1
$\begingroup$

Question: The price of a stock is 100. With equal probabilities, it either goes up to 130 or down to 70. What is the price of a 1 year call option with exercise price 100. Risk free rate is 5%.

Attempt: I use black scholes.

  • Given: $Su=130. Sd=70.rf=5% S_0=100$
  • $Cu=max(0,130-100)=30. Cd=max(0,70-100)=30$

Now, $$HedgeRatio = (30-0)/(130-70)=1/2$$ $$B=(Cd-Sd \cdot HedgeRatio)/(1+rf)=(0-70/2)/(1.05)=-(33+1/3)$$ So the price of the call option is $$C_0=S_0*Hedgeratio+B= 100/2 -(33+1/3)=16+2/3$$ but it is wrong.

$\endgroup$
  • $\begingroup$ Seems you are using the binomial option pricing method, for which I get the same answer (assuming discrete discounting of 1 year). $\endgroup$ – MikeRand May 16 '15 at 10:31
3
$\begingroup$

I don't know the BS formula you are trying to use.

The price is the expected value of the discounted payoff under the risk neutral probability measure (I.e. Under which S is a martingale)

So the you need to compute the risk neutral probabilities for S to go up or down. The probabilities given in the problem have no impact. They are just there to trick the candidate.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.