Suppose that today the stock price of the Tesla Inc is $600/share and that the volatility of the stock price is 70% per annum. Tesla Inc is not expected to pay any dividend in the next few years. The risk-free interest rate is 2% per annum with continuous compounding. European call and put options on Tesla Incs stock with strike price $700 are available. The European call and put options will both expire in 6 months.

Answer

questions regarding to a two-step binomial model with 3-month time step.

1. (a) What is the percentage up movement of the stock price in the binomial model? (1 points)(rounding to 4 decimals)

2. (b) What is the percentage down movement of the stock price in the binomial model ? (1 points)

   (rounding to 4 decimals)

3. (c) What is the probability of an up movement of the stock price in the binomial model in a risk- neutral world ?(2 points) (rounding to 4 decimals)

4. (d) Use this two-step binomial model to compute the price of the European call ? (5 points)

5. (e) Use this two-step binomial model to compute the price of the European put ? ( 5 points)

6. (f) Suppose an investor writes 10,000 European puts today, assuming each put gives the buyer of

   the put the right to sell one share of the stock.

   1. (i) how many shares of Tesla Incs stock the investor has to long(or short)

      to hedge his short position in the European put for the first 3-month

      period ? (2 points)

   2. (ii) If at the end of first 3-month period the stock price goes up, how many

      shares of Tesla Incs stock the investor has to long(or short) to hedge his short position in the European put for the second 3-month period ? (2 points)

   3. (iii) If at the end of first 3-month period the stock price goes down, how many shares of Tesla Incs stock the investor has to long(or short) to hedge his short position for the second 3-month period ? ( 2 points)