TAILIEUCHUNG - Lecture Financial modeling - Topic 13B: BSM option greeks and dynamic delta hedging

Topic 13B - BSM option greeks and dynamic delta hedging. After completing this unit, you should be able to: Compute and utilize BSM greeks to estimate value change, understand the risks of option trading strategies, simulated dynamic hedging strategies of options. | Financial Modeling Topic #13b: BSM option Greeks and Dynamic Delta Hedging L. Gattis 1 Learning Objectives Compute and utilize BSM greeks to estimate value change Understand the risks of option trading strategies Simulated dynamic hedging strategies of options 2 3 Trade: Buy or Sell the 615 MAR Call? Buy the call If you believe the implied volatility (and option price) are too low (Cheap) and you estimate the volatility will be closer to If you buy the call at the implied volatility of , you are now long volatility (option price will increase if vol estimates rise) and long the stock (call prices will rise if the underlying spot price rises) You could hedge the stock price risk by short selling shares of the underlying stock and leaving only exposure to volatility Short Sales Short sales involve (1) borrowing shares (usually from your broker) (2) selling the shares now to another party (3) buying the shares back at a later date (4) returning the borrowed shares If the price falls after you sell the shares, you profit because it is cheaper to buy them back and return to the share lender Example: Short selling your friends Maserati 4 Delta Hedging an Option Delta hedging is the taking of a position in the option and the stock to hedge stock price risk and only take on volatility risk. Specifically, you delta hedge an option by taking a position (buy or short sell) a number of shares that has the same stock price sensitivity as the option. “Delta” is a term for the sensitivity of the option price with respect to changes in the underlying stock price. It is calculated by taking the first derivative of the BSM formula (BSCALL or BSPUT) . the spot price of the underlying stock. For example, an ATM call option may have a delta of This means that if the underlying stock price increases by $1, the option will increase by $ So, you hedge the price risk of an option of 100 shares by shorting 50 shares of the stock. 5 6 BSM Option Greeks The BSM .

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