Question I Value Derivatives

An investor is very bullish on LewCo, a nondividend paying company. The current spot price of the companys equity is $50 per share. The investor is confident the company will solve the social distancing issue and that the value of the stock will be at least $100 in 12 months.

The investor uses a 12-period binomial tree assuming

S0 = $50

T = 12 months

r = 30 basis points per month

u=1.1 per month

d = 1/u= 1.1-1 per month 1.

1. Apply the binomial tree model to value a 12-month European style call with a strike of $100. What is the call premium?

2. Use put-call parity to value the put on the same asset, for the same expiration, and with the same strike. What is the put premium?

3. The investor is considering two other calls. One with a strike of $200. Another with a strike of $0. The values of these structures should be evident to you. What is the premium on the call with a strike of $200? Why? What is the premium on the call with the strike of $0? Why?

4. Why do investors use options? To answer this, we consider an investor with $5,000 to invest. Assume the spot price in 12 months is $100, as predicted by the investor. Calculate the amount the investor will make spending the $5,000 to buy shares of stock, spending the $5,000 to buy puts with a strike of $100, or spending the $5,000 to buy calls with a strike of $100? Based on this analysis, what is the advantage of using options?

5. What would be the premium of a derivative structure paying the square of the call payoff in each node of the terminal distribution?