6.2. BASIC DEFINITIONS

A European call option gives the owner the right but not the obligation (that is the option)to buy a unit of the underlying asset days from now at the price X . We refer to as the days to maturity and X as the strike price of the option. We denote the price of the European call option today by c, the price of the underlying asset today by S _t , and at maturity of the option by .

A European put option gives the owner of the option the right to sell a unit of the underlying asset days from now at the price X. We denote the price of the European put option today by p. The European option restricts the owner from exercising the option before the maturity date. American options can be exercised any time before the maturity date.

We note that the number of days to maturity, , is counted in calendar days and not in trading days. A standard year of course has 365 calendar days but only around 252 trading days. In previous chapters we have been using trading days for returns and value-at-risk (VaR) horizons, for example, referring to a two-week VaR as a 10-day VaR. In this chapter it is therefore important to note that we are using 365 days per year when calculating volatilities and interest rates.

The payoff function is the option s...