what are greek letters
•One way in which managers can hedge their positions is through the use of the Greek letters.
Delta and gamma
- Delta: a measure of an option’s sensitivity to changes in the price of the underlying asset.
- Gamma: a measure of the Delta’s sensitivity to changes in the price of the underlying asset.
Vega
Theta
Rho
- Vega: a measure of an options sensitivity to changes in the volatility of the underlying asset.
- Theta: a measure of an options sensitivity to time decay.
- Rho: a measure of an options sensitivity to changes in the risk free interest rate.
•Assume that the Delta of a call option on a stock is 0.5.
–when the stock price changes by a small amount, the option price changes by approximately 50% of that amount.
–Delta Neutral portfolio.
taking a position in the underlying stock, so that the combined position in our options and the underlying stock is no longer sensitive to changes in the underlying asset price.
Delta hedging involves
•maintaining a Delta neutral portfolio through time.
Issues encountered in Delta Hedging
Delta is not constant.
- With large movements in the share price, the value of Delta will change.
- To maintain a Delta neutral portfolio, traders must adjust their position to take into account changes in Delta.
This process can be time consuming as the portfolio must be rebalanced every time Delta changes
Issues encountered in Delta Hedging
•To maintain a Delta neutral portfolio, traders must adjust their position to take into account changes in Delta.
is this expensive? How?
•The process can be quite expensive. If a trader is short in call options:
–When the spot price rises, they must buy more shares to maintain a Delta neutral portfolio.
–When the spot price falls they must sell shares to maintain a Delta neutral portfolio.
–This strategy is costly as the trader must buy high, and sell low.
