Option pricing

I only said that the price of an option is current share price – exercise price in my introduction. That would only be the case if the option were exercisable immediately. (If the share price today is $5 and you could buy the right to get the share for only $4 then you would expect to pay $1 for that right (the option). You would pay $1 for the option, then use it to buy the share for $4 – you have spent $5 in total and then have a share that is worth 5$)

However, where options are useful is suppose the share price today is $5 and you can buy the right now to buy a share for $4 in three months time. In three months time the share price could be much more than $5 (or it could obviously have fallen) but you would still be able to buy it in 3 months time for $4. Provided the share price turned out to be more than $4 this would be great – it might end up being (say) $8 and you could still buy it for $4 and make a nice profit. For that reason you would expect to have to pay more for the option now, and the cost of it could be calculated using the Black Scholes formulae.

There are several reasons why you might be interested in buying options in practice. Here is one simple reason: I know I am going to get a lot of money and I want to use it to buy shares in X plc.. The problem is that the money will not be available to me for another two months, and the problem is that if they share price increases a lot then I will not be able to buy as many shares as I would be able to if I had the money today. If I buy a call option today, then it will fix the most I will have to pay per share in 2 months time, whatever happens to the share price.

More importantly you can use options to hedge against the risk of share price changes – but it would take too long to explain here. The lecture does explain this.

Most important for the exam is that you are able to use the Black Scholes formulae to calculate the price of the option.