iosr-Jm   Volume-16 ~ Issue-5 ~ Sep. – Oct. 2020

Abstract: In this paper an inversion formula for integral transform of I- function of several complex variables has been
established. Certain special cases are also given.

Keywords: I- function, Mellin transform, Mellin-Barnes contour integral.

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Abstract: In this paper, we develop a solution for pricing a European put option under the assumption that the distribution returns (losses) are Gumbel distributed at maturity. Further, we use the derived solution to check its relevancy with the data of actual market. We compare the Black- Scholes model which is based on assumption that distribution returns follow log-normal distribution with our derived solution which is based on the assumption that returns follow truncated Gumbel distribution numerically and observe some interesting underlying phenomenon.

Keywords: European put, Truncated Gumbel distribution, Fat tail, Black- Scholes model

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Abstract: The Black-Scholes model is widely used to determine price of European type options. The underlying stock prices have taken as normally distributed in Black-Scholes model. But it can be observed that, the underlying price of any option can never reach infinity in reality. So, there is a generalization of the Black-Scholes model by changing the distribution of underlying. We price some selected call options of Stocks listed on NSE by using this modified model and compare their prices with classical Black-Scholes model.

Keywords: Black-Scholes model, normal distribution, truncated distribution, options pricing, NSE.

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[5]. Sherrick B. J., Garcia P., Tirupattur V. (1996), Recovering probabilistic information from option markets: Tests of distributional assumptions, J. Futures Mark. 16 (5) 545–560.

Abstract: Let 𝓖 be the set of all 3 X 3 non-singular matrices 𝑎𝑏𝑐𝑑𝑒𝑓𝑔𝑕𝑖 , where a,b,c,d,e,f,g,h,i are integers modulo p. Then 𝓖 is a group under matrix multiplication modulo p, of order 𝑝𝑛−1 𝑝𝑛−𝑝 𝑝𝑛−𝑝2……𝑝𝑛−𝑝𝑛−1. Let G be the subgroup of 𝓖 defined by 𝐺=𝑎𝑏𝑐𝑑𝑒𝑓𝑔𝑕𝑖∈𝓖:𝑎𝑏𝑐𝑑𝑒𝑓𝑔𝑕𝑖=1. Then G is of order 𝑝𝑛−1 𝑝𝑛−𝑝 𝑝𝑛−𝑝2 …… 𝑝𝑛−𝑝𝑛−1 𝑝−1. Let L(G) be the lattice formed by all subgroups G. In this paper, we give the structure of the subgroups of order 16 of L(G) in the case when P=3.

Keywords: Matrix group, subgroups,Lagrange's theorem,Lattice, Atom.

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