Current stock price S is $22. Time to maturity T is six months. Continuously com
ID: 2814683 • Letter: C
Question
Current stock price S is $22. Time to maturity T is six months. Continuously compounded, risk-free interest rate r is 5 percent per annum. European options prices are given in the following table Strike Price K1 $17.50 K2 $20.00 K3 $22.50 K4 $25.00 Call Price S5.00 $3.00 $1.75 $0.75 Put Price $0.05 $0.75 $1.75 $3.50 (a) What is the aim of a long (or bottom) straddle strategy? Create a long straddle by buying a call and put with strike price K3- $22.50 [10 marks] (b) What is the aim of a short (or top) strangle strategy? Create a short strangle by writing a call with strike price K3 $22.50 and a put with strike price K2- $20 10 marksExplanation / Answer
(a) A long straddle is created by purchasing a call and a put option of the same strike price and expiration. This strategy is profitable when the stock price moves strongly in either direction. This strategy bets on volatility
Purchase a call and put option with a premium of $1.75.
Stock price = $22; Exercise price call = $22.50
Payoff = max(0,Stock price - exercise price) + max(0,exercise price - Stock price) - call premium - put premium
Payoff = max(0,22-22.50) + max(0,22.50-22) - 1.75 - 1.75 = -$3
(b) A Short Strangle strategy is the combination of short call and short put. Predictiion is that the stock price will remain somewhere between strike of call and strike of put, and the options you sell will expire worthless.
Write a call and put option with a premium of $1.75 and $0.75 respectively
Stock price = $22; Exercise price call = $22.50; Exercise price put = $20
Since the stock price is below the call price and higher than the put price the options will expire worthless and the profit will be equal to the amount of premium received
= 1.75 + 0.75 = $2.5
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