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 XYZ stock is currently trading at $50 per share. We ask our favourite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information 0.569 0.530 0.299 0.065 For each option price we've run the price through the Black-Scholes formula and solved for implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend 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" price of the option Numerally compute the derivative AOptions/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 delta analytically by taking the partial derivative (With respect to S) of the functions C(5,t) and P(5,t). 1. Suppose you bought the $40-strike put and the $60-strike call. This would cost you $0.77 + $0.15 = $0.92 Please draw a graph that shows the value of this combined position at the expiration date. The x-axis will be S(T), the value of the stock at expiration; the y-axis will be the value of the position (put and call)
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 XYZ stock is currently trading at $50 per share. We ask our favourite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information 0.569 0.530 0.299 0.065 For each option price we've run the price through the Black-Scholes formula and solved for implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend 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" price of the option Numerally compute the derivative AOptions/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 delta analytically by taking the partial derivative (With respect to S) of the functions C(5,t) and P(5,t). 1. Suppose you bought the $40-strike put and the $60-strike call. This would cost you $0.77 + $0.15 = $0.92 Please draw a graph that shows the value of this combined position at the expiration date. The x-axis will be S(T), the value of the stock at expiration; the y-axis will be the value of the position (put and call)
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
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Transcribed Image Text:Current stock price for XYZ $50.00
Interestrate
3%
Dividend rate
0%
Option
PUT
PUT
PUT
PUT
CALL
CALL
CALL
CALL
-
Strike Expiration Option Price
$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
$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
XYZ stock is currently trading at $50 per share. We ask our favourite trading desk to price a bunch of
6-month options on XYZ: 4 puts and 4 calls. The table above gives the information
0.569
0.530
0.299
0.065
For each option price we've run the price through the Black-Scholes formula and solved for implied
volatility.
The tables also gives the deltas: the derivative of each option price with respect to the stock price. As
you know this means:
Leave the implied volatility, the interest rate, and the dividend 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" price of the option
Numerally compute the derivative AOptions/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 delta analytically
by taking the partial derivative (with respect to S) of the functions C(5,t) and P(S,t).
1. Suppose you bought the $40-strike put and the $60-strike call. This would cost you
$0.77+ $0.15 = $0.92
Please draw a graph that shows the value of this combined position at the expiration date.
The x-axis will be S(T), the value of the stock at expiration; the y-axis will be the value of the
position (put and call)
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