Quick, what's your trade?

Quantitative Finance Level 2

The call on the 30 strike is trading $2.10 at $2.11, the call on the 32 strike is trading $1.34 - $1.35. Your broker calls you up and says that his market for the 31 call is $1.80 bid at $1.81.

Assuming no transaction fees (other than the bid ask spread) or execution risk , how would you trade the 31 call?

It depends on the volatility of the options Buy the 31 call at $1.81 Buy the 31 call at $1.80 Sell the 31 call for $1.81 The market is fairly priced Sell the 31 call for $1.80

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Calvin Lin by Calvin Lin

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1 solution

Calvin Lin Staff
Feb 4, 2015

Since a long butterfly position with equidistant strikes has a non-negative payoff, it follows that the price must always be non-negative.

This means that if we buy the 30 strike once, sell the 31 strike twice, and buy the 32 strike once, this should give us a non-negative number. Checking the math, we obtain

$ 2.11 − 2 × $ 1.80 + $ 1.35 = − $ 0.14 \$2.11 - 2 \times \$1.80 + \$1.35 = - \$0.14

This means that we should buy the butterfly for 14 cents credit, and choose to wait till expiration to collect the non-negative payoff.

Hence, we should sell the 31 call for $1.80.

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