Question

Your boss know wants you to price some call options. Explain to your boss the relative benefits and defects of each of the pricing models below:

1. Pricing using Put-Call Parity
2. Pricing using the Binomial model
3. Pricing using the Black-Scholes-Merton model

Answer 1

Pricing using Put-Call Parity: The theory of put-call parity implies that value of a short position in a European put option and value of  Long position in European Call option is same given the same expiry and strike price.

Benefits:

• Simple and easy to understand and apply
• It helps in taking synthetic positions in the market by combination of derivatives and futures/stock. These positions are more less volatile and economical.
• Any deviation in the put-call parity gives rise to arbitrage opportunity.

Defects:

• Can only be applied to European Options and not American Options
• It ignores taxes, transaction costs, and interest rates.

Pricing using Binomial model: It helps in predicting potential option prices under different conditions at various points in future.

Benefits:

• It works for both American and European options. In case of American options Binomial method works better as it can predict the price of exercising the options at different point of time.
• It also takes into account dividend payments and any other factors which might impact stock price.
• It can take into account probabilities of event too.

Defects:

• It is one of the most complex and slow method of option pricing.
• It is also based on certain assumptions like perfect market, information symmetry and constant interest rate

Pricing using Black-Scholes-Merton Model - It uses a mathematical formula comprising of various variables to calculate price of an option.

Benefits:

• It is fastest method to calculate value of multiple options and determine if there is any mispricing of options.

Defects:

• It is more applicable for European Options as the model predicts the value of option only at the time of expiry.
• It ignores transaction costs, dividend payout, no taxes.
• It is based on assumptions like constant interest rate, constant volatility and effective market which might not be always true.