♦ Is the implied volatility consistent with the stock? 100
Implied Volatility of the S&P500 (VIX Index) 0 10 20 30 40 50 60 70 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 Implied Volatility (%) 0 200 400 600 800 1000 1200 1400 1600 1800 S&P500 Index Level VIX Volatility S&P 500 VIX Futures and Options ♦ Futures on the VIX started trading in 2004. ♦ Options on the VIX started trading in 2006. ♦ Trading futures or options on the S&P 500 index is a bet on both the future level of the S&P 500 and the volatility of the S&P 500. ♦ In contrast, a futures or option contract on the VIX is a bet only on volatility. ♦ One contract is on a dollar value of 1,000 times the index. For example, you buy one futures contract when the VIX is at 18 and close it when the VIX is at 21.5. You made $3,500. Hedging ♦ The number of stocks required to hedge against the price risk of holding one option is referred to as the hedge ratio or the option . HR for a Call = N (d 1 ) HR for a Put = N (d 1 ) – 1 ♦ In the example just looked at, the hedge ratio of the call option is equal to N (d 1 ) which was .6664. ♦ Thus, the change in the price of the option for a $1 increase in the stock price is 67 cents. ♦ If you bought 2 shares of stock for every 3 call options written, you would be hedged against stock price movements. Hedging ♦ The percentage change in the option’s value given a 1% change in the value of the underlying stock is referred to as the option . ♦ In our example, the call option price was $13.70 and the stock price was $100. A $1 increase in stock price corresponds to a 1% change. A $.67 increase in the option price corresponds to a 4.89% change. ♦ Thus, the elasticity is Portfolio Insurance - Protecting Against Declines in Stock Value ♦ Buying puts results in downside protection with unlimited upside potential. ♦ Limitations – errors if indexes are used for the puts – Maturity of puts may be too – Hedge ratios or deltas change as stock values change ♦ Portfolio insurance can be synthesized by moving a portion of funds out of stocks and into . ♦ The amount to move out of stocks is given by the hedge ratio of a put option on the portfolio with a given strike price. The strike price chosen represents the desired level of protection. 101
Futures Markets Futures and Forwards Forward An agreement calling for a future delivery of an asset at an agreed-upon price. No money changes hands today. Futures Similar to a forward, but has highly features. No money changes hands today (but margin is required). Key differences in futures ¾ Secondary trading - liquidity ¾ Marked to market or “pay-as-you-go” ¾ Standardized contract units ¾ Clearinghouse performance Key Terms for Futures Contracts Futures price Today’s agreed-upon price F 0 for the transaction to take place at maturity, time T.