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.

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 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 A fuzzy approach to option pricing in a Levy process setting

2013 ◽  
Vol 23 (3) ◽  
pp. 613-622 ◽  
Author(s):  
Piotr Nowak ◽  
Maciej Romaniuk
Keyword(s):  
Option Pricing ◽  
Lévy Process ◽  
Fuzzy Numbers ◽  
Levy Process ◽  
Martingale Measure ◽  
Fuzzy Arithmetic ◽  
European Option ◽  
European Call Option ◽  
Log Price ◽  
Geometric Levy Process

Abstract In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.

QUADRATIC HEDGING FOR THE BATES MODEL

2007 ◽  
Vol 10 (05) ◽  
pp. 873-885 ◽  
Author(s):  
FRIEDRICH HUBALEK ◽  
CARLO SGARRA
Keyword(s):  
Option Pricing ◽  
Explicit Expression ◽  
Martingale Measure ◽  
Risk Minimization ◽  
Hedging Strategy ◽  
Preliminary Results ◽  
Quadratic Hedging ◽  
The Mean ◽  
Mean Variance ◽  
Martingale Case

In the present paper we give some preliminary results for option pricing and hedging in the framework of the Bates model based on quadratic risk minimization. We provide an explicit expression of the mean-variance hedging strategy in the martingale case and study the Minimal Martingale measure in the general case.

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.

LOCALLY RISK-MINIMIZING HEDGING FOR EUROPEAN CONTINGENT CLAIMS WRITTEN ON NON-TRADABLE ASSETS WITH COMMON JUMP RISK

2021 ◽  
pp. 1-25
Author(s):  
Xiaonan Su ◽  
Yu Xing ◽  
Wei Wang ◽  
Wensheng Wang
Keyword(s):  
Closed Form Solution ◽  
Contingent Claims ◽  
Form Solution ◽  
Martingale Measure ◽  
Call Option ◽  
Transform Method ◽  
Jump Risk ◽  
European Call Option ◽  
Hedging Strategies ◽  
Optimal Hedging

This article investigates the optimal hedging problem of the European contingent claims written on non-tradable assets. We assume that the risky assets satisfy jump diffusion models with a common jump process which reflects the correlated jump risk. The non-tradable asset and jump risk lead to an incomplete financial market. Hence, the cross-hedging method will be used to reduce the potential risk of the contingent claims seller. First, we obtain an explicit closed-form solution for the locally risk-minimizing hedging strategies of the European contingent claims by using the Föllmer–Schweizer decomposition. Then, we consider the hedging for a European call option as a special case. The value of the European call option under the minimal martingale measure is derived by the Fourier transform method. Next, some semi-closed solution formulae of the locally risk-minimizing hedging strategies for the European call option are obtained. Finally, some numerical examples are provided to illustrate the sensitivities of the optimal hedging strategies. By comparing the optimal hedging strategies when the underlying asset is a non-tradable asset or a tradable asset, we find that the liquidity risk has a significant impact on the optimal hedging strategies.

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