Problem 3 You anticipate that the volatility of the Google stock will increase o

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Problem 3 You anticipate that the volatility of the Google stock will increase over the course of next year, but you do not have a strong view about future direction of Google stock price. You decide to invest today in either one or two at the money European Google options maturing in one year The strike price of both options is $30 a share and today's Google stock price is $30 a share. The call option premium is $2 and put option premium is S3. (a) Describe your options position. Buy one call, buy one put (b) Draw profit diagram describing your position's profit as a function of Google's stock price at maturity. Draw profit diagram for all options (if applicable) and total profit as a function of IBM's stock price at maturity Profit Long Call, Strike 30 30 -2 -3 -5 Long Put, Strike 30 25 35 (c) Calculate breakeven price or prices) for your position. Lower breakeven price = 30-2-3 # 25 Upper breakeven price 30+2+3-35 (c) At what price your position will incur maximum loss and what this loss is. Price = 30, Loss "-3-2-=-5

Explanation / Answer

a. You know that google stock will be highly volatile in future however you are not sure whether the prices will increase or decrease.In such scenario you know that there will be large move in prices from $30 either downward or upward, so we implement Straddle trading strategy.

In this strategy, one buys a put and a call together with the same strike price and same expiration. So if the google price increases, the call option will cover the losses and if the price decreases, the put option will cover the losses.

b. Since Straddle is a combination of 1 call and 1 put option, we will have to first draw payoff diagram for both Buy call and buy put options and then its total profit diagram.

In the diagram, on X axis you have stock price and on Y axis profits. Since the option is at the money option both stock and strike price are same which is $30 ( as shown in figure).

Call Option Profit Diagram :

                 Call option payoff = max((S - K), 0) where S is Stock Price and K is Strike Price

1. When Stock price less than strike price and Call option payoff is 0. However the investor has paid a premium of $2 to the Option seller so, Total Profit of the investor will be

Profit = Payoff - premium paid

      = 0-2 = - $2

So till the stock price reaches a value of 29.99, investor will be at loss of $-2, as shown in the diagram.

2. When Stock Price is equal to Strike Price( At the money option).

Int his case both S and K are $30. So pay off is Zero

Profit = 0-2= -2, Investor will be lossing $2 till stock price is $30.

3. when Stock price is more than strike price

As the stock price starts increasing from $30, say it reached to $31,

Payoff will be max(31-30,0) = 1

However profit will be Payoff - premium paid = 1-2 =-1, so though the loss has decreased but investor is still at loss of $1. He will be at loss till the Stock price touches $32. In this case there will be no loss no profit.

As the prices increase further say 35.

Payoff= 35-30 = 5

Profit = 5-2 = 3 and the graph will show a increasing trend beyond $30.

Put Option Profit Diagram :

Put option payoff = max( (K-S),0)    Long Put option is just reverse of long call option.

1. When Stock priceis more than strike price and Put option payoff is 0. However the investor has paid a premium of $3 to the Option seller so, Total Profit of the investor will be

Profit = Payoff - premium paid

      = 0-3 = - $3

So till the stock price comes down to a value of 29.99, investor will be at loss of $3, as shown in the diagram.

2. When Stock Price is equal to Strike Price( At the money option).

Int his case both S and K are $30. So pay off is Zero

Profit = 0-3= -3, Investor will be lossing $3 till stock price is $30.

3. when Stock price is less than strike price

As the stock price starts decreasing from $30, say it reached to $29,

Payoff will be max(30-29,0) = 1

However profit will be Payoff - premium paid = 1-3 =-2, so though the loss has decreased but investor is still at loss of $2. He will be at loss till the Stock price touches $33. In this case there will be no loss no profit.

As the prices decrease further say 25.

Payoff= 30-25 = 5

Profit = 5-3 = 2 and the graph will show a increasing trend for all values less than $30.

Combining Call and Put Option Profit

There will be profit if the stock is priced above $35 or below $25, as the total Premium paid for both call and put option is $5. The maximum loss of $5 occurs if the stock remains priced at $30 at expiration. This is explained with red line in the graph.

c. Breakeven price is the point of No loss and No gain situation.

Upper breakeven price = 30+2 ( premium of Call)+3 ( Premium of Put) = 35, beyond which there will be profit

Lower breakeven price = 30 -2-3= 25, beyond which you will make profit.

d. Maximum loss will be at " At the money" option that is when stock price is $30. In this case, You will be at a loss of $5 which is sum of the total premium paid.

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