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Today's prices of 6-month call option on stocks XYZ Current price of the stock, S(t), is $50 Call Call Call Expiration 6 months 6 months 6 months Strike $50 $60 $70 Option Price $5.50 Sell (write) 2 $60-strike calls Buy 1 $70-strike call $3 $1 Considering buying an option "butterfly spread" on XYZ. This consists of: Buy 1 $50-strike call Implied vol 40% 35% 32% a) What would you pay or get paid to establish this butterfly spread? b) Plot the payoff of this option as a function of S(T), the terminal price of the stock. X-axis is S(t) and y-axis is payoff c) Only the price for 3 different 6-month option on XYZ. Why can we say, "The information give suggest that the 6-month volatility skew on XYZ is downward sloping"? Can we be 100% certain that lower-strike 6-month options (For instance, out of the money puts) would trade at higher vols? d) What do we mean by the "total delta" of this option portfolio

Today's prices of 6-month call option on stocks XYZ Current price of the stock, S(t), is $50 Call Call Call Expiration 6 months 6 months 6 months Strike $50 $60 $70 Option Price $5.50 Sell (write) 2 $60-strike calls Buy 1 $70-strike call $3 $1 Considering buying an option "butterfly spread" on XYZ. This consists of: Buy 1 $50-strike call Implied vol 40% 35% 32% a) What would you pay or get paid to establish this butterfly spread? b) Plot the payoff of this option as a function of S(T), the terminal price of the stock. X-axis is S(t) and y-axis is payoff c) Only the price for 3 different 6-month option on XYZ. Why can we say, "The information give suggest that the 6-month volatility skew on XYZ is downward sloping"? Can we be 100% certain that lower-strike 6-month options (For instance, out of the money puts) would trade at higher vols? d) What do we mean by the "total delta" of this option portfolio

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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Today's prices of 6-month call option on stocks XYZ Current price of the stock, S(t), is $50 Call Call Call Expiration 6 months 6 months 6 months Strike $50 $60 $70 Option Price $5.50 $3 $1 Considering buying an option "butterfly spread" on XYZ. This consists of: Buy 1 $50-strike call Sell (write) 2 $60-strike calls Buy 1 $70-strike call Implied vol 40% 35% 32% a) What would you pay or get paid to establish this butterfly spread? b) Plot the payoff of this option as a function of S(T), the terminal price of the stock. X-axis is S(t) and y-axis is payoff c) Only the price for 3 different 6-month option on XYZ. Why can we say, "The information give suggest that the 6-month volatility skew on XYZ is downward sloping"? Can we be 100% certain that lower-strike 6-month options (For instance, out of the money puts) would trade at higher vols? d) What do we mean by the "total delta" of this option portfolio e) Suppose that, one day after putting on this position, the price of the stock stays at $50 but the $60-strike and $70 strike calls have gotten more expensive (because the implied vols at those strikes have gone up). What can we say about the deltas of those two out of the money calls? Have their delta increase, decreased or we cannot be sure?
Transcribed Image Text:Today's prices of 6-month call option on stocks XYZ Current price of the stock, S(t), is $50 Call Call Call Expiration 6 months 6 months 6 months Strike $50 $60 $70 Option Price $5.50 $3 $1 Considering buying an option "butterfly spread" on XYZ. This consists of: Buy 1 $50-strike call Sell (write) 2 $60-strike calls Buy 1 $70-strike call Implied vol 40% 35% 32% a) What would you pay or get paid to establish this butterfly spread? b) Plot the payoff of this option as a function of S(T), the terminal price of the stock. X-axis is S(t) and y-axis is payoff c) Only the price for 3 different 6-month option on XYZ. Why can we say, "The information give suggest that the 6-month volatility skew on XYZ is downward sloping"? Can we be 100% certain that lower-strike 6-month options (For instance, out of the money puts) would trade at higher vols? d) What do we mean by the "total delta" of this option portfolio e) Suppose that, one day after putting on this position, the price of the stock stays at $50 but the $60-strike and $70 strike calls have gotten more expensive (because the implied vols at those strikes have gone up). What can we say about the deltas of those two out of the money calls? Have their delta increase, decreased or we cannot be sure?
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