Call Option Price Formula

Call option price formula for the single period binomial option pricing model:

c = (πc+ + (1-π) c-) / (1 + r)

  • π = (1+r-d) / (u-d)

  • "π" and "1-π" can be called the risk neutral probabilities because these values represent the price of the underlying going up or down when investors are indifferent to risk.

  • r = The risk free rate

  • The same formula is applied for put options.

  • Steps for solving the value of a call option with the single period binomial model:

  • Calculate "u" and "d".

  • Calculate "π" (note: the risk free rate should be provided)

  • Combine "π" with c+ and c- to value the call.

  • NOTE: This can be repeated for the put option.

Test Tip:

Whenever pricing options on an exam question, it is a good idea to give your answer the laugh test; in other words, does the answer you are calculating make sense given the data provided.

For example a call that is deep out of the money should be relatively inexpensive; whereas a call that is deep in the money should be close to its intrinsic value plus a small time premium.