Financial Instrument Modeling IT for Financial Services (IS356)

1. Financial Instrument ModelingIT for Financial Services (IS356) The content of these slides is heavily based on a Coursera course taught by Profs. Haugh and Iyengar from the Center for Financial Engineering at the Columbia Business School, NYC. I attended the course in Spring 2013 and again in Fall 2013 and Spring 2014 when the course was offered in 2 parts.

3. Options… The Basics

4. Payoff and Intrinsic Value of a Call

5. Payoff and Intrinsic Value of a Put

6. Put-Call Parity

7. European Options(Using Simple Binomial Modeling)

8. Profit Timing and Determination

9. Stock Price Dynamics – binomial lattice Stock price goes up/down by the same amount each time period. In this example: 1.07 and 1/1.07

10. Options Pricing – call option formula The value of the option at expiration is Max(ST - K,0). You will only exercise a European option if it is in-the-money at expiration, in which case the price of the stock (ST) at expiration is greater than the strike price K. We will move backwards in the lattice to compute the value of the option at time 0.

11. European Call Option Pricing Example A European put option uses the same formula. The only difference is in the last column: max(0, K-ST). You only exercise a put option if the strike price > current price. You can buy shares at the current price and sell them at the higher strike K. 15.48 = 1/R( 22.5q + 7(1-q)) R=1.01 Q=(R-d)/(u-d) d=1/1.07 u=1.07

12. European Options: Excel Modeling

13. Does Put Call Parity Hold?

14. American Options(Using Simple Binomial Modeling)

15. Pricing American Options

16. Reverse through the Lattice

17. American Put vs. Call – early or not?

18. Black-Scholes Model Geometric Brownian Motion Models random fluctuations in stock prices

19. Black-Scholes Model… continued

20. Black-Scholes Modelin Excel

21. Implied Volatility

22. Futures and Forwards

23. Forwards Contracts

24. Futures and Forwards… Problems with Forwards Futures Contracts

25. Mechanics of a Futures Contract

26. Excel Example with Daily Settlement

27. Hedging using Futures A Perfect Hedge Isn’t Always Possible…

28. Term Structure of Interest Rates

29. Yield Curves (US Treasuries) Rates are climbing – highest in Dec 2013 Source: http://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/TextView.aspx?data=yieldYear&year=2013

30. Sample Short Rate Lattice 9.375% = 7.5% x 1.25

31. Pricing a Zero-coupon Bond (ZCB) 9.375% comes from the last slide Assumes a 50:50 chance of rates increasing/decreasing

32. Excel Modeling Again, we work backwards through the lattice. 89.51 = 1/1.1172 * ( 100 x 0.5 + 100 x 0.5)

33. Pricing European Call Option on ZCB Max(0, 87.35-84) Max(0, 83.08-84) Max(0, 90.64-84)

34. Pricing American Put Option on ZCB

35. Pricing Forwards on Bonds

36. Pricing Forwards on Bonds - excel Start at the end and work back to t=4 Then work from t=4 backwards

37. Mortgage Backed Securities (MBS)Collateralized Debt Obligations (CDO)

38. Mortgage Backed Securities Markets

39. The Logic of Tranches (MBS)

40. The Logic of Tranches (CDO)

41. A Simple Example: A 1-period CDO

42. Excel model of CDO 1-probability of default = probability of survival

43. CDON

44. Portfolio Optimization

45. Return on Assets and Portfolios

46. Two-asset Example

47. Optimization Example (solver)

48. Optimization with trading costs