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