Derivatives and Risk Management

  

1) In a file named “Alphabet Option Prices.xlsx” available from Canvas, the prices for call and put options expiring on January 19, 2018 are listed. These prices were pulled at noon on Monday, October 23, 2017 at which point the stock price was $990.19.

Suppose that you have $1,000 to invest. The strategies that you may choose from are the following:

i. Long Calls, any strike

ii. Long Puts, any strike

iii. Butterfly, any strikes

iv. Straddle, any strike

v. Strangle, any strikes

The table below lists several predicted stock values and constraints. For each row, choose the strategy and any required strike(s) that will maximize the profits of a $1,000 investment at the predicted stock value while still fulfilling the constraints. If the constraints cannot be satisfied by any of these strategies, say so. You can assume that no margins are required.

  

Stock Price

Constraint

 

$1,000

Positive profits at any future spot   price

 

$1,000

None

 

$1,100

None

 

$1,100

No losses for spot prices below $950

2) Suppose that Alphabet stock is trading at $1,000 on Wednesday, 10/25/2017. An at-the-money call option exists that expires 3 weeks from that date, on 11/15/2017.
Assume that every week, Alphabet stock will either increase or decrease by a factor of 1.05. That is, in one week, the price will either be $1,000*1.05 = $1,050 or $1,000/1.05 = $952.38.
You can assume that the risk-free rate is 5% per year. You can assume that this is either the continuously compounded rate or the APY.

a. At the end of three weeks, what possible prices can the stock take?

b. At the stock prices listed in (a), what is the value of the call option at expiration?

c. Draw this scenario as a multi-step binomial tree.

d. At any particular node, what is the risk-neutral probability that the stock price will increase? Write this probability, as well as the probability of a price decrease, on the tree from part (c).

Complete the tree by finding the price of the call option at every node.