Presentation on binomial model

8/10/2019 Presentation on binomial model

1/16

The Binomial No-Arbitrage Pricing Model

Mohammad Arifur Rahman

University of Texas at El Paso

[email protected]

November 7, 2014

Mohammad Arifur Rahman (UTEP) The Binomial No-Arbitrage Pricing Model November 7, 2014 1 / 15
http://find/


2/16

Overview

1 What is an option?

2 What is Binomial No-Arbitrage Model?

Meaning of No-ArbitrageCreating Binomial TreeFinding option value after each periodFinding arbitrage value

3 Pros and Cons of Binomial Pricing Model

http://find/


3/16

What is an option?

A Option is the security that gives the owner the right, but not theobligation, to buy(or sell) shares, underlying asset or instrument or anindex at a certain price by a certain date. That certain price is calledthe strike price, and that certain date is called the expiration date.

In call option owner gets the right to buy. And in put option owner getsthe right to sell.

http://find/


4/16

Example

As a quick example of how call options make money, lets say IBM stock iscurrently trading at $100 dollar per share. Now lets say an investor

purchases one call option contract on IBM with a $100 dollar strike and ata price of $2.00 dollar per contract. Note: Because each options contractrepresents an interest in $100 underlying shares of stock, the actual cost ofthis option will be $200 dollar ($100 shares x $2.00 = $200).

http://find/


5/16

Meaning of No-Arbitrage

A situation in which all relevant assets or shares are priced appropriately

and there is no way for ones gains to outpace market gains without takingon more risk. Assuming an arbitrage-free condition is important infinancial models, thought its existence is mainly theoretical.

http://find/


6/16

One-Period Binomial Model

Assumptions

At the beginning time is 0 and at the end of the period time is 1.

At time 0, stock price is S0, which is positive.

at each step, the stock price will change to one of two positive values,S1(H) and S1(T).

Probability of Head is positive, say p, and the probability of tail isq= 1 p, which is also positive

Ther are two positive numbers, d and u, such that 0


7/16

One-Period Binomial Model

http://find/http://goback/


8/16

Option Value

A money market with interest rate r

$1 invested in the money market $(1+r) in the next period

A call option with strike price K>0 and expiration time 1this option confers the right to buy the stock at time 1 for $K

it is worth of max[S1 K, 0]

we denote V() =max[S1() K, 0] the value(payoff) at expiration.



9/16

Arbitrage price of the option

We compute the arbitrage price of the call option at time zero,V0.

Suppose,at time zero we sell the call option for V0 dollars.

http://find/


10/16




11/16


http://find/


12/16


13/16

Pros and Cons

Pros:

The Binomial options pricing model approach is widely used as it isable to handle a variety of conditions for which other models cannot

easily be applied.Although computationally slower than the BlackScholes formula, it ismore accurate, particularly for longer-dated options

It can be used to price American and Bermudan options also.

It can be implemented in computer programs.

http://find/


14/16

Pros and Cons

Cons:

For options with several sources of uncertainty (e.g., real options) and

for options with complicated features (e.g., Asian options), binomialmethods are less practical.

By hand, it would take a long time to price an option using a lot oftime intervals.



15/16

References

Wikipedia

http://www.investinganswers.comStochastic Calculus for Finance I: The Binomial Asset Pricing Model(Springer) By Steven Shreve



16/16

The End

http://find/

Documents

Presentation on binomial model