Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model
Issue:
Volume 6, Issue 2, April 2020
Pages:
19-27
Received:
5 April 2020
Accepted:
22 April 2020
Published:
15 May 2020
Abstract: Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.
Abstract: Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to ...
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A Necessary Condition for the Existence of a Certain Resolvable Pairwise Balanced Designa
Satoru Kadowaki,
Sanpei Kageyama
Issue:
Volume 6, Issue 2, April 2020
Pages:
28-30
Received:
14 January 2020
Accepted:
19 February 2020
Published:
30 June 2020
Abstract: A mathematical topic using the property of resolvability and affine resolvability was introduced in 1850 and the designs having such concept have been statistically discussed since 1939. Their combinatorial structure on existence has been discussed richly since 1942. This concept was generalized toα-resolvability and affine α-resolvability in 1963. When α = 1, they are simply called a resolvable or an affine resolvable design, respectively. In literature these combinatorial arguments are mostly done for a class of block designs with property of balanced incomplete block (BIB) designs and α-resolvability. Due to these backgrounds, Kadowaki and Kageyama have tried to clarify the existence of affine α-resolvable partially balanced incomplete block (PBIB) designs having association schemes of two associate classes. The known 2-associate PBIB designs have been mainly classified into the following types depending on association schemes, i.e., group divisible (GD), triangular, Latin-square (L2), cyclic. First, it could be proved that an affine α-resolvable cyclic 2-associate PBIB design does not exist for any α ≥ 1. Also, Kageyama proved the non-existence of an affine α-resolvable triangular design for 1 ≤ α ≤ 10 in 2008. Furthermore, the existence of affine resolvable GD designs and affine resolvable L2 designs with parameters υ ≤ 100 and r, k ≤ 20 was mostly clarified by Kadowaki and Kageyama in 2009 and 2012. As a result, only three designs (i.e., two semi-regular GD designs, only one L2 design) are left unknown on existence within the practical range of parameters. In the present paper, a necessary condition for the existence of a certain resolvable pairwise balanced (PB) design (i.e., some block sizes are not equal) is newly provided. Existence problems on PB designs are far from the complete solution. By use of the necessary condition derived here, we can also show a non-existence result of the affine resolvable L2 design which is left as only one unknown among L2 designs.
Abstract: A mathematical topic using the property of resolvability and affine resolvability was introduced in 1850 and the designs having such concept have been statistically discussed since 1939. Their combinatorial structure on existence has been discussed richly since 1942. This concept was generalized toα-resolvability and affine α-resolvability in 1963....
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