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 price of $170 per share by trading a total of 20 option contracts (10 put contracts and 10 call contracts). Each contract is written on 100 shares of stock. The put option is worth $18 per share, and the call option is worth $15 per share.
   1. What is the value (payoff) of the strangle at maturity as a function of the then stock price?
   2. What is the profit of the strangle at maturity as a function of the then stock price?

Answer 1

Given
Long Strangle
This Strategy says that we have to buy a Call Option with higher Strike price and buy a put option with a lower strike price.

Put Option --- Strike Price = 160 --------- 18 Price of the option
Call Option  --- Strike Price = 170 --------- 15 Price of the option
1 contract = 100 shares
Both Have 10 Contracts

A.
What is the value (payoff) of the strangle at maturity as a function of the then stock price?

Pay Off Call option = Max (0, Spot (Underlying Stock then Price) - Strike Price)
Pay Off Put option = Max (0, (Strike Price - Spot (Underlying Stock then Price))

Strangle Pay off = Pay off Call Option + Pay off Put Option


Pay Off Call Option = Max (0, (Underlying Price-170))
Pay Off Put Option = Max (0, (160 - Underlying Price))
Strangle Pay off = Max (0, (Underlying Price -170)) + Max (0, (160 - Underlying Price))

Each Contract Contain 100 shares So,
We have 10 Call and 10 Put contracts

= 10*100 * Pay Off Call Option + 10*100* Pay Off Put Option
= 1000 * (Pay Off Call Option + Pay Off Put Option)
Strangle Pay off = 1000 * (Max (0, (Underlying Price -170)) + Max (0, (160 - Underlying Price)))

B
What is the profit of the strangle at maturity as a function of the then stock price?
Profit of Call/Put Option = Pay Off - Premium (Price of Option)

Premium (Price Of Option)
Call Premium = 15
Put Premium = 18

Profit Call option = Pay off call option - Premium (Price of Option)
Profit Put Option = Pay off call option - Premium (Price of Option)

Profit Call option = (Max (0, (Underlying Price-170)) - 15)
Profit Put option = (Max (0, (160-Underlying Price)) - 18)

Overall Profit = Total Pay Off - total Premium

Total Premium = Call Premium + Put Premium

Each Contract Contain 100 shares So,
We have 10 Call and 10 Put contracts

Total premium = 100*10 (18 + 15) = 1000 * 33

Profit = Payoff value (as a function of Stock Price) - Total Premium
=  1000 * (Max (0, (Underlying Price -170)) + Max (0, (160 - Underlying Price))) - 1000 * 33

Profit  = 1000* ((Max (0, (Underlying Price -170)) + Max (0, (160 - Underlying Price))) - 33)

In case of any Confusion/Clarification feel free to comment, I will try to revert back as soon as possible. And If you liked it, please give a thumbs up​​​​​​​