Binomial option pricing model is very simple model that is used to price options. When to compared to Black Scholes model and other complex models, binomial option pricing model is mathematically simple and easy to use. This model is based on the concept of no arbitrage. Binomial Option pricing model is an important topic as far as FRM Part 1 exam is concerned. There are both conceptual and numerical questions in exams to test this topic. In this article, I will talk about various concepts related to binomial option pricing model.
The assumptions in binomial option pricing models are as follows
Let us consider that we have a share of a company whose current value is S0. Now in the next month, the price of this share is going to increase by u% (up state) or it is going to go down by d% (down state). No other outcome of price is possible for this stock in next month. Let p be the probability of up state. Therefore the probability of down state is 1-p.
Now let us assume that call option exist for this stock which matures at the end of the month. Let the strike price of the call option be X. Now in case, the option holder decides to exercise the call option at the end of month, what will be the payoffs?
The payoffs are given the below diagram
Now, the expected payoff using the probabilities of up state and down state. From the above diagram, the expected value of payoff is
Once the expected value of the payoff is calculated, this expected value of payoff has to be discounted by risk free rate to get the arbitrage free price of call option. Use continuous discounting for discounting the expected value of the payoff. FRM Part 1 uses continuous compounding and discounting for all numerical problems on derivatives.
In some questions, the probability of up state is not given. In such case, probability of up state can be calculated with the formula
p = up state probability
r = risk free rate
D = Down state factor
u = Up state factor
Using the above the model building process, similar model can be build for multi period options and also for put options.
One major limitation of binomial option pricing model is its slow speed. Computation complexity increases in multi period binomial option pricing model.
Binomial Option pricing model is an important topic as far as FRM Part 1 exam is concerned. There are both conceptual and numerical questions in exams to test this topic.
Vivek Sayal, MBA from XIMB, is currently working as a trainer for various finance courses. He has over 3 years of industry experience in organizations like J P Morgan Chase and Tata Consultancy Services. He has passed CFA Level 1 exam and FRM Part 1 exam. He is also NCMP Level 2 certified.
Disclaimer: "PMI®", "PMBOK®", "PMP®", "PMI-RMP®", "CAPM®" and "PMI-ACP®" are registered marks of the Project Management Institute, Inc.
The Swirl logoTM is a trade mark of AXELOS Limited.
ITIL® is a registered trade mark of AXELOS Limited.
PRINCE2® is a Registered Trade Mark of AXELOS Limited.
MSP® is a Registered Trade Mark of AXELOS Limited
Certified ScrumMaster® (CSM) and Certified Scrum Trainer® (CST) are registered trade marks of SCRUM ALLIANCE®
Professional Scrum Master is a registered trademark of Scrum.org
The APMG-International Finance for Non-Financial Managers and Swirl Device logo is a trade mark of The APM Group Limited.
The Open Group®, TOGAF® are trademarks of The Open Group.
IIBA®, the IIBA® logo, BABOK® and Business Analysis Body of Knowledge® are registered trademarks owned by International Institute of Business Analysis.
CBAP® is a registered certification mark owned by International Institute of Business Analysis. Certified Business Analysis Professional, EEP and the EEP logo are trademarks owned by International Institute of Business Analysis.
COBIT® is a trademark of ISACA® registered in the United States and other countries.
CISA® is a Registered Trade Mark of the Information Systems Audit and Control Association (ISACA) and the IT Governance Institute.
CISSP® is a registered mark of The International Information Systems Security Certification Consortium ((ISC)2).
CISCO®, CCNA®, and CCNP® are trademarks of Cisco and registered trademarks in the United States and certain other countries.