Abstract
The objective of this paper is to present a methodology for deriving Black Scholes formulae via a simple lognormal distribution approach and introduce European capped non automatically exercise (NAE) call option pricing theory. DOI : http://dx.doi.org/10.22342/jims.13.2.69.215-221
Highlights
Option or option contract is a security which gives its holder the right to buy or sell the underlying asset under the contracting conditions
The valuation standard option pricing theory based on distribution approach has been done by many researchers such as Brooks in [2] with normal and lognormal distribution, Corrado in [3] with generalized lambda distribution, and Markose and Alentorn in [4] with generalized gamma distribution
The objective of this paper is to present a methodology for deriving Black Scholes formulae via a simple lognormal distribution approach and introduce European capped non automatically exercise (NAE) call option pricing theory
Summary
Option or option contract is a security which gives its holder the right to buy or sell the underlying asset under the contracting conditions. The objective of this paper is to present a methodology for deriving Black Scholes formulae via a simple lognormal distribution approach and introduce European capped non automatically exercise (NAE) call option pricing theory In this option, if the stock price at time of expiration is greater than the cap value L, we deal that L as the price of stock and the payoff is capped at L−K, if the cap is not crossed the payoff becomes the standard call, max (0, ST − K). From solution of two integration in (7), the European standard call option price based on lognormal distribution and Brownian motion is CLog(K) = S0N (d1) − K exp(−rT )N (d2) This result is exactly the same as the Black Scholes standard [1]
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