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#1
02-10-2010, 12:02 PM
 gaofeng807 Join Date: Dec 2009 Posts: 13
Confused in option elasticity

I still can't understand the concept of elasticity about call and put option

The question is very easy

why for a call elasticity is highest when the call is out of money, on the 6th edition P195 ASM it says "since then the value of the call is very small compared to the value of the underlying stock"

but the numerator of the formular of elasticity is not only S (value of the stock) but also "delta" times "S"

Thank you ^^
#2
02-10-2010, 03:08 PM
 Joe F Member Join Date: May 2007 Posts: 200

Quote:
 Originally Posted by gaofeng807 I still can't understand the concept of elasticity about call and put option ... why for a call elasticity is highest when the call is out of money, ...^^
Here's another way to look at it. The elasticity can be expressed as the risk premium of the option divided by the risk premium of the stock:

$\Omega = \frac{\gamma-r}{\alpha-r}$

As the stock price decreases, the call option becomes riskier, and therefore $\gamma$ increases. Looking at the equation above, as $\gamma$ increases, the elasticity increases as well.
#3
02-10-2010, 03:25 PM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 6,095

Not to play devil's advocate, but as the stock price decreases, by the same logic, wouldn't $\alpha$ increase as well?
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#4
02-10-2010, 03:34 PM
 Joe F Member Join Date: May 2007 Posts: 200

Quote:
 Originally Posted by Actuarialsuck Not to play devil's advocate, but as the stock price decreases, by the same logic, wouldn't $\alpha$ increase as well?
In the Black-Scholes framework, we assume that $\alpha$ does not change as the stock price changes. That is, the expected return remains the same on the stock.

Last edited by Joe F; 02-10-2010 at 03:40 PM..
#5
02-10-2010, 10:41 PM
 gaofeng807 Join Date: Dec 2009 Posts: 13
I am sorry I still confusing,please explain again thank you

Quote:
 Originally Posted by Joe F Here's another way to look at it. The elasticity can be expressed as the risk premium of the option divided by the risk premium of the stock: $\Omega = \frac{\gamma-r}{\alpha-r}$ As the stock price decreases, the call option becomes riskier, and therefore $\gamma$ increases. Looking at the equation above, as $\gamma$ increases, the elasticity increases as well.
Thank you for your help but I still confused

1 the more out-of-money the more risky?

2 the more risky so why you can entail that higher option return?

3 which is most I confused : the difference between delta and elasticity
since the graph of delta is opposite to the graph of elasticity options, However what they discribe is similar:
delta:
delta is perincrease in stock how much increase in option price
elasticity
the each percentage increase in stock how much percentage increase in option price

PS: on the DM textbook the reason author said is something about leverage

So I am dizzy
#6
02-10-2010, 11:06 PM
 Actuarialsuck Member Join Date: Sep 2007 Posts: 6,095

If something is more risky, would you require more or less return on it gaofeng?
__________________
Quote:
 Originally Posted by Buru Buru i'm not. i do not troll.
#7
02-10-2010, 11:52 PM
 Joe F Member Join Date: May 2007 Posts: 200

Quote:
 Originally Posted by gaofeng807 1 the more out-of-money the more risky?
Yes. The more out-of-the-money a call option is, the riskier it is. Take a look at Figure 11.4 on page 350 of the textbook. Consider the node where the option price is $22.202. From there, the option value will either increase by 56% to$34.678 or decrease by 42% to $12.814. Sounds pretty risky, doesn't it? The investment either increases by 56% or decreases by 42%. But at the node below it, where the option price is$5.70, the option is an even riskier investment because from there it will then either increase by 125% to $12.814 or fall by 100% to zero. At this lower node, the investor will either make 125% or lose everything, so the risk is higher at this lower node. That's why the expected return on the option is higher at the more out-of-the-money node. Quote:  2 the more risky so why you can entail that higher option return? Yes. The higher risk means that the expected return must be higher. Quote:  PS: on the DM textbook the reason author said is something about leverage Suppose a sum of money,$X, is used to buy some quantity of call options. The same payoff could be obtained by investing $X in the following replicating portfolio: Invest $\small \Omega \cdot (X)$ in the stock and lend $\small (1-\Omega) \cdot (X)$ at the risk-free rate. The out of pocket cost is$X. So, for example, if the elasticity is 150%, then the replicating portfolio is 150% invested in stock, and 50% of the portfolio is borrowed at the risk-free rate (lending -50% of $X is the same as borrowing 50% of$X). This shows that a call option is equivalent to a leveraged position in the stock.
#8
02-11-2010, 12:35 AM
 gaofeng807 Join Date: Dec 2009 Posts: 13

Quote:
 Originally Posted by Actuarialsuck If something is more risky, would you require more or less return on it gaofeng?
Hi Actuarialsuck

I got it, the answer is simple and easy "I would require more return"

Thank you again for help^^
#9
02-11-2010, 12:37 AM
 gaofeng807 Join Date: Dec 2009 Posts: 13

Quote:
 Originally Posted by Joe F Yes. The more out-of-the-money a call option is, the riskier it is. Take a look at Figure 11.4 on page 350 of the textbook. Consider the node where the option price is $22.202. From there, the option value will either increase by 56% to$34.678 or decrease by 42% to $12.814. Sounds pretty risky, doesn't it? The investment either increases by 56% or decreases by 42%. But at the node below it, where the option price is$5.70, the option is an even riskier investment because from there it will then either increase by 125% to $12.814 or fall by 100% to zero. At this lower node, the investor will either make 125% or lose everything, so the risk is higher at this lower node. That's why the expected return on the option is higher at the more out-of-the-money node. Yes. The higher risk means that the expected return must be higher. Suppose a sum of money,$X, is used to buy some quantity of call options. The same payoff could be obtained by investing $X in the following replicating portfolio: Invest $\small \Omega \cdot (X)$ in the stock and lend $\small (1-\Omega) \cdot (X)$ at the risk-free rate. The out of pocket cost is$X. So, for example, if the elasticity is 150%, then the replicating portfolio is 150% invested in stock, and 50% of the portfolio is borrowed at the risk-free rate (lending -50% of $X is the same as borrowing 50% of$X). This shows that a call option is equivalent to a leveraged position in the stock.
Thanks again

but it's too late now I have to go to bed^^, I will go over it carefully tomorrow morning.
#10
02-11-2010, 10:13 AM
 gaofeng807 Join Date: Dec 2009 Posts: 13

Quote:
 Originally Posted by Joe F Yes. The more out-of-the-money a call option is, the riskier it is. Take a look at Figure 11.4 on page 350 of the textbook. Consider the node where the option price is $22.202. From there, the option value will either increase by 56% to$34.678 or decrease by 42% to $12.814. Sounds pretty risky, doesn't it? The investment either increases by 56% or decreases by 42%. But at the node below it, where the option price is$5.70, the option is an even riskier investment because from there it will then either increase by 125% to $12.814 or fall by 100% to zero. At this lower node, the investor will either make 125% or lose everything, so the risk is higher at this lower node. That's why the expected return on the option is higher at the more out-of-the-money node. Yes. The higher risk means that the expected return must be higher. Suppose a sum of money,$X, is used to buy some quantity of call options. The same payoff could be obtained by investing $X in the following replicating portfolio: Invest $\small \Omega \cdot (X)$ in the stock and lend $\small (1-\Omega) \cdot (X)$ at the risk-free rate. The out of pocket cost is$X. So, for example, if the elasticity is 150%, then the replicating portfolio is 150% invested in stock, and 50% of the portfolio is borrowed at the risk-free rate (lending -50% of $X is the same as borrowing 50% of$X). This shows that a call option is equivalent to a leveraged position in the stock.
I got it
Thank you very much and I find that I need to read more on the text book than ASM

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