Actuarial Finance

5 Options

If you hold a long position in a forward contract, you have the obligation to buy the underlying asset at the maturity date, no matter the discrepancy between the delivery price and the price of the asset, if any. In a forward contract, the investor with the short position has the opposite obligation.

In an option contract, the obligation is replaced by the possibility to run away whenever the situation is not profitable. Indeed, if you have the long position in an option to buy, you have the right to buy the underlying asset at the maturity date. Of course, this will be the case only when the delivery price is less than the price of the asset, i.e. only when it is rational to do so. On the other hand, the investor with the short position still has the obligation to sell you this asset. However, this optionality in the option contract comes at a price: a premium must be paid (at inception).

Example 5.0.1 Comparing a forward and an option to buy

Suppose that you can find the following two securities:

• a forward maturing in 3 months and written on a stock with a 3-month forward price of $48;
• an option to buy a stock maturing in 3 months, with a delivery price of $48 and actually trading for $2 (premium).

Let us describe the cash flows in the following two scenarios: in 3 months, the price of the stock will be $45 or it will be $53.

At inception, buying this option requires the payment of a premium of $2 while the forward can be entered at no cost.

In the first scenario, ...