Question

# A trader creates a long strangle with put options with a strike price of \$90 per...

A trader creates a long strangle with put options with a strike price of \$90 per share, and call options with a strike of \$105 per share by trading a total of 40 option contracts (buy 20 put contracts and buy 20 call contracts). Each contract is written on 100 shares of stock. The put option is worth \$10.5 per share, and the call option is worth \$6.5 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? Make sure to derive the exact range of then stock prices where the trade is profitable.

Payoff from a strangle,

 Range of Stock Price Payoff from Call Payoff from Put Total Payoff S<=K1 0 K1-S K1-S K1K2 S-K2 0 S-K2

Where, K2 = call strike price, K1= Put Strike price, K2> K1, S= Stock price at maturity

Contracts Strike Price Price Cost
20 105 6.5 -13000
20 90 10.5 -21000
 S 65 73 85 90 98 105 110 122 140 20 (Call) 0 0 0 0 0 10000 34000 70000 20 (Put) 50000 34000 10000 0 0 0 0 0 0 Value 50000 34000 10000 0 0 0 10000 34000 70000 Cost -34000 -34000 -34000 -34000 -34000 -34000 -34000 -34000 -34000 Profit 16000 0 -24000 -34000 -34000 -34000 -24000 0 36000

When Stock price is S<73 or S>122, this trade is profitable

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