Question

Problem 1

As an option trader you decide to sell a straddle by selling a put option and a call option on the same stock. The put option has a strike price of K1 = $50 and is priced for P = $5, and the call option has a strike price K2 = K1 = $50 and priced for C = $7.

1. Construct a table showing the payoff and profit you would get from this strategy based on the stock price (you can insert a table or use spacing to present the information in the form of a table).
2. For what range of prices of the underlying stock you would be making a positive profit?
3. What is the maximum profit you could possibly get from selling this straddle?
4. What aspects relating to a trader’s views regarding stock price movements affect his/her decision when choosing between buying a straddle or buying a strangle? Explain in which case he/she would choose one of these 2 strategies and not the other.

Answer 1

Payoff of short straddle = payoff of short call option + payoff of short put option

Payoff of a short call option = P - Max[0, S-X]

Payoff of a short put option = P - Max[0, X-S]

S = underlying price at expiry,

X = strike price

P = premium received  

Table showing the payoff and profit are below :

The formulas are shown below :

A positive profit is made when the prices of the underlying stock are between $39 and $61

Maximum profit = $12 (total premium received)

When choosing between buying a straddle or buying a strangle, the trader expects the stock price to make a large move in either direction, but the trader is unsure of the direction of movement.

A strangle is chosen to decrease the total cost of the strategy. This is because a strangle is entered with out-of-the-money options whereas a straddle is entered with at-the-money options. The premium of at-the-money options is higher, which makes a buying a straddle more expensive than buying a strangle.