Current stock price for XYZ $50.00 3% 0% Interestrate Dividend rate Option PUT PUT PUT PUT CALL CALL CALL CALL Strike Expiration $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months $50.00 6-months $50.75 6-months $55.00 6-months $60.00 6-months Option Price $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Implied Vol 40% 32% 22% 21% 22% 21% 19% 15% Delta (AOption/AS) -0.023 -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favorite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information. For each option price we've run the price through the Black-Scholes formula and solved for the implied volatility. The table also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: ■ Leave the implied vol, the interest rate, and the dividend rate unchanged; ■ Change the current price of the stock by a small amount up and down, say +/- $0.01; Apply the call-price or the put-price formulas, C(S,t) or P(S,t), and obtain the "stock- price-up" and "stock-price-down" prices of the options; ■ Numerically compute the derivative AOption/AS. This is the option's delta at that value of the underlying stock and that implied volatility. It's a measure of how sensitive the option price is to the price of the underlying stock. Note that we could also obtain the delta analytically by the taking the partial derivative (with respect to S) of the functions C(S,t) and P(S,t). [1] Suppose you buy the $40-strike put at the offer price of $0.77. You come in the next day and that the stock price has fallen to $44. Will the put price have gone up or down? [2] Say you bought the $40-strike put (at $0.77); you decide to sell it back after the price of the stock has fallen to $44. Would the trader bid a price corresponding to 32% implied volatility (which is what you "paid" back when the stock was at $50)... or would they bid at a higher or lower implied volatility? Explain.
Current stock price for XYZ $50.00 3% 0% Interestrate Dividend rate Option PUT PUT PUT PUT CALL CALL CALL CALL Strike Expiration $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months $50.00 6-months $50.75 6-months $55.00 6-months $60.00 6-months Option Price $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Implied Vol 40% 32% 22% 21% 22% 21% 19% 15% Delta (AOption/AS) -0.023 -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favorite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information. For each option price we've run the price through the Black-Scholes formula and solved for the implied volatility. The table also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: ■ Leave the implied vol, the interest rate, and the dividend rate unchanged; ■ Change the current price of the stock by a small amount up and down, say +/- $0.01; Apply the call-price or the put-price formulas, C(S,t) or P(S,t), and obtain the "stock- price-up" and "stock-price-down" prices of the options; ■ Numerically compute the derivative AOption/AS. This is the option's delta at that value of the underlying stock and that implied volatility. It's a measure of how sensitive the option price is to the price of the underlying stock. Note that we could also obtain the delta analytically by the taking the partial derivative (with respect to S) of the functions C(S,t) and P(S,t). [1] Suppose you buy the $40-strike put at the offer price of $0.77. You come in the next day and that the stock price has fallen to $44. Will the put price have gone up or down? [2] Say you bought the $40-strike put (at $0.77); you decide to sell it back after the price of the stock has fallen to $44. Would the trader bid a price corresponding to 32% implied volatility (which is what you "paid" back when the stock was at $50)... or would they bid at a higher or lower implied volatility? Explain.
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
Problem 1PS
Related questions
Question
![Current stock price for XYZ
Interestrate
Dividend rate
Option
PUT
PUT
PUT
PUT
CALL
CALL
CALL
CALL
$50.00
3%
0%
Strike Expiration
$30.00 6-months
$40.00 6-months
$50.00 6-months
$50.75
6-months
$50.00 6-months
$50.75 6-months
$55.00 6-months
$60.00 6-months
Option Price Implied Vol
$0.14
$0.77
$2.74
$2.97
$3.48
$2.97
$1.20
$0.15
40%
32%
22%
21%
22%
21%
19%
15%
Delta
(AOption/AS)
-0.023
-0.123
-0.431
-0.470
0.569
0.530
0.299
0.065
XYZ stock is currently trading at $50 per share. We ask our favorite trading desk to price a
bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information.
For each option price we've run the price through the Black-Scholes formula and solved for the
implied volatility.
The table also gives the deltas: the derivative of each option price with respect to the stock
price. As you know this means:
■ Leave the implied vol, the interest rate, and the dividend rate unchanged;
■ Change the current price of the stock by a small amount up and down, say +/- $0.01;
■ Apply the call-price or the put-price formulas, C(S,t) or P(S,t), and obtain the "stock-
price-up" and "stock-price-down" prices of the options;
■ Numerically compute the derivative AOption/AS. This is the option's delta at that
value of the underlying stock and that implied volatility. It's a measure of how sensitive
the option price is to the price of the underlying stock. Note that we could also obtain
the delta analytically by the taking the partial derivative (with respect to S) of the
functions C(S,t) and P(S,t).
[1] Suppose you buy the $40-strike put at the offer price of $0.77. You come in the next
day and see that the stock price has fallen to $44. Will the put price have gone up or down?
[2] Say you bought the $40-strike put (at $0.77); you decide to sell it back after the price of
the stock has fallen to $44. Would the trader bid a price corresponding to 32% implied
volatility (which is what you "paid" back when the stock was at $50)... or would they bid at
a higher or lower implied volatility? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85fafaa4-de34-47c7-98e7-8408756b8b80%2F14b3cce0-7e23-4679-a967-c6005cae8c3e%2F22voj9e_processed.png&w=3840&q=75)
Transcribed Image Text:Current stock price for XYZ
Interestrate
Dividend rate
Option
PUT
PUT
PUT
PUT
CALL
CALL
CALL
CALL
$50.00
3%
0%
Strike Expiration
$30.00 6-months
$40.00 6-months
$50.00 6-months
$50.75
6-months
$50.00 6-months
$50.75 6-months
$55.00 6-months
$60.00 6-months
Option Price Implied Vol
$0.14
$0.77
$2.74
$2.97
$3.48
$2.97
$1.20
$0.15
40%
32%
22%
21%
22%
21%
19%
15%
Delta
(AOption/AS)
-0.023
-0.123
-0.431
-0.470
0.569
0.530
0.299
0.065
XYZ stock is currently trading at $50 per share. We ask our favorite trading desk to price a
bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information.
For each option price we've run the price through the Black-Scholes formula and solved for the
implied volatility.
The table also gives the deltas: the derivative of each option price with respect to the stock
price. As you know this means:
■ Leave the implied vol, the interest rate, and the dividend rate unchanged;
■ Change the current price of the stock by a small amount up and down, say +/- $0.01;
■ Apply the call-price or the put-price formulas, C(S,t) or P(S,t), and obtain the "stock-
price-up" and "stock-price-down" prices of the options;
■ Numerically compute the derivative AOption/AS. This is the option's delta at that
value of the underlying stock and that implied volatility. It's a measure of how sensitive
the option price is to the price of the underlying stock. Note that we could also obtain
the delta analytically by the taking the partial derivative (with respect to S) of the
functions C(S,t) and P(S,t).
[1] Suppose you buy the $40-strike put at the offer price of $0.77. You come in the next
day and see that the stock price has fallen to $44. Will the put price have gone up or down?
[2] Say you bought the $40-strike put (at $0.77); you decide to sell it back after the price of
the stock has fallen to $44. Would the trader bid a price corresponding to 32% implied
volatility (which is what you "paid" back when the stock was at $50)... or would they bid at
a higher or lower implied volatility? Explain.
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