Course 2: Nov 01, #25

[bg23516]

Q: A stoci has a price of 45 and pays no dividends. One year from now, there is a 50% probability that the price will be 30 and a 50% probability that the price will be greater than 40.

The risk free rate is 4%. Find the price of a one year European call with an exercise price of 40.
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The problem is throwing me for some reason. The fact that it says the price wll be either 30 or greater than 40 is odd. The solution solves for a value of a put, as
(.5*0) + (.5*10)/1.04 = 4.81, and then uses PC Parity to find Call value, but I'm not even sure why they are using the numbers they use for a put value. I mean, the value of a put is (Pfall * fall amount) + ((1-pfall)*0), and discount, but here, which is the fall amount? Why 10 and not 15, considering the price is 45?

Can anyone help?

[Gandalf]

Reminder: I've read none of the syllabus material, so this is another "look at the solution and see what they did" guess.

10 = 40 - 30. That seems to be a useful quantity to compute, since the exercise price is 40. Maybe the fall amount in valuing a put is the amount it could fall below the price you could put it at, rather than the amount it would fall from its current price?

Have patience. Someone else will give you the right answer if this is off the wall.

[ASA_Woman]

Q: A stoci has a price of 45 and pays no dividends. One year from now, there is a 50% probability that the price will be 30 and a 50% probability that the price will be greater than 40.

The risk free rate is 4%. Find the price of a one year European call with an exercise price of 40.
-----

The problem is throwing me for some reason. The fact that it says the price wll be either 30 or greater than 40 is odd. The solution solves for a value of a put, as
(.5*0) + (.5*10)/1.04 = 4.81, and then uses PC Parity to find Call value, but I'm not even sure why they are using the numbers they use for a put value. I mean, the value of a put is (Pfall * fall amount) + ((1-pfall)*0), and discount, but here, which is the fall amount? Why 10 and not 15, considering the price is 45?

Can anyone help?

I think it has something to do with the exercise price of 40. A put option is an option to sell at the exercise price. If the stock price falls to 30, then if you exercise your put option, you make a gain of 10. If the stock price is 40 or above, the put option has a value of 0 to you.

[bg23516]

I noticed that, but unfortunately, I can't compare it to any other questions in the book. The examples in the text deal with stocks with exercise price = current price, which is far from explanatory.

[johnny]

Let X = the value of the stock in a year. Then for a call option, it's value in a year will be X-40. Take the prsent value of this and you'll get one equation. Also make use of the Black and Scholes formula for a call option. I think you can solve these two equations to find the price of the option. Hope this helps.