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The share price follows a random walk and that the possible share prices are based on a normal distribution. One of the limitations of the Black-Scholes formula is that it assumes that the shares will not pay dividends before the option expires.
In fact, if no dividends are payable before the option expiry date, the American call option will be worth the same as a European call option.
Simply deduct the present value of dividends to be paid before the expiry of the option from the current share price. The following information relates to a call option: Black-Scholes model is a model for determining the price of a call option.
The market value of a call option can be calculated as: The formula will be given in the examination paper. You need to be aware only of the variables which it includes, to be able to plug in the numbers. Using the Black-Scholes model to value put options The put call parity equation is on the examination formula sheet: Value the corresponding call option using the Black-Scholes model. Then calculate the value the put option using the put call parity equation. Underlying assumptions and limitations The model assumes that: The options are European calls.
There are no transaction costs or taxes. The investor can borrow at the risk free rate. The future share price volatility can be estimated by observing past share price volatility. No dividends are payable before the option expiry date. Application to American call options One of the limitations of the Black-Scholes formula is that it assumes that the shares will not pay dividends before the option expires.
If this holds true then the model can also be used to value American call options. Illustration The following information relates to a call option: The dividend-adjusted share price for Black-Scholes option pricing model can be calculated as: Application of option pricing theory in investment decisions.