Question

1. A trader creates a long strangle with put options with a strike price of $160 per share, and call options with a strike of $170 per share by trading a total of 30 option contracts (15 put contracts and 15 call contracts). Each contract is written on 100 shares of stock. The put option is worth $13 per share, and the call option is worth $11 per share.

   A. What is the value of the strangle at maturity as a function of the then stock price? B. What is the profit of the strangle at maturity as a function of the then stock price?

Answer 1

A Strangle is a strategy by which a trader buys both call and put options on a stock of differing strike price. Thus the trader bets on stock volatility where he will gain if the stock moves either downward or upward by a huge margin.

In the given example Call is bought with a strike price of 170 while put is bought with a strike price of 160. This means the buyer of strangle will exercise put option if price goes below 160 and will exercise call option if price moves above 170.

Thus ,

Value of the strangle at maturity is a function of the stock price at maturity.

a. If the stock price is between 160 and 170, value of strangle = 0.

b. If stock price is greater than 170, value of strangle = (S - 170)* 15.
(Considering 15 calls are bought)

c. If stock price is less than 160, value of Strangle = (160 - S) * 15
(Considering 15 Puts are bought)

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Cost of buying the strangle is cost of bying call and put = (15*13) + (15*11) = 360.

Profit = Value - Premium cost.

Thus profit is :

a. If stock price is between 160 and 170, there is a loss of 360.

b. If stock price is greater than 170, Profit = ((S-170)*15)-360

c. If stock price is less than 160, Profit = ((160-S)*15)-360