FINANCIAL INSTRUMENT MODELING IT 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.

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

Options Pricing – call option formula 10 The value of the option at expiration is Max(S T - 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 (S T ) 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.

European Call Option Pricing Example = 1/R( 22.5q + 7(1-q)) R=1.01 Q=(R-d)/(u-d) d=1/1.07 u=1.07 A European put option uses the same formula. The only difference is in the last column: max(0, K-S T ). 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.

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 18 Geometric Brownian Motion Models random fluctuations in stock prices

Black-Scholes Model… continued 19

Black-Scholes Model in Excel 20

Implied Volatility 21

Futures and Forwards 22

Forwards Contracts 23

Futures and Forwards… 24 Problems with Forwards Futures Contracts

Mechanics of a Futures Contract 25

Excel Example with Daily Settlement 26

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

Term Structure of Interest Rates 28

Yield Curves (US Treasuries) 29 Source: Rates are climbing – highest in Dec 2013

Sample Short Rate Lattice % = 7.5% x 1.25

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

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

Pricing European Call Option on ZCB 33 Max(0, ) Max(0, ) Max(0, )

Pricing American Put Option on ZCB 34

Pricing Forwards on Bonds 35

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

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 42 1-probability of default = probability of survival

CDO N 43

Portfolio Optimization 44

Return on Assets and Portfolios 45

Two-asset Example 46

Optimization Example (solver) 47

Optimization with trading costs 48