Finance math comparison of puts
up vote
0
down vote
favorite
I am looking for some expert advice in answering this finance question. I am having trouble figuring out how to compare these put and strikes. Is there a formula to approach this type of problem?
Let $p_K$ be the current price of a European put expiring at time $T$
with strike price $K$.
Let $S_0$ be the spot price of the underlying asset.
Compare the following quantities if possible.
(a) Compare $p_{50}$, $p_{55}$, $p_{60}$.
(b) Compare $p_{50}$ and 50
finance
asked Feb 28 '17 at 14:22
user_123945839432
19910
add a comment |
up vote
0
down vote
favorite
I am looking for some expert advice in answering this finance question. I am having trouble figuring out how to compare these put and strikes. Is there a formula to approach this type of problem?
Let $p_K$ be the current price of a European put expiring at time $T$
with strike price $K$.
Let $S_0$ be the spot price of the underlying asset.
Compare the following quantities if possible.
(a) Compare $p_{50}$, $p_{55}$, $p_{60}$.
(b) Compare $p_{50}$ and 50
finance
asked Feb 28 '17 at 14:22
user_123945839432
19910
Well, $p_K$ has to be worth less than $K$ since it would be discounted by the interest rate, i.e., $p_K leq Ke^{-rT} < K$ for a continuously compounded rate $r>0$. Additionally, we see that if $K_1 < K_2$, then $$p_{K_1} leq p_{K_2}$$ since being able to sell the stock for $K_1$ at time $T$ is worth less than selling the same stock for $K_2$ at the same time.
– Giuseppe
Feb 28 '17 at 14:28
Ok. So for (a), can we compare? The way I read it is that we can't since we don't have any info on S. is this correct?
– user_123945839432
Feb 28 '17 at 14:35
2
No, as a matter of fact, it's (mostly) independent of stock price -- a 50-strike put is worth less than a 55-strike put, no matter the current stock price, at expiry, the 55 strike put is worth at least as much as the 50 strike put.
– Giuseppe
Feb 28 '17 at 17:24
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am looking for some expert advice in answering this finance question. I am having trouble figuring out how to compare these put and strikes. Is there a formula to approach this type of problem?
Let $p_K$ be the current price of a European put expiring at time $T$
with strike price $K$.
Let $S_0$ be the spot price of the underlying asset.
Compare the following quantities if possible.
(a) Compare $p_{50}$, $p_{55}$, $p_{60}$.
(b) Compare $p_{50}$ and 50
finance
asked Feb 28 '17 at 14:22
user_123945839432
19910
I am looking for some expert advice in answering this finance question. I am having trouble figuring out how to compare these put and strikes. Is there a formula to approach this type of problem?
Let $p_K$ be the current price of a European put expiring at time $T$
with strike price $K$.
Let $S_0$ be the spot price of the underlying asset.
Compare the following quantities if possible.
(a) Compare $p_{50}$, $p_{55}$, $p_{60}$.
(b) Compare $p_{50}$ and 50
finance
finance
asked Feb 28 '17 at 14:22
user_123945839432
19910
asked Feb 28 '17 at 14:22
user_123945839432
19910
asked Feb 28 '17 at 14:22
user_123945839432
19910
asked Feb 28 '17 at 14:22
user_123945839432
19910
asked Feb 28 '17 at 14:22
user_123945839432
19910
19910
Well, $p_K$ has to be worth less than $K$ since it would be discounted by the interest rate, i.e., $p_K leq Ke^{-rT} < K$ for a continuously compounded rate $r>0$. Additionally, we see that if $K_1 < K_2$, then $$p_{K_1} leq p_{K_2}$$ since being able to sell the stock for $K_1$ at time $T$ is worth less than selling the same stock for $K_2$ at the same time.
– Giuseppe
Feb 28 '17 at 14:28
Ok. So for (a), can we compare? The way I read it is that we can't since we don't have any info on S. is this correct?
– user_123945839432
Feb 28 '17 at 14:35
2
No, as a matter of fact, it's (mostly) independent of stock price -- a 50-strike put is worth less than a 55-strike put, no matter the current stock price, at expiry, the 55 strike put is worth at least as much as the 50 strike put.
– Giuseppe
Feb 28 '17 at 17:24
add a comment |
Well, $p_K$ has to be worth less than $K$ since it would be discounted by the interest rate, i.e., $p_K leq Ke^{-rT} < K$ for a continuously compounded rate $r>0$. Additionally, we see that if $K_1 < K_2$, then $$p_{K_1} leq p_{K_2}$$ since being able to sell the stock for $K_1$ at time $T$ is worth less than selling the same stock for $K_2$ at the same time.
– Giuseppe
Feb 28 '17 at 14:28
Ok. So for (a), can we compare? The way I read it is that we can't since we don't have any info on S. is this correct?
– user_123945839432
Feb 28 '17 at 14:35
2
No, as a matter of fact, it's (mostly) independent of stock price -- a 50-strike put is worth less than a 55-strike put, no matter the current stock price, at expiry, the 55 strike put is worth at least as much as the 50 strike put.
– Giuseppe
Feb 28 '17 at 17:24
Well, $p_K$ has to be worth less than $K$ since it would be discounted by the interest rate, i.e., $p_K leq Ke^{-rT} < K$ for a continuously compounded rate $r>0$. Additionally, we see that if $K_1 < K_2$, then $$p_{K_1} leq p_{K_2}$$ since being able to sell the stock for $K_1$ at time $T$ is worth less than selling the same stock for $K_2$ at the same time.
– Giuseppe
Feb 28 '17 at 14:28
Well, $p_K$ has to be worth less than $K$ since it would be discounted by the interest rate, i.e., $p_K leq Ke^{-rT} < K$ for a continuously compounded rate $r>0$. Additionally, we see that if $K_1 < K_2$, then $$p_{K_1} leq p_{K_2}$$ since being able to sell the stock for $K_1$ at time $T$ is worth less than selling the same stock for $K_2$ at the same time.
– Giuseppe
Feb 28 '17 at 14:28
Ok. So for (a), can we compare? The way I read it is that we can't since we don't have any info on S. is this correct?
– user_123945839432
Feb 28 '17 at 14:35
Ok. So for (a), can we compare? The way I read it is that we can't since we don't have any info on S. is this correct?
– user_123945839432
Feb 28 '17 at 14:35
2
2
No, as a matter of fact, it's (mostly) independent of stock price -- a 50-strike put is worth less than a 55-strike put, no matter the current stock price, at expiry, the 55 strike put is worth at least as much as the 50 strike put.
– Giuseppe
Feb 28 '17 at 17:24
No, as a matter of fact, it's (mostly) independent of stock price -- a 50-strike put is worth less than a 55-strike put, no matter the current stock price, at expiry, the 55 strike put is worth at least as much as the 50 strike put.
– Giuseppe
Feb 28 '17 at 17:24
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
You can use the Black and Scholes formula to answer this questions rigorously: https://en.wikipedia.org/wiki/Black–Scholes_model
This should help you confirm that $p_{50}leq p_{55}leq p_{60}$. This is because a put is like an insurance, it allows you to sell something at no less than $K$. Therefore, the higher is $K$ the more valuable the insurance. To see this, note that if at time $T$ the price is higher than $K$, then selling the good at the market price is better than exercising your put and selling it at $K$. In that case, the put is worthless. It is clear that the higher the strike price, the less likely it is for your put to be worthless.
As for the second question, you can use the formula of Black and Scholes to see that $Pleq K$ for any positive interest rate $rgeq 0$.
answered Nov 12 at 16:39
Gabriel Martínez
926
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
You can use the Black and Scholes formula to answer this questions rigorously: https://en.wikipedia.org/wiki/Black–Scholes_model
This should help you confirm that $p_{50}leq p_{55}leq p_{60}$. This is because a put is like an insurance, it allows you to sell something at no less than $K$. Therefore, the higher is $K$ the more valuable the insurance. To see this, note that if at time $T$ the price is higher than $K$, then selling the good at the market price is better than exercising your put and selling it at $K$. In that case, the put is worthless. It is clear that the higher the strike price, the less likely it is for your put to be worthless.
As for the second question, you can use the formula of Black and Scholes to see that $Pleq K$ for any positive interest rate $rgeq 0$.
answered Nov 12 at 16:39
Gabriel Martínez
926
add a comment |
up vote
0
down vote
You can use the Black and Scholes formula to answer this questions rigorously: https://en.wikipedia.org/wiki/Black–Scholes_model
This should help you confirm that $p_{50}leq p_{55}leq p_{60}$. This is because a put is like an insurance, it allows you to sell something at no less than $K$. Therefore, the higher is $K$ the more valuable the insurance. To see this, note that if at time $T$ the price is higher than $K$, then selling the good at the market price is better than exercising your put and selling it at $K$. In that case, the put is worthless. It is clear that the higher the strike price, the less likely it is for your put to be worthless.
As for the second question, you can use the formula of Black and Scholes to see that $Pleq K$ for any positive interest rate $rgeq 0$.
answered Nov 12 at 16:39
Gabriel Martínez
926
add a comment |
up vote
0
down vote
up vote
0
down vote
You can use the Black and Scholes formula to answer this questions rigorously: https://en.wikipedia.org/wiki/Black–Scholes_model
This should help you confirm that $p_{50}leq p_{55}leq p_{60}$. This is because a put is like an insurance, it allows you to sell something at no less than $K$. Therefore, the higher is $K$ the more valuable the insurance. To see this, note that if at time $T$ the price is higher than $K$, then selling the good at the market price is better than exercising your put and selling it at $K$. In that case, the put is worthless. It is clear that the higher the strike price, the less likely it is for your put to be worthless.
As for the second question, you can use the formula of Black and Scholes to see that $Pleq K$ for any positive interest rate $rgeq 0$.
answered Nov 12 at 16:39
Gabriel Martínez
926
You can use the Black and Scholes formula to answer this questions rigorously: https://en.wikipedia.org/wiki/Black–Scholes_model
This should help you confirm that $p_{50}leq p_{55}leq p_{60}$. This is because a put is like an insurance, it allows you to sell something at no less than $K$. Therefore, the higher is $K$ the more valuable the insurance. To see this, note that if at time $T$ the price is higher than $K$, then selling the good at the market price is better than exercising your put and selling it at $K$. In that case, the put is worthless. It is clear that the higher the strike price, the less likely it is for your put to be worthless.
As for the second question, you can use the formula of Black and Scholes to see that $Pleq K$ for any positive interest rate $rgeq 0$.
answered Nov 12 at 16:39
Gabriel Martínez
926
answered Nov 12 at 16:39
Gabriel Martínez
926
answered Nov 12 at 16:39
Gabriel Martínez
926
answered Nov 12 at 16:39
Gabriel Martínez
926
926
add a comment |
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2165377%2ffinance-math-comparison-of-puts%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Well, $p_K$ has to be worth less than $K$ since it would be discounted by the interest rate, i.e., $p_K leq Ke^{-rT} < K$ for a continuously compounded rate $r>0$. Additionally, we see that if $K_1 < K_2$, then $$p_{K_1} leq p_{K_2}$$ since being able to sell the stock for $K_1$ at time $T$ is worth less than selling the same stock for $K_2$ at the same time.
– Giuseppe
Feb 28 '17 at 14:28
Ok. So for (a), can we compare? The way I read it is that we can't since we don't have any info on S. is this correct?
– user_123945839432
Feb 28 '17 at 14:35
2
No, as a matter of fact, it's (mostly) independent of stock price -- a 50-strike put is worth less than a 55-strike put, no matter the current stock price, at expiry, the 55 strike put is worth at least as much as the 50 strike put.
– Giuseppe
Feb 28 '17 at 17:24