IT & Finance

1. IT & Finance Stefano Grazioli

2. Critical Thinking • Lab on Friday • Office hours added Tue & Th 3-6pm (and beyond) • Easy meter

3. The Hedge Tournament • Questions? • Team formation • Simplified IPs on Beta for testing

4. Delta Hedging The Greeks

5. Delta Hedging Objective: obtain the right type and quantity of securities to counterbalance the movements of a security that we own. DeltaNeutralPortfolio

6. What is Delta? • Delta is a parameter. Roughly, it is the change in an option price when the underlying stock price changes by a unit (e.g., one dollar). O2 – O1 U2 – U1 • Example1: a call option price goes down by $1.60 when a stock goes down by $2.Delta = -1.60 / -2.00 = +0.8 • Example2: a put option is up by $0.5, when the stock is down by $1. Delta = 0.50 / -1.00 = -0.5 Delta =

7. Balancing a Position I own 100,000 IBM stocks. I am bearish - I think that the Stock price may go down. What kind andhow many options do I need, in order to counter-balance possible price changes and preserve my portfolio value?

8. We want to hedge 100,000 long IBM stocks that we found in our IPs. First, we need to find a security with the appropriate hedging behavior Delta Hedging Example long Stock Stock price Current Price

9. Hedging a Long Stock Profit & Loss Profit & Loss long call Stock price Stock price strike strike short call Profit & Loss Profit & Loss short put Stock price Stock price long put strike strike

10. - Short calls have the right behavior (also long puts) - How many short calls? Delta Hedging Example long Stock short call Strike Stock price Current Price

11. How many calls are needed to make our position price-neutral? gain/loss from options = - gain/loss from stocks Noptions * (O2-O1) = - Nstocks * (U2-U1) Noptions= - Nstocks * (U2-U1)/(O2-O1) Noptions= - Nstocks * 1/Deltacall Noptions= - 100,000 * 1/0.8 Noptions = - 125,000 i.e., we need 125,000 short calls.

12. Suppose that the IBM stock price decreases by $10. What happens to my portfolio? by assumption: Option price change / Underlier price change = 0.8 so: Option price will change by 0.8 * (-$10) = -$8 Change in Portfolio value = 100,000 * (-$10) + (-125,000) * (-$8) = = -1,000,000 + 1,000,000 = $0 We have a Delta neutral portfolio Numeric Check

13. Delta of a Call Option = N(d1) Delta of a Put Option = N(d1) -1 d1 = {ln(S/X) + (r + s 2/2) t} s t Computing Delta

14. What Hedges What ...this is what you need If your position is...

15. Need for Recalibration There is a catch. Delta changes with time....

16. Delta changes with S, r, sand t. Since they all change in time, the hedge needs to be periodically readjusted – a practice calledrebalancing (r, s are fixed in the HT). Example:Yesterday we wanted to hedge 100,000 long stock and so we shorted 125,000 calls.But now the delta is 0.9. 100,000= - Noptions * 0.9 Noptions= - 111,111 so, we need to buy 13,889 calls (=125,000-111,111)to maintain delta neutrality. Dynamic Delta Hedging

17. Next Time • When/how to rebalance • Balancing a whole portfolio • Other types of hedging

18. WINIT What Is NewIn Technology?

19. Homework The Spartan Trader

20. Suggestions • Give yourself plenty of time • Test the numbers!