Option Assumptions
By SmallStocks on Aug 2, 2008 in Options
Below is a list of all assumptions relative to Option pricing and calculation. Please keep these in mind whenever you are considering trading and/or dealing with options.
Full assumptions about the calculation of option prices
Some of the assumptions which must be made include:
- There are market participants such as large investment banks
- There are no transactions costs
- That all trading profits (the net of trading losses) will be subject to the same tax rate (meaning there are no marginal tax rates). (This will mean that every investor’s gains or losses will have the same effect regardless if the figure is $1 or $1million).
- That borrowing as well as lending is both possible at the risk-free interest rate.
- That all market participants will be prepared to take advantage of arbitrage opportunities as and when they arise. (Meaning that such opportunities will disappear quickly as the market efficiently corrects itself).
- Therefore there are no arbitrage opportunities.
- The interest rate is the nominal rate of interest and not the real rate of interest.
- Also that such a rate must be greater than 0 (i.e. a rate exists). Otherwise if this rate was 0 then there would be no advantage that the risk-free investment would provide over cash.
Typical Options notation:
- S0: Current stock price
- K: The strike price of the option
- T: The time until the option will expire
- ST: Stock price at maturity
- r: The continuously compounded risk-free rate of interest for an investment which will mature in time T
- C: The value of an American call option to purchase 1 share
- P: The value of an American call option to sell 1 share
- c: The value of an European call option to purchase 1 share
- p: The value of an European call option to sell 1 share
