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On option pricing in the multidimensional Cox-Ross-Rubinstein model

100%
Motoczyński M., Stettner Ł.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 1
55-72
EN
Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.
2
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Optimality of replication in the CRR model with transaction costs

100%
Rutkowski M.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 1
29-53
EN
Recently, there has been a growing interest in optimization problems associated with the arbitrage pricing of derivative securities in imperfect markets (in particular, in models with transaction costs). In this paper, we examine the valuation and hedging of European claims in the multiplicative binomial model proposed by Cox, Ross and Rubinstein [5] (the CRR model), in the presence of proportional transaction costs. We focus on the optimality of replication; in particular, we provide sufficient conditions for the optimality of the replicating strategy in the case of long and short positions in European options. This work can be seen as a continuation of studies by Bensaid et al. [2] and Edirisinghe et al. [13]. We put, however, more emphasis on the martingale approach to the claims valuation in the presence of transaction costs, focusing on call and put options. The problem of optimality of replication in the CRR model under proportional transaction costs was recently solved in all generality by Stettner[30].
3
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A fuzzy approach to option pricing in a Levy process setting

88%
Nowak P., Romaniuk M.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 3
613-622
EN
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.
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