Hi Wayne,
Thanks for the detailed reply.
So the risk premium is a combination of this:
Current share price
Strike price
Time till expiry
Risk free interest rates
Dividends
Volatility
Have I understood this?
Hello Snake,
Yes, you’ve got it pretty much right in a nutshell, however, here’s something to think about which might add to Wayne’s excellent answer.
While this subject has been covered elsewhere in the derivative area, essentially the option price is the premium a seller of the option requires like the premium you pay to an insurance company. Think of it like that and the values will start to make sense.
Essentially writing (selling) options can be seen as issuing an insurance policy to the other party, or perhaps a bet that the option will go down in price and can either be left to expire worthless or bought back at a cheaper rate later. Hence the premium (price) demanded is in part a market driven value (included market maker tactics and involvement, especially in less liquid a markets) and in part a theoretical value.
Option pricing is an involved process since you are dealing with a range of concepts simultaneously in order to arrive at a theoretical valuation on one level as you know, and an actual market price on another.
Various pricing models have been developed in an attempt to establish relatively objective methods of valuing an option at a particular price over an underlying financial instrument at a particular time.
The two dominant mathematical models which have pages of formulas involved are “Black and Scholes” and “Binomial” (I prefer Binomial since it tends to be more robust in my view).
The key attributes of each option makes it unique in the way it will perform given movement in time and price.
Hence inputs into the model as you have identified are time to expiry, strike (or exercise) price, value of the underlying the option is over, dividends, and the interest rate component. In addition this gets complicated because of “volatility” which encompasses the inflation of the theoretical flat price since the effects of supply and demand inflate the option value, and volatility measures this level (this has been covered in detail on many of the derivative threads).
All these inputs result in a theoretical value, and then the market conditions alter this as an expression of volatility. Hence the price is the base value inflated by the odds the selling side are giving, very much like the way a bookmaker discounts some contenders in a horse race which are unlikely to win, while increasing the cost on others they consider more likely to win, or sometimes in order to hedge their book.
So, in your example, if the option was an out of the money call with 2 months to expiry, with a volatility of “X”, and a specific interest rate, and the underlying was trading at “Y”, you’d arrive at a theoretical value. Then the fun begins since there will probably be a spread between the bid and the ask, which will be jumping around as the underlying trades – each with its own fluctuating value and volatility measure.
Since no one has a crystal ball, the valuation is based on what the market thinks is likely to happen which is where the shadow falls between the theory and the practice.
Hope that helps!
Regards
Magdoran
