l*******1
发帖数: 113 | 1 基于这两道题：
1.
S=100, k1=90, k2=100, which put is more risky?
2.
which one has bigger VaR? Put on the stock or the stock itself?
这就涉及到option的risk 问题。
哪位大牛可以来解释一下如何求option的VaR(which volatility to use for
computing the VaR)? | l*******1
发帖数: 113 | 2 @rrua
thanks for your response.
in your notation, is F_s delta of the put? I dont see why P(k1) and P(k2)
have the same delta at t=T.
For k1
Even for the case where they are both in the money (s
k1 will be less than delta of k2 in absolute value.
thanks | r**a
发帖数: 536 | 3 Sorry, I was wrong. For the binominal tree, the bigger strike is less risky.
The reason is as follows: Using the actual probability you can find that
the bigger strike has bigger actual rate of return, where all the actual
rate of return are using the absolute value. After assuming the vanishing
bank interest rate, you can show that the actual return rate equals is
propotional to the valotility. Thus we get the initial statement.
of
【在 l*******1 的大作中提到】
: @rrua
: thanks for your response.
: in your notation, is F_s delta of the put? I dont see why P(k1) and P(k2)
: have the same delta at t=T.
: For k1: Even for the case where they are both in the money (s: k1 will be less than delta of k2 in absolute value.
: thanks
| o**o
发帖数: 3964 | 4 In the money option delta approaches 1 or -1. At the money delta is roughly
0.5. Out of the money smaller. Same reason for the var. "bigger strike" is
not
risky.
★ 发自iPhone App: ChineseWeb - 中文网站浏览器
【在 r**a 的大作中提到】
: Sorry, I was wrong. For the binominal tree, the bigger strike is less risky.
: The reason is as follows: Using the actual probability you can find that
: the bigger strike has bigger actual rate of return, where all the actual
: rate of return are using the absolute value. After assuming the vanishing
: bank interest rate, you can show that the actual return rate equals is
: propotional to the valotility. Thus we get the initial statement.
:
: of
| r**a
发帖数: 536 | 5 Sorry, may I ask what your conclusion is? Is the bigger strike less risky or
not?
I think the bigger strike is less risky. The reason is that the bigger
strike gives rise to bigger rate of return. (Forget about my statements on
the delta, it should not be correct.) According to the CAPM, the one with
bigger rate of return should be have bigger risk. Am I wrong?
roughly
【在 o**o 的大作中提到】
: In the money option delta approaches 1 or -1. At the money delta is roughly
: 0.5. Out of the money smaller. Same reason for the var. "bigger strike" is
: not
:
: risky.
: ★ 发自iPhone App: ChineseWeb - 中文网站浏览器
| W*******d
发帖数: 63 | 6 1. larger gamma, larger risk
2. larger delta, larger VaR. so stock has larger VaR
【在 l*******1 的大作中提到】
: 基于这两道题：
: 1.
: S=100, k1=90, k2=100, which put is more risky?
: 2.
: which one has bigger VaR? Put on the stock or the stock itself?
: 这就涉及到option的risk 问题。
: 哪位大牛可以来解释一下如何求option的VaR(which volatility to use for
: computing the VaR)?
| r**a
发帖数: 536 | 7
I want to say that your statement is correct but not applicable to this case
. The reason is as follows:
We know that the portfolio loss can be approximately written as
$$
\delta R+0.5*\gamma R^2,
$$
where $R$ is the rate of return of the underlying stock. So if $\delta(k1)=\
delta(k2)$, then you may say "larger gamma, larger risk". But if $\delta(k1)
\neq\delta(k2)$, how can you say "larger gamma, larger risk"?
In my opinion, we need to use the linear approximation of the portfolio loss
to compare first, if we can't get the answer, then go the 2nd order
approximation. But in this case, the delta is already different in the
continuous case if we strictly follow the BS formula, so why do we need to
go the 2nd order approximation?
If I am wrong, please correct me.
【在 W*******d 的大作中提到】
: 1. larger gamma, larger risk
: 2. larger delta, larger VaR. so stock has larger VaR
| S*******s
发帖数: 13043 | 8 it is quite a straight forward question. vanilla option's price is
monotonous. its loss is its future price minus its current price, also
monotonous. so given same VaR percentile, say 95%, the underlying price to
that perntile is the same and less than current price. in that case, just
draft the chart of two option with different strike, easily to find that ITM
option has larger loss than th ATM option. | S*******s
发帖数: 13043 | 9 oh, they are puts. then the OTM option has less VaR than the ATM option
ITM
【在 S*******s 的大作中提到】
: it is quite a straight forward question. vanilla option's price is
: monotonous. its loss is its future price minus its current price, also
: monotonous. so given same VaR percentile, say 95%, the underlying price to
: that perntile is the same and less than current price. in that case, just
: draft the chart of two option with different strike, easily to find that ITM
: option has larger loss than th ATM option.
| r**a
发帖数: 536 | 10 I do agree with u. I made a mistake before. The underlying theory on these statements is
the approximation of the P&L. In the linear approximation, we have
$$
P&L=\delta*R.
$$
We know the delta of puts is negative and a decreasing function of the
strike. So the bigger strike is more risky.
【在 S*******s 的大作中提到】
: oh, they are puts. then the OTM option has less VaR than the ATM option
:
: ITM
| o**o
发帖数: 3964 | 11 The point is, you don't necessarily make money from an in the money option,
because it depends on the price you paid to obtain it. That's why only
relative value matters.
In this put case, 90 is OTM, thus less sensitive to the underlying moves.
is
【在 r**a 的大作中提到】
: I do agree with u. I made a mistake before. The underlying theory on these statements is
: the approximation of the P&L. In the linear approximation, we have
: $$
: P&L=\delta*R.
: $$
: We know the delta of puts is negative and a decreasing function of the
: strike. So the bigger strike is more risky.
| r**a
发帖数: 536 | 12
,
Oh, yes, I made a stupid mistake. In fact, we have delta(k2)
when $k2>k1$.
In summary, the P&L is
$$
P&L=\delta*(\triangle S),
$$
where $\triangle S$ is the moving of underlying stock. So once we fix $\
triangle S$, then how the profit or loss moves is determined by the amount
of \delta. But we know the exact formula of delta for puts, just plug the k1
and k2 into the BS formula to compare these two delta. You will find that
all these two delta are negative. And delta(k2)k1$.
【在 o**o 的大作中提到】
: The point is, you don't necessarily make money from an in the money option,
: because it depends on the price you paid to obtain it. That's why only
: relative value matters.
: In this put case, 90 is OTM, thus less sensitive to the underlying moves.
:
: is
| r**a
发帖数: 536 | 13 I think another simple point of view is that for the bigger strike case the
stock price has more possibility to reach the status of in-the-money in
terms of the actual probability measure in the BS model, so it is more risky
. I check the binomial tree, it is consistent with the CAPM.
,
【在 o**o 的大作中提到】
: The point is, you don't necessarily make money from an in the money option,
: because it depends on the price you paid to obtain it. That's why only
: relative value matters.
: In this put case, 90 is OTM, thus less sensitive to the underlying moves.
:
: is
|
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