Unfortunately for the seller, the amount of profit he makes on the option that he writes is limited to the options price, if the option is not exercised. On the other hand, if the option is actually exercised, the seller’s loss is unlimited and depends on the change in the price of the stock.
According to the Black Scholes formula the price (P) of an option is:
P = SN(d1)-Xe-rtN(d2)
Where
S= Stock Price
d1={In(S/X)+(r+v2/2)t}/v(t)1/2
d2= d1-v(t) 1/2
t=time until expiration (% of year)
r=continuously compounded risk free interest rate
v=standard deviation of the short term stock returns over one year
In=Natural log
N(x)=Standard cumulative distribution function
e=exponential function
The binomial model calculates a tree of stock prices for given time intervals within the expiration period of the option using the volatility of a stock and time to expiration to find out how much a stock will increase or decrease in value. This calculation gives all possible prices of a stock. Then, the option prices of the stock are calculated backwards, from expiration to present. These prices are obtained by using risk neutral valuation. Ultimately, we get one price for the option.
To calculate the price of stock options using the Black Scholes formula:
Who is an option holder?
An option holder is the investor who buys the option. Who is an option writer?
The option writer is the seller of the option. What is the exercise price of an option?
Exercise price, sometimes also called the strike price of an option refers to the price at which the option holder or writer has the price to buy or sell the option. What is the expiration date?
Every option has a date by which the option ceases to exist i.e. the option holder has no rights and the option loses all value. This date is known as the expiration date of the option. What is a premium?
The premium of an option is just another word for the price of an option. Why would you want to buy an option?
Options allow investors to invest in stocks and take on only an assigned amount of risk because an investor cannot lose any more money than the money that he has invested in the option. An investor buying options can also invest in a larger basket of goods as compared to an investor investing in stocks, as the price of options is cheaper than the price of a stock. Thus, the investor can afford to hold a diversified portfolio for less money. What is a call option?
The buyer of a call option has the right to buy a fixed number of shares of a stock at a price fixed by the writer of the option at a certain point in time. What is a put option?
The buyer of a put option has the right to sell a fixed number of shares of a stock at a price fixed by the writer of the option at a certain point in time. What is option spread?
An option spread is when an investor sells one options on a security and then buys an option on the same security in order to reduce the risk associated with buying the option of that original security. There are three types of spreads, vertical, horizontal and diagonal. A vertical spread occurs when the option that is being bought and sold has the same striking prices but different expiration dates. A horizontal spread occurs when the options that are being bought and sold have the same expiration dates and different striking prices. A diagonal spread is a combination of vertical and horizontal spreads. What is a straddle?
A straddle is when an investor simultaneously buys and sells the same option with the same exercise price and expiration date. What are the kinds of options available in the market?
There are two different kinds of options available in the market. The first kind is a physical delivery option. In this case, the buyer receives the physical good if it is a call and if it is a sell option, the seller has to deliver the physical goods. The second kind of an option is cash settled option, which means that the owner of an option has the right to receive a cash payment based on the difference between the fixed exercise price of the option and the price at the time the option is exercised. The seller of the option has to make the cash payment. Options can also be categorized according to their expiration dates. An American style option can be exercised at any time prior to the expiration date whereas a European style option can be exercised only during a fixed period before its expiration date. The American option has more value than the European option. How do you price an option?
The Black Scholes formula is used to price a European style option by factoring in current stock price, strike price, time until expiration, level of interest rates, any dividends and the volatility of the underlying security. The binomial model is used to price American style options. Important Links:
To calculate the price of stock options using the binomial method:
