The following options prices were observed for calls and puts onLannister Ltd for the trading day of July 6 2019. Use thisinformation in Questions 3-8. The stock was priced at $163.37. Theexpirations were July 17, August 21 and October 16. Thecontinuously compounded risk-free rates associated with the threeexpirations were 0.0517, 0.0542 and 0.0565, respectively. Theoptions have European expiries.

Lannister Ltd CALLS
STRIKE	JUL	AUG	OCT
150	9.50	11.25	13.61
155	5.70	7.96	10.88
160	2.23	5.01	8.04
165	0.77	2.79	6.90

Lannister Ltd PUTS
STRIKE	JUL	AUG	OCT
150	0.17	1.18	2.69
155	0.71	2.66	4.44
160	2.22	4.63	6.60
165	5.61	7.42	8.81

Question: Showing all formula and workingswhere applicable; Let the standard deviation of the continuouslycompounded return on the stock be 20 percent. Ignore dividends.Respond to the following:

1. What is the theoretical fair value of the October 165 call?Calculate this answer by hand and then re-calculate it usingBlackScholesMertonBinomial10e.xlsm.
2. Based on your answer in part a, recommend a risklessstrategy.
3. If the stock price decreases by $1, how will the optionposition offset the loss on the stock?
4. Use the Black-Scholes-Merton European put option pricingformula for the October 160 put option. Repeat parts a, b and c ofQuestion 3 with respect to the put.
5. Buy 100 shares of Lannister Ltd at $163.37 and short oneOctober 165 call. Hold the position until expiration. Determine theprofits and graph the results. Identify the strategy, breakevenstock price at expiration, the maximum profit, and the maximumloss. Discuss any special considerations associated with thisstrategy. Note: use the OptionStrategyAnalyzer10e.xlsm to obtainthe required payoff diagram.
6. Buy 100 shares of Lannister Ltd at $163.37 and go long oneOctober 160 put. Hold the position until expiration. Determine theprofits and graph the results. Identify the strategy, breakevenstock price at expiration, the maximum profit, and the maximumloss. Discuss any special considerations associated with thisstrategy. Note: use the OptionStrategyAnalyzer10e.xlsm to obtainthe required payoff diagram.
7. Construct an options strategy by going short one October 160call and long one October 165 call using Lannister Ltd options.Hold the position until expiration. Determine the profits and graphthe results. Identify the strategy, breakeven stock price atexpiration, the maximum profit, and the maximum loss. Discuss anyspecial considerations associated with this strategy. Note: use theOptionStrategyAnalyzer10e.xlsm to obtain the required payoffdiagram.
8. Construct an options strategy by going long one October 165 putand long one October 165 call using Lannister Ltd options. Hold theposition until expiration. Determine the profits and graph theresults. Identify the strategy, breakeven stock price atexpiration, the maximum profit, and the maximum loss. Discuss anyspecial considerations associated with this strategy. Note: use theOptionStrategyAnalyzer10e.xlsm to obtain the required payoffdiagram