How to Calculate the Price of a Call Option With Replication

by Ryan Menezes, studioD

A call option is a contract that lets an investor buy stock in the future at a fixed price. The option is worth money when the stock's trading price exceeds its fixed price from the option. A replicating portfolio contains stock shares, which are the call option's underlying asset, along with a separate riskless asset. Through replication, asset managers choose the portfolio's components so their combined cash flow equals that of the call option. The far simpler reversal of this calculates the option price from the replicating portfolio.

Multiply the number of shares in the replicating portfolio by the stock's final price. For example, if the portfolio contains 50 shares, and its stock sells at $70 when the call option expires, multiply 50 by $70 to get $3,500.

Add one to the interest rate on the portfolio's borrowed funds. For example, if the interest rate is 8 percent (0.08), add 1 to 0.08, giving 1.08.

Multiply the number of borrowed dollars that went into the portfolio by the sum from the previous step. For example, if the portfolio contains $1,000, multiply $1,000 by 1.08, giving $1,080.

Subtract the sum in Step 3 from the sum in Step 1: $3,500 minus $1,080 is $2,420. This is the price of the call option whose cash flow the portfolio replicates.

About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.

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