1. Session 4

2. Tonight’s Class “Lab Mode” 3 Excel Models: Implied Volatility
Brownian Motion to Simulate Prices
Hedging with Futures

3. Two Previous Models Black-Scholes analytical model
Crystal Ball Monte Carlo model

4. Crystal Ball Template

5. Implied Volatility: Example
At the end of trading on February 1, DEO sold for $
A call option expiring on August 1 with exercise price $125 sold for $6.00.
Risk free rate is 4.00%.
What’s the implied volatility of DEO?

6. Goal Seek What is the value of B7 that makes B13 equal to $6.00?
Data  What if Analysis  Goal Seek

8. Brownian Motion: Example

10. Simulated Prices for 50 Months
Could use Crystal Ball to automate the generation of random numbers and analysis of the results.

11. Template: Hedging with Futures

12. Define E9 as a forecast cell.

13. Results if No Hedging
Mean cost $211,503, and standard deviation $40,393

15. Base Case: Buy 500,000 Futures
Mean cost $217,759, and standard deviation $10,862

16. Decision Variables
What value in E3 will optimize our risk (or other metric)?
Automate the simulation of many possible decisions
Define a decision variable in Crystal Ball:
Select the cell by clicking on it.
Click on the Define Decision button
Specify bounds and type of the decision variable.

23. Options
Number of simulations is NOT number of trials per simulation.

24. Number of simulations is set to be 1000
But total number of simulations is 21.

25. OptQuest Results
Amount of Futures to Buy: 450,000

26. OptQuest Results Mean cost $217,759, and standard deviation $10,862
Mean cost does not change much, but stdev is about 26% of unhedged!

27. Minimum-Variance Hedge Ratio
For 500,000 gallons spot market purchase
We buy about 450,000 futures to minimize the variance
The minimum-variance hedge ratio is
450, ,000 =0.9

31. Preparation for Next Class
Team Assignment 1 is due Saturday March 25. Kevin will make upload link in Classes.
Also, 3 models from tonight (team of 1 or 2).
Enjoy Spring Break!