Option Pricing Theory

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This is important because there has to be a method of deciding what premium to charge to the buyers. For a call option, the greater the price for the underlying item the greater the value of the option to the holder. The price of option pricing theory in investment decision underlying item is the market prices for buying and option pricing theory in investment decision the underlying item.

However, mid-price is usually used for option pricing, for example, if price is quoted as —, then a mid-price of should be used. The longer the remaining period to expiry, the greater the probability that the underlying item will rise in value. Call options are worth more the longer the time to expiry time value because there is more time for the price of the underlying item to rise.

The seller of a call option will receive initially a premium and if the option is exercised the exercise option pricing theory in investment decision at the exercised date. If interest rate rises the present value of the exercise price will diminish and he will therefore ask for a higher premium to compensate for his risk.

The greater the volatility of the price of the underlying item the greater the probability of the option yielding profits. The volatility represents the standard deviation of option pricing theory in investment decision price changes in the underlying item, expressed as an annualized percentage.

The pricing model for call options are based on the Black-Scholes model. Writers of options need to establish a way of pricing them. Factors determining the value price of option The major factors determining the price of options are as follows: The price of the underlying item For a call option, the greater the price for the underlying item the greater the value of the option to the holder.

For a put range trading best practice boundary binary options tunnel betting the lower the share price the greater the value of the option to the holder.

The exercise price For a call option the lower the exercise price the greater the value of the option. For a put option the greater the exercise price, the greater the value of the option. Time to expiry of the option The longer the remaining period to expiry, the greater the probability that the underlying item will rise in value. Put options are worth more if the price of the underlying item falls over time. Prevailing interest rate The seller of a call option will receive initially a premium and if the option is exercised the exercise price at the exercised date.

The risk free rate such as treasury bills is usually used as the interest rate. Volatility of underlying item The greater the volatility of the price of the underlying item the greater the probability of the option yielding profits. The following steps can be used to calculate volatility of underlying item, using historical information: Application of option pricing theory in investment decisions.

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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.