a. Whenever we enter into a derivative contract based on any underlying asset, we determine its exercise price at the future date (mostly the strike price at the time of expiration of the contract).
b. This strike price is generally different from the spot price at which the asset is currently trading. This price is usually arrived at, by adjusting the current spot price for the time value of money (giving due consideration to the risk and its premium). Also, the spot price is adjusted for the benefits of holding the assets and the cost of holding the same (which are usually quantified in monetary terms).
c. There are three basic fundamental principles based on which the pricing and valuation of derivatives are made:
i. The Arbitrage Principle. The derivatives should be priced in such a manner that there exist no arbitrage opportunities. This means that the assets should be trading at such a fair price at all the markets during the same time, otherwise, there would be an opportunity for the traders to make arbitrage profits.
ii. The Replication Principle. It is the ability to create an asset or portfolio from another asset or portfolio, and/or derivative. Using the derivatives, we can replicate a contract by adding the risk-free returns to the spot price of the underlying assets.
iii. The Risk Neutrality Principle. Here, it is assumed that the investor is not risk-averse (A risk-averse investor is an investor who demands higher returns, i.e. risk premium on the riskier assets). While pricing the derivatives we assume that the investor is not affected by the risk. Thus, the spot price is only adjusted for the risk-free rate.
d. The overall process of pricing the derivatives by arbitrage and risk neutrality is called arbitrage-free pricing. According to this principle, a derivative must be priced in such a manner that no arbitrage opportunity exists and there exists only one price for the derivative that earns the risk-free returns. That is,
Spot Price + Risk-Free Return = Future Strike Price |