TY - JOUR

T1 - Construction of risk-neutral measure in a brownian motion with exotic option

AU - Prabakaran, S.

N1 - Publisher Copyright:
© 2016 Pushpa Publishing House, Allahabad, India.

PY - 2016/11

Y1 - 2016/11

N2 - Binomial option pricing is a simple but powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes and other complex option-pricing models that require solutions to stochastic differential equations, the binomial option-pricing model is mathematically simple. We are trying to show how to price a derivative security by determining the initial capital which requires hedging a short position in the derivative security. The overriding objective of this research paper is to discover a clever way to solve the partial differential equation using risk-neutral probability measure. The main goal of this study is fourfold: (1) to derive the joint density for a Brownian motion with drift and its maximum to data, (2) to introduce the change of the probability measure with risk-neutral approach in the pricing of equity derivatives from real-world to risk-neutral by using Binomial structure model, (3) to extend this approach to treat the price the special type of option called a barrier option, and (4) to compute the risk-neutral price at time zero of the up-and-out call.

AB - Binomial option pricing is a simple but powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes and other complex option-pricing models that require solutions to stochastic differential equations, the binomial option-pricing model is mathematically simple. We are trying to show how to price a derivative security by determining the initial capital which requires hedging a short position in the derivative security. The overriding objective of this research paper is to discover a clever way to solve the partial differential equation using risk-neutral probability measure. The main goal of this study is fourfold: (1) to derive the joint density for a Brownian motion with drift and its maximum to data, (2) to introduce the change of the probability measure with risk-neutral approach in the pricing of equity derivatives from real-world to risk-neutral by using Binomial structure model, (3) to extend this approach to treat the price the special type of option called a barrier option, and (4) to compute the risk-neutral price at time zero of the up-and-out call.

KW - Binomial option pricing

KW - Black-Scholes-Merton equation

KW - Brownian motion

KW - Partial differential equation

KW - Risk-neutral measure

KW - Up-and-out call

UR - http://www.scopus.com/inward/record.url?scp=84994885414&partnerID=8YFLogxK

U2 - 10.17654/MS100101643

DO - 10.17654/MS100101643

M3 - Article

AN - SCOPUS:84994885414

SN - 0972-0871

VL - 100

SP - 1643

EP - 1674

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

IS - 10

ER -