventional binary option, proposing more useful and actual pricing way of the option. This methodology with the analysis is examined, comparing with Monte Carlo simulations.

AN APPLICATION OF MELLIN TRANSFORM TECHNIQUES TO A BLACK–SCHOLES EQUATION PROBLEM

2007 ◽  
Vol 05 (01) ◽  
pp. 51-66 ◽  
Author(s):  
MARIANITO R. RODRIGO ◽  
ROGEMAR S. MAMON
Keyword(s):  
Existence And Uniqueness ◽  
Mellin Transform ◽  
Formal Solution ◽  
Option Price ◽  
Contingent Claims ◽  
Time Dependent ◽  
European Option ◽  
Equation Problem ◽  
Black Scholes Model ◽  
Black Scholes

In this article, we use a Mellin transform approach to prove the existence and uniqueness of the price of a European option under the framework of a Black–Scholes model with time-dependent coefficients. The formal solution is rigorously shown to be a classical solution under quite general European contingent claims. Specifically, these include claims that are bounded and continuous, and claims whose difference with some given but arbitrary polynomial is bounded and continuous. We derive a maximum principle and use it to prove uniqueness of the option price. An extension of the put-call parity which relates the aforementioned two classes of claims is also given.

scholarly journals Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Winter Sinkala ◽  
Tembinkosi F. Nkalashe
Keyword(s):  
Option Pricing ◽  
Coupled System ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
First Order ◽  
Feedback Model ◽  
Black Scholes Model ◽  
Black Scholes

A first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one-dimensional subalgebras. We also construct some invariant solutions of the model.

scholarly journals VALUATION OF EUROPEAN PUT OPTION BY USING THE QUADRATURE METHOD UNDER THE VARIANCE GAMMA PROCESS

2020 ◽  
Vol 4 (5) ◽  
pp. 1-5
Author(s):  
Akash Singh ◽  
Ravi Gor Gor ◽  
Rinku Patel
Keyword(s):  
Quadrature Method ◽  
European Option ◽  
Brownian Motion Process ◽  
Asset Pricing Model ◽  
Pricing Options ◽  
Put Option ◽  
Variance Gamma Process ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Dynamic Asset Pricing

Dynamic asset pricing model uses the Geometric Brownian Motion process. The Black-Scholes model known as standard model to price European option based on the assumption that underlying asset prices dynamic follows that log returns of asset is normally distributed. In this paper, we introduce a new stochastic process called levy process for pricing options. In this paper, we use the quadrature method to solve a numerical example for pricing options in the Indian context. The illustrations used in this paper for pricing the European style option.  We also try to develop the pricing formula for European put option by using put-call parity and check its relevancy on actual market data and observe some underlying phenomenon.

scholarly journals Solving Black-Schole Equation Using Standard Fractional Brownian Motion

2019 ◽  
Vol 11 (2) ◽  
pp. 142
Author(s):  
Didier Alain Njamen Njomen ◽  
Eric Djeutcha
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Financial Market ◽  
Implied Volatility ◽  
Classical Model ◽  
Hurst Index ◽  
European Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
The Cost

In this paper, we emphasize the Black-Scholes equation using standard fractional Brownian motion BHwith the hurst index H ∈ [0,1]. N. Ciprian (Necula, C. (2002)) and Bright and Angela (Bright, O., Angela, I., & Chukwunezu (2014)) get the same formula for the evaluation of a Call and Put of a fractional European with the different approaches. We propose a formula by adapting the non-fractional Black-Scholes model using a λHfactor to evaluate the european option. The price of the option at time t ∈]0,T[ depends on λH(T − t), and the cost of the action St, but not only from t − T as in the classical model. At the end, we propose the formula giving the implied volatility of sensitivities of the option and indicators of the financial market.

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