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 |
| K1<S<K2 | 0 | 0 | 0 |
| S=>K2 | 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
Get Answers For Free
Most questions answered within 1 hours.