# Option Question

Suppose that u=1.5, d=0.5, r=0.10, S=100. What is the price of a call option struck at K=0. a)150.00 b) 100.00 c) 50.00 d) 90.909 e) None of the above.

Uh what? It’s B. Zero strike call is like owning the stock. Think about it…

well, I would argue that it’s A. my logic: It can’t be c, or d since intrinsic value is s-k (100). assuming the option isn’t at expiration since there’s a probability of the option to move up (u) or down (d), then there’s time value as well. Given, price of an option is intrinsic value + time value, then answer should be A. Not sure if time value = 50, but it has to be greater than 0 if the option isn’t at expiration. Disclaimer: I haven’t read the options chapter and am not sure if there’s a formula to solve this. But, I know my option’s logic is correct since price of option = intrinsic value + time value.

dont we need to calculate probability of up and down first? forgot the forumla

Think about it this way: Up scenario: Price of Stock = 150 (you can sell the stock for \$150). Value of option = 150-0 = 150. *So, in the Up scenario, the stock and option are equivalent.* Down scenario: Price of Stock = 50 (you can sell the stock for \$50). Value of option = 50-0 = 50. *So, in the Down scenario, the stock and option are equivalent.* In all scenarios, the price of the stock and option are equivalent. Therefore, both must have the same price. Normally, you would need P(U) and P(D). However, these are not provided and are not necessary in this case.

ohia, please explain why probability is not a concern in this case. risk free rate is 10%, we discount value of option back 1 period or not?

I thought I just explained this… But anyway, there are implicit P(U) and P(D). In fact, you can probably solve for these using 100 = (150*P(U) + 50*P(D))/1.1 . The option price of 100 already takes the 10% discount rate into consideration, since implicitly, P(U) > P(D). Therefore, the expected payoff > 100. But forget all that. Just consider this statement: "In all scenarios, the price of the stock and option are equivalent. Therefore, both must have the same price. "

makes sense now, u and d shud be irrelavant

noel, do you have the answer?

I’ll pick B, the reason being the payoff of the call option is like a long stock position (since price >= 0 always). So the law of one price should apply which should make the price of the stock and the option the same.