Overview:
- When the investors assume that market volatility is going to be very little they employ butterfly spread strategy.
- In a butterfly spread, when the stock price wanders around K2, the midpoint - it gives profit.
- However, at the date of expiry if the stock price is less than K1 or greater than K3, the whole position will expire worthless.
- Construction of a butterfly spread involves,
- Buying of a European call option at price K1
- Buying of a European call option at price K3
- Selling of two European call options at a price, which is a midpoint between K1 and K3.
Example:
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# Python example code that models the option strategy - butterfly spread K1 = 100 K2 = 200 K3 = 300
stockPrice = 200
i = 0
while i < 10: stockPrice = stockPrice + 25 payoff = 0 if (stockPrice > K1 and stockPrice <= K2): payoff = stockPrice - K1; elif (stockPrice > K2 and stockPrice < K3): payoff = K3 - stockPrice; elif (stockPrice <= K1): payoff = 0; elif (stockPrice >= K3): payoff = 0; else: payoff = 0; print("Stock price:%2.2f"%stockPrice); print("Payoff from butterfly spread:%2.2f"%payoff); print("-") i = i + 1;
stockPrice = 200
while i >= 0 : stockPrice = stockPrice - 25 payoff = 0 if (stockPrice > K1 and stockPrice <= K2): payoff = stockPrice - K1; elif (stockPrice > K2 and stockPrice < K3): payoff = K3 - stockPrice; elif (stockPrice <= K1): payoff = 0; elif (stockPrice >= K3): payoff = 0; else: payoff = 0; print("Stock price:%2.2f"%stockPrice); print("Payoff from butterfly spread:%2.2f"%payoff); print("-") i = i - 1; |
Output:
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Stock price:225.00 Payoff from butterfly spread:75.00 - Stock price:250.00 Payoff from butterfly spread:50.00 - Stock price:275.00 Payoff from butterfly spread:25.00 - Stock price:300.00 Payoff from butterfly spread:0.00 - Stock price:325.00 Payoff from butterfly spread:0.00 - Stock price:350.00 Payoff from butterfly spread:0.00 - Stock price:375.00 Payoff from butterfly spread:0.00 - Stock price:400.00 Payoff from butterfly spread:0.00 - Stock price:425.00 Payoff from butterfly spread:0.00 - Stock price:450.00 Payoff from butterfly spread:0.00 - Stock price:175.00 Payoff from butterfly spread:75.00 - Stock price:150.00 Payoff from butterfly spread:50.00 - Stock price:125.00 Payoff from butterfly spread:25.00 - Stock price:100.00 Payoff from butterfly spread:0.00 - Stock price:75.00 Payoff from butterfly spread:0.00 - Stock price:50.00 Payoff from butterfly spread:0.00 - Stock price:25.00 Payoff from butterfly spread:0.00 - Stock price:0.00 Payoff from butterfly spread:0.00 - Stock price:-25.00 Payoff from butterfly spread:0.00 - Stock price:-50.00 Payoff from butterfly spread:0.00 - Stock price:-75.00 Payoff from butterfly spread:0.00 - |