Derivative Hedging

There are 4 equally-weighted sections.
Topics:

1. Quantitative Derivatives
2. Option Valuation Models
3. Derivatives applied to Private Wealth Management
4. Derivative Hedging
   Q1 Quantitative Derivatives
   a. Apple stock (AAPL) is priced at $141.66. The 12/16/22 (176 day) (strike 150) put is valued at 16.45. Its delta is .552, gamma .013, theta .032. Based on only these Greeks, if the stock rises by $20 in 10 days and you have shorted a put, provide:
5. The projected value of the put.
6. The projected profit of one contract.

b. Another AAPL option is 12/16-176 days, strike 115, bid $3.95, delta .176, gamma .007.

1. At what delta should you close the position if you have shorted it assuming an deterioration has occurred?
2. Based on your answer, provide the projected stock price.

c. If the old stock price is $15, the new stock price is $20, the old call option is $2.00 and the new call option is $3.5, what is the call option delta?

Q2 Option Valuation Models
a. Using the Put Call Parity, show the equation for a SHORT STOCK.

b. For the Black Scholes Option Pricing Model, list three important assumptions and then explain the real world deficiencies.

c. Explain if and how the Binomial Option Pricing Model can be applied to valuing a call option in a corporate bond, known as a callable bond.

Q3 Derivatives applied to Private Wealth Management
a. Explain the advantages of using an index option over an equity option.

b. Explain THREE methods and measures of RISK when trading options.

c. Based on the CNBC article below, briefly explain why retail option traders do not do well.
https://www.cnbc.com/2021/12/22/options-trading-activity-hits-record-powered-by-retail-investors.html#:~:text=Markets-,Options%20trading%20activity%20hits%20record%20powered%20by%20retail%20investors%2C%20but,are%20playing%20a%20losing%20game&text=A%20record%20of%2039%20million,25%25%20of%20this%20trading%20activity.

Q4 Derivative Hedging
a. Using an Interest Rate Swap, fully hedge a $100M bond portfolio. The portfolio has a duration of 7 years. The swap has a duration of 3 years. Solve for the required Notional Principal of the swap.

b. An investor has a $2M portfolio of RUT (Russell 2000 Index). The RUT price is $1,765.74. The 7/6/22 (12 day) strike put delta is 0.759. Based on this information, USING CALLS, calculate the number of required options to be delta neutral.

c. The equity portfolio you manage is $500M (with a 1.3 beta) and the fixed income portfolio is $500M (with an 8- year duration). The following futures are available: ES, beta 1.00, multiplier 50, futures index 3,795, ZB, duration 4 years, price 98. Establish a full hedge on the $1 billion portfolio (stocks and bonds). Provide the number of contracts.