Optimal Hedging Monte Carlo Methods

Abstract

Leverage in the financial markets is one of the oldest techniques to increase one’s gains in an investment. It has also has lead to colossal losses and defaults. Leverage within an investment exists when an investor is exposed to a higher capital base than his or her original capital inlay. The margin mechanism of buying futures, as explained in Chapter 1, is a typical example of leverage. One posts margin of 5%–15% of the futures contract value but is exposed to 100% of the gains or losses of the notional amount of the futures contract. Exchanges will reduce the risk of this leverage in futures contracts by remargining daily using margin calls. Derivatives securities are another way to increase leverage. The call and put options described in Chapter 1 are standard ways to go long or short an underlying asset using leverage. A call option costing $5 and expiring $10 in the money creates a 200% return on investment. If this call expires out of the money, the loss is 100%.