Binomial Model.pptx

7/29/2019 Binomial Model.pptx

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Binomial

Option Pricing

ModelPresented By:-

Yash Deep Srivastava


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Outline Introduction

Assumptions

BOPM pricing Process Examples


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Introduction

The binomial model was first proposed by Cox,Ross and Rubinstein (1979).

The binomial options pricing model (BOPM)provides a generalizable numerical method forthe valuation of options.

It begin with a single period.

The binomial model takes a risk-neutralapproach to valuation.


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Contd..

Model uses an iterative procedure, allow for thespecification of nodes, or points in time, duringthe time span between the valuation date and

the option's expiration date.

Model reduces possibilities of price changes,removes the possibility for arbitrage.

It is able to provide a mathematical valuation ofthe option at each point in time specified.


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Assumptions of the BOPM There are two (and only two) possible prices for the

underlying asset on the next date. The underlying price willeither:

Increase by a factor of u% (an uptick) Decrease by a factor of d% (a downtick)

The uncertainty is that we do not know which of the twoprices will be realized.

The underlying security prices can only either increase ordecrease with time until the option expires worthless.

No dividends.


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Contd

The one-period interest rate r, is constantover the life of the option (r% per period).

Markets are perfect (no commissions, bid-askspreads, taxes, price pressure, etc.)

BOPM assumes a perfectly efficient market,and shortens the duration of the option.


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Contd

The model uses a discrete-time (latticebased) model of the varying price over time ofthe underlying financial instrument. In general,binomial options pricing models do not have

closed-form solutions.


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Binomial Option Pricing Model

Process The binomial model represents the price

evolution of the options underlying asset as thebinomial tree of all possible prices at equally-

spaced time.

Each node in the lattice represents a possibleprice of the underlying at a given point in time.

The value computed at each stage is the valueof the option at that point in time.


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.Option valuation using this method is a three-step

process:-

1) Price tree generation.

2) Calculation of option value at each final node.3) Sequential calculation of the option value at

each preceding node.


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01- Generation of Price Tree

The price can only move up and down at fixedrates and with respective pseudo-probabilitiesPu and Pd. Pd=(1-Pu)

Each column of the tree represents all the

possible prices at a given time, and each nodeof value S has two child nodes of values u Sand d S.

u and d are derived from volatility v :

dT :- Single time step

= u/2


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Binomial Tree for 2 time steps


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Binomial Tree for 4 time steps


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A simplified example of a binomial

tree:

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The Stock Pricing Process

Time T is the expiration day of a call option. Time T-

1 is one period prior to expiration.


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Another Example

A stock is currently priced at $40 per share.

In 1 month, the stock price may

go up by 25%, or

go down by 12.5%.


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03-Finding Option value at earlier

nodesWe move back to the root, using the following

formula:-


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Thank You.

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Binomial Model.pptx