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Financial Instrument Modeling IT for Financial Services (IS356)

Financial Instrument Modeling IT for Financial Services (IS356).

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Financial Instrument Modeling IT for Financial Services (IS356)

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  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.

  2. Options… The Basics

  3. Payoff and Intrinsic Value of a Call

  4. Payoff and Intrinsic Value of a Put

  5. Put-Call Parity

  6. European Options(Using Simple Binomial Modeling)

  7. Profit Timing and Determination

  8. 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

  9. 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.

  10. 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

  11. European Options: Excel Modeling

  12. Does Put Call Parity Hold?

  13. American Options(Using Simple Binomial Modeling)

  14. Pricing American Options

  15. Reverse through the Lattice

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

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

  18. Black-Scholes Model… continued

  19. Black-Scholes Modelin Excel

  20. Implied Volatility

  21. Futures and Forwards

  22. Forwards Contracts

  23. Futures and Forwards… Problems with Forwards Futures Contracts

  24. Mechanics of a Futures Contract

  25. Excel Example with Daily Settlement

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

  27. Term Structure of Interest Rates

  28. 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

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

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

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

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

  33. Pricing American Put Option on ZCB

  34. Pricing Forwards on Bonds

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

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

  37. Mortgage Backed Securities Markets

  38. The Logic of Tranches (MBS)

  39. The Logic of Tranches (CDO)

  40. A Simple Example: A 1-period CDO

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

  42. CDON

  43. Portfolio Optimization

  44. Return on Assets and Portfolios

  45. Two-asset Example

  46. Optimization Example (solver)

  47. Optimization with trading costs

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