## Biomial Pricing

s.roy
Good Student
Posts: 25
Joined: Wed Jul 26, 2017 7:32 am

### Biomial Pricing

Currently shares of ABC trade at USD 100. The monthly risk neutral probability of the price increasing by USD 10 is 30% and the probability of the price decreasing by USD 10 is 70%. What are the mean and SD of the price after 2 months if price changes on consecutive months are independent.

In the model answer you have soled mean value as under

Mean : 9% (120) + 42% (100) + 49% ( 80) = 92

how 9%, 42% and 49% is calculated. Please explain in details.

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: Biomial Pricing

In this problem, Probabilities of change in price are given for one month and we require to compute the deviation for two months period.
Accordingly,
Prob of price hike = 0.30 X 0.30 = .09 or 9%
Prob of price fall = 0.70 X .070 = .49 or 49%

s.roy
Good Student
Posts: 25
Joined: Wed Jul 26, 2017 7:32 am

### Re: Biomial Pricing

In connection with the above problem how 42% (100) is calculated . Not clear . Please explain

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: Biomial Pricing

Probabilities computed as under for Price Up & Down Situation = 0.3 × 0.7 × 2

s.roy
Good Student
Posts: 25
Joined: Wed Jul 26, 2017 7:32 am

### Re: Biomial Pricing

If the current stock price is 100 then how up and down prob ( 0.3 and 0.7) is multiplied with 100.

100 means no change in stock price.

Please explain in details . Not clear at all

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: Biomial Pricing

The Working of binomial model is attached herewith this text. Please see that.
Attachments
Book1.xlsx

s.roy
Good Student
Posts: 25
Joined: Wed Jul 26, 2017 7:32 am

### Re: Biomial Pricing

In 2 step binominal model we take stock price up and stock price down value and multiply with the respective probability. But no where I have seen multiply the original stock price by up and down probability. That is 100 * 0.7* 0.3.

My doubt is why it is done here . Even in the text book I have not seen .

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: Biomial Pricing

Please quote the question which you are referring.

And we are computing the mean under binomial option pricing model, which assumes the following:
1.the market is perfectly efficient,
2 the underlying security prices can only either increase or decrease with time until the option expires worthless, by taking a risk-neutral approach to valuation.

s.roy
Good Student
Posts: 25
Joined: Wed Jul 26, 2017 7:32 am

### Re: Biomial Pricing

That means when we have to calculate mean under binomial model, we need to multiply the stock up value with respective prob. stock down value with respective prob. and the original stock value with up * down prob.

please tell me whether my understanding is correct.

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: Biomial Pricing

No, We do not multiply the probability of price up & down with the stock price every time. Here it is done since we have to compute the mean for two periods (i.e for 2 months or 2 paths), so accordingly we extended the branches of binomial model. Please go through that chart once again it may be clear to you now.
If still any query pls let me know.