Existence of Maximum Entropy Problem Solution in a General N-Dimensional Case

In the following paper, we will define conditions, which need to be satisfied in order for the maximum entropy problem applied in European call options to have a solution in a general n-dimensional case. We will also find a minimum right boundary for the price range in order to have at least one risk neutral measure satisfying the option pricing formula. The results significantly reduce the computational time of optimization algorithms used in maximum entropy problem.

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Risk-Neutral and Physical Jumps in Option Pricing

SSRN Electronic Journal ◽

10.2139/ssrn.1099368 ◽

2007 ◽

Author(s):

Jian Chen ◽

Xiaoquan Liu ◽

Chenghu Ma

Keyword(s):

Option Pricing ◽

Risk Neutral

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An Empirical Study of the Option Pricing Formula with the Underlying Banned from Short Sell

SSRN Electronic Journal ◽

10.2139/ssrn.3478355 ◽

2019 ◽

Author(s):

Mesias Alfeus ◽

Xin-Jiang He ◽

Song-Ping Zhu

Keyword(s):

Empirical Study ◽

Option Pricing ◽

Short Sell ◽

Pricing Formula

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An Image Segmentation Method Based on Two-Dimensional Entropy and Chaotic Lightning Attachment Procedure Optimization Algorithm

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001420540300 ◽

2020 ◽

Vol 34 (11) ◽

pp. 2054030 ◽

Cited By ~ 1

Author(s):

Wei Liu ◽

Shuai Yang ◽

Zhiwei Ye ◽

Qian Huang ◽

Yongkun Huang

Keyword(s):

Image Segmentation ◽

Maximum Entropy ◽

Optimization Algorithm ◽

Search Algorithm ◽

Computational Time ◽

Two Dimensional ◽

Threshold Segmentation ◽

Grasshopper Optimization Algorithm ◽

Grasshopper Optimization ◽

Competitive Algorithms

Threshold segmentation has been widely used in recent years due to its simplicity and efficiency. The method of segmenting images by the two-dimensional maximum entropy is a species of the useful technique of threshold segmentation. However, the efficiency and stability of this technique are still not ideal and the traditional search algorithm cannot meet the needs of engineering problems. To mitigate the above problem, swarm intelligent optimization algorithms have been employed in this field for searching the optimal threshold vector. An effective technique of lightning attachment procedure optimization (LAPO) algorithm based on a two-dimensional maximum entropy criterion is offered in this paper, and besides, a chaotic strategy is embedded into LAPO to develop a new algorithm named CLAPO. In order to confirm the benefits of the method proposed in this paper, the other seven kinds of competitive algorithms, such as Ant–lion Optimizer (ALO) and Grasshopper Optimization Algorithm (GOA), are compared. Experiments are conducted on four different kinds of images and the simulation results are presented in several indexes (such as computational time, maximum fitness, average fitness, variance of fitness and other indexes) at different threshold levels for each test image. By scrutinizing the results of the experiment, the superiority of the introduced method is demonstrated, which can meet the needs of image segmentation excellently.

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A General Closed-Form Spread Option Pricing Formula

SSRN Electronic Journal ◽

10.2139/ssrn.2133923 ◽

2013 ◽

Cited By ~ 1

Author(s):

Ruggero Caldana ◽

Gianluca Fusai

Keyword(s):

Option Pricing ◽

Closed Form ◽

Spread Option ◽

Pricing Formula

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On Market Completions Approach to Option Pricing

Review of Business and Economics Studies ◽

10.26794/2308-944x-2021-9-3-77-93 ◽

2021 ◽

Vol 9 (3) ◽

pp. 77-93

Author(s):

I. Vasilev ◽

A. Melnikov

Keyword(s):

Option Pricing ◽

Incomplete Markets ◽

Option Price ◽

Optimal Investment ◽

Market Model ◽

Option Prices ◽

End Points ◽

Hedging Strategies ◽

Risk Neutral ◽

Interesting Approach

Option pricing is one of the most important problems of contemporary quantitative finance. It can be solved in complete markets with non-arbitrage option price being uniquely determined via averaging with respect to a unique risk-neutral measure. In incomplete markets, an adequate option pricing is achieved by determining an interval of non-arbitrage option prices as a region of negotiation between seller and buyer of the option. End points of this interval characterise the minimum and maximum average of discounted pay-off function over the set of equivalent risk-neutral measures. By estimating these end points, one constructs super hedging strategies providing a risk-management in such contracts. The current paper analyses an interesting approach to this pricing problem, which consists of introducing the necessary amount of auxiliary assets such that the market becomes complete with option price uniquely determined. One can estimate the interval of non-arbitrage prices by taking minimal and maximal price values from various numbers calculated with the help of different completions. It is a dual characterisation of option prices in incomplete markets, and it is described here in detail for the multivariate diffusion market model. Besides that, the paper discusses how this method can be exploited in optimal investment and partial hedging problems.

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Reverse Bonus Certificate Design and Valuation Using Pricing by Duplication Methods

Annals of the Alexandru Ioan Cuza University - Economics ◽

10.1515/aicue-2015-0019 ◽

2015 ◽

Vol 62 (3) ◽

pp. 277-289

Author(s):

Martina Bobriková ◽

Monika Harčariková

Keyword(s):

Option Pricing ◽

Exotic Options ◽

Pricing Models ◽

Underlying Asset ◽

Replication Method ◽

Maturity Date ◽

Derivative Market ◽

Replicating Portfolio ◽

Pricing Formula

Abstract In this paper we perform an analysis of a capped reverse bonus certificate, the value of which is derived from the value of an underlying asset. A pricing formula for the portfolio replication method is applied to price the capped reverse bonus certificate. A replicating portfolio has profit that is identical to profit from a combination of positions in spot and derivative market, i.e. vanilla and exotic options. Based upon the theoretical option pricing models, the replicating portfolio for capped reverse bonus certificate on the Euro Stoxx 50 index is engineered. We design the capped reverse bonus certificate with various parameters and calculate the issue prices in the primary market. The profitability for the potential investor at the maturity date is provided. The relation between the profit change of the investor and parameters’ change is detected. The best capped reverse bonus certificate for every estimated development of the index is identified.

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