An Explicit Formula for Option Pricing in Discrete Incomplete Markets

1998 ◽  
Vol 01 (02) ◽  
pp. 283-288 ◽  
Author(s):  
Grażyna Wolczyńska
Keyword(s):  
Option Pricing ◽  
Explicit Formula ◽  
Incomplete Markets ◽  
Multinomial Distribution ◽  
Incomplete Market ◽  
Call Option ◽  
Risk Minimization ◽  
Optimal Price ◽  
European Call Option

Some aspects of the pricing of European call option are disscussed. We consider the simplest case of an incomplete market in the situation when the model of the market is discrete and increments of shares prices have a multinomial distribution. We look for similarities between this model and the model of Cox, Ross and Rubinstein. In particular we consider the possibility of using induction backwards and we look for an optimal price and strategy using the method of risk-minimization step by step from the date of realization T to 0.

scholarly journals Continuous-Time Portfolio Selection and Option Pricing under Risk-Minimization Criterion in an Incomplete Market

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Xinfeng Ruan ◽  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Shuang Li
Keyword(s):  
Option Pricing ◽  
Portfolio Selection ◽  
Incomplete Market ◽  
Martingale Measure ◽  
Call Option ◽  
Risk Minimization ◽  
European Call Option ◽  
Optimal Portfolio Selection ◽  
Transformation Methods ◽  
Special Case

We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset are governed by a jump diffusion equation. We obtain the Radon-Nikodym derivative in the minimal martingale measure and a partial integrodifferential equation (PIDE) of European call option. In a special case, we get the exact solution for European call option by Fourier transformation methods. Finally, we employ the pricing kernel to calculate the optimal portfolio selection by martingale methods.

scholarly journals Option Pricing under Risk-Minimization Criterion in an Incomplete Market with the Finite Difference Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xinfeng Ruan ◽  
Wenli Zhu ◽  
Shuang Li ◽  
Jiexiang Huang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Incomplete Market ◽  
Martingale Measure ◽  
Risk Minimization ◽  
European Option ◽  
The Finite Difference Method ◽  
Nikodym Derivative

We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE) of European option. The finite difference method is employed to compute the European option valuation of PIDE.

scholarly journals EUROPEAN CALL OPTION APPLICATION IN INCOMPLETE MARKET-ANALYSIS AND DEVELOPMENT

2014 ◽  
Vol 10 (1) ◽  
pp. 157-168
Author(s):  
Ro’fah Nur Rachmawati ◽  
Sufon ◽  
Widodo Budiharto
Keyword(s):  
Incomplete Market ◽  
Market Analysis ◽  
Call Option ◽  
European Call Option

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

scholarly journals ARBITRAGE-FREE OPTION PRICING MODELS

2009 ◽  
Vol 87 (2) ◽  
pp. 145-152 ◽  
Author(s):  
DENIS BELL ◽  
SCOTT STELLJES
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Square Root ◽  
Call Option ◽  
Pricing Models ◽  
European Call Option

AbstractWe describe a scheme for constructing explicitly solvable arbitrage-free models for stock price. This is used to study a model similar to one introduced by Cox and Ross, where the volatility of the stock is proportional to the square root of the stock price. We derive a formula for the value of a European call option based on this model and give a procedure for estimating parameters and for testing the validity of the model.

scholarly journals Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Congyin Fan ◽  
Kaili Xiang ◽  
Peimin Chen
Keyword(s):  
Option Pricing ◽  
Stock Prices ◽  
Call Option ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Dynamic Elasticity ◽  
European Call Option ◽  
Efficient Option ◽  
Nicolson Scheme

Market crashes often appear in daily trading activities and such instantaneous occurring events would affect the stock prices greatly. In an unstable market, the volatility of financial assets changes sharply, which leads to the fact that classical option pricing models with constant volatility coefficient, even stochastic volatility term, are not accurate. To overcome this problem, in this paper we put forward a dynamic elasticity of variance (DEV) model by extending the classical constant elasticity of variance (CEV) model. Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. In addition, Kalman filtering method is employed to estimate the volatility term of our model. Our main finding is that the prices of European call option under our model are more accurate than those calculated by Black-Scholes model and CEV model in financial crashes.

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