HW3 FIN9797 SPRING 2023

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Baruch College, CUNY *

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9797

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Finance

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Jan 9, 2024

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docx

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0 William Lopez Flores 3 ¥ [U) 2023 Fall Term (1) Options Markets FIN 9797 UWA[16297] (Baruch College) Homework Sets Review Test Submission: HW3-Binomial Tree Review Test Submission: HW3-Binomial Tree User William L Lopez Flores Course 2023 Fall Term (1) Options Markets FIN 9797 UWA[16297] (Baruch College) Test HW3-Binomial Tree Started 11/27/23 10:48 PM Submitted 11/27/23 10:58 PM Due Date 11/29/23 1:00 PM Status Completed Attempt Score 130 out of 130 points Time Elapsed 10 minutes Results Displayed All Answers, Submitted Answers, Correct Answers Question 1 10 out of 10 points Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $120 or down to $80 in 1 year. The stock does not pay dividend and interest rates are zero. We want to price the 1-year $90-strike European put option on this tree. (i) What's the put option payoff 1 year later if the stock price ends up at $1207? [a] (ii) What's the payoff if the stock price ends at $807? [b] (iii) Use the tree to compute the value [c] and delta [d] of the put option. (iv) What's the risk-neutral probability of the stock price going up to the $120 node of the tree ? [e] (v) What's the risk-neutral probability of going down to the $80 node? [f] (Round answers to 2 decimals) Specified Answer for:a @ 0 Specified Answer for:b @ 10 Specified Answer for:c & 5 Specified Answer for: d @ -0.25 Specified Answer for:e @ 0.5 Specified Answer for: f @ 0.5 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 0 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 10 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity @ Exact Match 5 Correct Answers for: d Evaluation Method Correct Answer Case Sensitivity @ Exact Match -0.25 Correct Answers for: e Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.5 Correct Answers for: f Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.5
Question 2 10 out of 10 points Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $120 or down to $80 in 1 year. The stock does not pay dividend. The continuously compounding interest rate is 5%(per year). We want to price the 1-year $100-strike European put option on this tree. (i) What's the put option payoff 1 year later if the stock price ends up at $120? [a] (ii) What's the payoff if the stock price ends at $80? [b] (iii) Use the tree to compute the value [c] and delta [d] of the put option. (iv) What's the risk-neutral probability of the stock price going up to the $120 node of the tree ? [e] (v) What's the risk-neutral probability of going down to the $80 node? [f] (Round answers to 2 decimals) Specified Answer for:a @ 0 Specified Answer for: b @ 20 Specified Answer for: ¢ @ 7.07 Specified Answer for:d @ -0.5 Specified Answer for: e @ 0.63 Specified Answer for: f @ 0.37 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity @ Exact Match 0 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 20 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity & Exact Match 7.07 Correct Answers for: d Evaluation Method Correct Answer Case Sensitivity @ Exact Match -0.5 Correct Answers for: e Evaluation Method Correct Answer Case Sensitivity @ Exact Match 0.63 Correct Answers for: f Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.37
Question 3 10 out of 10 points Consider a one-step binomial tree on stock with a current price of $200 that can go either up to $220 or down to $180 in 2 year. The stock does not pay dividend. The continuously compounding interest rate is 4%(per year). We want to price the 2-year $200-strike European call option on this tree. (i) What's the option payoff at expiry if the stock price ends up at $220? [a] (ii) What's the payoff if the stock price ends at $1807? [b] (iii) Use the tree to compute the value [c] and delta [d] of the option. (iv) What's the risk-neutral probability of the stock price going up to the $220 node of the tree ? [e] (v) What's the risk-neutral probability of going down to the $180 node? [f] (Round answers to 2 decimals) Specified Answer for:a @ 20 Specified Answer for:b @ 0 Specified Answer for: ¢ @ 16.92 Specified Answer for:d @ 0.5 Specified Answer for: e @ 0.92 Specified Answer for: f @ 0.08 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity @ Exact Match 20 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity @ Exact Match 0 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity & Exact Match 16.92 Correct Answers for: d Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.5 Correct Answers for: e Evaluation Method Correct Answer Case Sensitivity @ Exact Match 0.92 Correct Answers for: f Evaluation Method Correct Answer Case Sensitivity @ Exact Match 0.08
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Question 4 10 out of 10 points Consider a one-step binomial tree on stock with a current price of $200 that can go either up to $220 or down to $180 in 1 year. The stock does not pay dividend. The continuously compounding interest rate is 0. We want to price the 2-year $210-strike European call option on this tree. (i) What's the option payoff at expiry if the stock price ends up at $2207? [a] (i) What's the payoff if the stock price ends at $1807 [b] (iii) Use the tree to compute the value [c] and delta [d] of the option. (iv) What's the risk-neutral probability of the stock price going up to the $220 node of the tree ? [e] (v) What's the risk-neutral probability of going down to the $180 node? [f] (Round answers to 2 decimals) Specified Answer for:a @ 10 Specified Answer for:b @ 0 Specified Answer for:c @ 5 Specified Answer for: d @ 0.25 Specified Answer for: e @& 0.5 Specified Answer for: f @ 0.5 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 10 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 0 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity @ Exact Match 5 Correct Answers for: d Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.25 Correct Answers for: e Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.5 Correct Answers for: f Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.5
Question 5 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the risk-neutral probability of going up at each branch of the tree? (round answer to 0.01)" Selected Answer: @ 0.42 Correct Answer: @ 0.424454424 Answer range +/- 0.02 (0.404454424 - 0.444454424) Question 6 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the delta of the option? (round answer to 0.01)" Selected Answer: @ -0.21 Correct Answer: @ -0.209757322 Answer range +/- 0.02 (-0.229757322 - -0.189757322) Question 7 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the value of the option? (round answer to 0.01)" Selected Answer: @ 27.28 Correct Answer: @ 27.27741135 Answer range +/- 0.02 (27.25741135 - 27.29741135) Question 8 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the lowest possible value of the stock at expiry? (round answer to 0.01)" Selected Answer: @ 113.43 Correct Answer: @ 113.4317902 Answer range +/- 0.02 (113.4117902 - 113.4517902)
Question 9 10 out of 10 points "AAPL's current stock price is $150. Its return volatility is 30%. Assume no dividend and a continuously compounding interest rate of 4%. Construct a two-step binomial tree with each step being 3-month based on the approach on the lecture notes, and value a 6-month $150-strike call option on this tree (You will be asked about the option’s payoff, value, delta, and the tree probability in separate numerical questions. So please keep the tree result to avoid repetition). What's the risk-neutral probability of going up at each branch of the tree? (round answer to 0.01)" Selected Answer: @& 0.49 Correct Answer: @ 0.495945414 Answer range +/- 0.02 (0.475945414 - 0.515945414 ) Question 10 10 out of 10 points What's the delta of the option? (round answer to 0.01) Selected Answer: & 0.57 Correct Answer: @ 0.570473015 Answer range +/- 0.02 (0.550473015 - 0.590473015) Question 11 10 out of 10 points What's the value of the option? (round answer to 0.01) Selected Answer: @ 12.65 Correct Answer: & 12.65219677 Answer range +/- 0.02 (12.63219677 - 12.67219677 ) Question 12 10 out of 10 points What's the lowest possible value of the stock at expiry? (round answer to 0.01) Selected Answer: @ 111.12 Correct Answer: @ 111.1227331 Answer range +/- 0.02 (111.1027331 - 111.1427331) Question 13 10 out of 10 points What's the highest possible value of the stock at expiry? (round answer to 0.01) Selected Answer: @ 202.48 Correct Answer: @ 202.4788211 Answer range +/- 0.02 (202.4588211 - 202.4988211) lay, November 27, 2023 10:58:17 PM EST
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Question 5 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the risk-neutral probability of going up at each branch of the tree? (round answer to 0.01)" Selected Answer: @ 0.42 Correct Answer: @ 0.424454424 Answer range +/- 0.02 (0.404454424 - 0.444454424) Question 6 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the delta of the option? (round answer to 0.01)" Selected Answer: @ -0.21 Correct Answer: @ -0.209757322 Answer range +/- 0.02 (-0.229757322 - -0.189757322) Question 7 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the value of the option? (round answer to 0.01)" Selected Answer: @ 27.28 Correct Answer: @ 27.27741135 Answer range +/- 0.02 (27.25741135 - 27.29741135) Question 8 10 out of 10 points "ULTA's current stock price is $265. Its return volatility is 60%. Assume no dividend and a continuously compounding interest rate of 5%. Construct a two-step binomial tree with each step being 6-month based on the approach on the lecture notes, and value a 1-year $200- strike ULTA put option on this tree (You will be asked about the option's payoff, value, delta, and the tree probability in separate numerical questions on ULTA. So please keep the tree result to avoid repetition). What's the lowest possible value of the stock at expiry? (round answer to 0.01)" Selected Answer: @ 113.43 Correct Answer: @ 113.4317902 Answer range +/- 0.02 (113.4117902 - 113.4517902)