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FIN 4170
Derivatives
Spring 2017
Assignment 11
Due May 1, 2017

Option pricing using simulation

Part 1.
1a. Select a spot market price for the underlying asset between \$25 and \$75.

Select a strike price for an option that is within \$7.50 of the spot market price. (It can be greater or less than the spot price.)
Select an annual return on the underlying asset that is between 9% and 12%
Select an annual dividend yield for the underlying asset that is between 0.5% and 2.5%.
Select an annual standard deviation for returns on the underlying asset that is between 0.25 and 0.65.
Select an annual risk free rate between 1% and 4%.
Select an expiration date between 6 and 18 months.

Using the variables selected above, construct 100 simulated outcomes for the value of the underlying asset at the expiration date of the option. Use (Save these 100 results as values)

3a. Determine the payoff on a call option with the strike price from 1b for each simulation result in question 2.

Determine the average payoff on call options for all simulation results.
Determine the value of the call option based on your simulation.

4a. Determine the payoff on a put option with the strike price from 1b for each simulation result in question 2.

Determine the average payoff on call options for all simulation results.
Determine the value of the put option based on your simulation.

Part 2.

Using the variables selected in a through e of question 1 in part 1, construct 100 sequences of weekly prices for the underlying asset for 26 consecutive weeks. Use the following formula: to estimate each successive weekly price. Since a, d and s are annual rates, h in the previous equation is 1/52. (Save these 2600 results as values).

6a. Determine the geometric average price of the underlying asset for each 26-week simulation.

Determine the arithmetic average price of the underlying asset for each 26-week simulation.

7a. Using the data from 5 and the answer to 6a, determine the value of a 6-month average price call option that is based on the geometric average.

Using the data from 5 and the answer to 6b, determine the value of a 6-month average price call option that is based on the arithmetic average.

8a. Using the data from 5 and the answer to 6a, determine the value of a 6-month average strike call option that is based on the geometric average.

Using the data from 5 and the answer to 6b, determine the value of a 6-month average strike call option that is based on the arithmetic average.

Select a barrier that is greater than, but within \$5.00, of the strike price.
Using the data from 5, calculate the value of an up and in barrier call option on the stock.
Using the data from 5, calculate the value of an up and out barrier call option on the stock.
Using the data from 5, calculate the value of an up and in barrier put option on the stock.
Using the data from 5, calculate the value of an up and out barrier put option on the stock.

Select a barrier that is less than, but within \$5.00, of the strike price.
Using the data from 5, calculate the value of a down and in barrier call option on the stock.
Using the data from 5, calculate the value of a down and out barrier call option on the stock.
Using the data from 5, calculate the value of a down and in barrier put option on the stock.
Using the data from 5, calculate the value of a down and out barrier put option on the stock.

11a. Using the data from 5, calculate the value of a chooser call option on the stock.
b.. Using the data from 5, calculate the value of a chooser put option on the stock.

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