Question

Currently Zebe Corporation stock is trading at a price of $50. You are considering two options that expire in January 2019.

a. As a function of Zebe Corp’s stock price at expiration, draw a payoff diagram for a call option with a strike price of $60.

b. As a function of Zebe Corp’s stock price at expiration, draw a payoff diagram for a put option with a strike price of $60.  

c. Suppose the call option in (a) trades at a price of $2, while the put in (b) trades at $14. For each of the options, compute the break even price of the stock such that the cost of the option is retrieved by the option buyer.

d. Using a payoff diagram, show how a put option can be used to provide portfolio insurance.  

e. A long straddle involves purchasing both a call and put option on the same stock at the same strike price and expire at the same time. Draw a payoff diagram for a long straddle.

f. When might an investor use a long straddle?

Answer 1

Solution :

Part A ) Pay off of a call option is = MAX(Spot Price -strike price,0) - premium paid

Payoff diagram is prepared in excel

Part B )

Pay off of a put option = Max ( strike price - spot price , 0) - premium paid

Payoff diagram is prepared in excel

Part C ) Break-even point is where there is no profit and no loss

So in case of a call option, where premium paid = 2, strike price = 60

pay off =  MAX(Spot Price -strike price,0) - premium paid

0 = MAX(Spot Price -strike price,0) - 2

0 = Spot price - 60 - 2

Spot Price = 62

So in case of a put option, where premium paid = 14, strike price = 60

pay off =  MAX(Strike -Spot,0) - premium paid

0 = MAX(Spot Price -strike price,0) - 14

0 = 60- Spot - 14

Spot Price = 46

So , Breakeven in case of call option is 62, while in case of put option it is 46

Part D )

If we look at the payoff diagram in the below image for put option then maximum loss = 14 ( premium )

Maximum gain can be when spot price becomes zero = 60-14 =46

So it's a kind of insurance policy whereby paying 14 as premium you are ensuring the loss in the price of the share

Part E )

Payoff diagram is prepared in the excel

Part F )

An investor may use this strategy when there is high volatility and investor is not sure whether the stock will go up or down. By using this strategy he will gain through put option if share price goes down , and he will gain through call option if share price goes up