1. Financial Engineering Professor Brooks BA 444 03/5/08

2. Chapter 16 – Financial Engineering What is Financial Engineering? Designing a new financial asset where one does not exist from existing financial assets Example – Synthetic Put Call Options started trading in 1973 Puts would not appear until 1982 What did traders do between 1973 and 1982? Shorted the stock and bought the call option Created a synthetic put

3. Risk Management with Delta Delta is the sensitivity of a portfolio or asset to changes in prices A stock has a delta of 1.0 (100%) as its price changes $1 for $1 with the stock price Calls and puts have deltas Delta is the price change of the option given a $1 change in the underlying asset Delta hedging is changing the sensitivity of the portfolio and there are three methods Sell some stock and put cash in bank Buy Puts Sell Calls

4. Risk Management with Delta Investor has a portfolio of 1,000 shares of a stock with current portfolio delta of 1,000 For a $1 change in the stock, the portfolio value changes by $1,000 Investor wants to lower exposure to 90% Sell 100 shares…put $ in bank, permanent change Buy puts…how many? First, each put has a different delta (1 – N(d 1 )) Each put is for 100 shares… 1,000 + (N x (1 – N(d 1 )) x 100) = Target

5. Risk Management with Delta Solve for N If (1 – N(d 1 )) = - 0.50 1,000 + (N x (– 0.50) x 100) = 900 N = 2 Put contracts If Puts cost $2, then you must come up with $400 ($2 x 2 X 100) What about writing a call?

6. Risk Management with Delta Call delta is N(d 1 ) Assume call delta is 0.25 How many calls should investor write? 1,000 - (N x( N(d 1 )) x 100) = Target 1,000 - (N x (0.25) x 100) = 900 N = 4 Calls Investor writes four calls and receives $, no margin because investor can place 400 shares with the clearinghouse

7. Problem with Delta Hedge Delta of the options change over time Delta is a function of time, risk-free rate, price of the stock, and volatility of the stock… As delta changes so does delta of the portfolio (temporary hedge) Dynamic hedge As deltas change must hedge again Same three choices…stock, puts, calls Can get expensive to keep hedge