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Hello Mr john, can you correct me if im wrong?
If i recall correctly, in one of your lectures you said strike price/ exercise price – underlying price of the security will result in the value of the option. On the other hand the black scholes pricing model is also used to put a value on an option. So couldn’t we just use the price of the security(at X point in time before expiration) – the exercise price to get the value of the option instead of using the black schole model?No, no.
What I said was just introducing the idea. I said that if we were able to exercise immediately then the value of a call option would be the the market value minus the strike price.
So, for example if we had an call option at an exercise price of $2.00 (i.e. the right to buy a share for $2) and the market value of the share was $3. Then if we were able to exercise today then the option would be worth $1. (Someone could by the option for $1, use it to buy a share for $2, and end up with a share worth $3).
However, the problem is that normally the option will be exercisable on a fixed date in the future. Using the same example as above, suppose the option was not exercisable until a date 3 months in the future.
Someone buying the call option would have to pay for the option now, and then in 3 months time pay $2 for a share. Obviously in 3 months time the share might be worth a lot more than the current $3 (which would be great – the option would be exercised and the share bought for only $2), but in 3 months time the share price might be worth a lot less than the current $3. Suppose in 3 months time it was only worth $1.50 – in that case it would not be worth exercising the option – nobody would want to pay $2 for a share only worth $1.50!!
So the price of the option is affected by how uncertain the share price is – if it is fluctuation a lot then it is more risky. Also, it is affected by the time period – if it is not able to be exercised for 6 months, there is more risk of the price having fallen. It is also affected by the interest cost of money (because we are having to pay for the option today, but won’t get any potential benefit from it until 3 or 6 months or whenever).
These are the factors that the Black Scholes formula are taking into account.
So the black scholes model is attempting to give us the potential gain in today’s value from an option if it is in the money at the date of expiration>?
So lets say i get 4$ from the blacks scholes for a call option and the exercise is 20$. So hypothetically the underlying price of the security should be 24$ at the time the option is exercised?
No – Black Scholes is valuing the option. It is calculating how much we would have to pay now to buy the option (or how much we could sell it for now).
Over time, the value of the option will change (because all of the factors in the formula will change). On the day that the option can be exercised then the value will be the then market value of the share less the exercise price. (Unless this was negative in which case it would have no value at all because it would not be exercised – nobody would want to buy it.)
(Which I suppose does agree with what you are saying 🙂 The price of the option on that date will be $4 because it is $24 – $20. (And the Black Scholes formula would give the same answer on that date.)
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