l*********t
发帖数: 89 | 1 请各位兄弟路过此题拔刀相助。
本题我有一定的思路但最终结果不明朗。
题目：
You long a straddle(ie. long a call, long a put). When the risk-free rate
goes up. what happens to your position?
我求的是Greeks里的rho, 即option value对risk-free rate的偏导，最后此portfolio
的rho的表达式是 K*(T-t)*exp(-r(T-t))*(2N(d2)-1）
不过此式对r求导始终会留下N(d2)项，这样risk-free rate 总在normal distribution
里，不方便分析。
请诸位大侠指教，先谢了~ | z****u
发帖数: 185 | 2 think about this way,
1. for stock options, if rate increases, call price will increase but put
price will decrease.
2. if the straddle strike is way lower than the forward, the call option
dominates while put is almost worthless. So if rate increases, straddle
price should increase.
3. if the straddle strike is way higher than the forward, put option
dominates. So if rate increases, straddle price should decrease.
4. somewhere in between, very likely it is close to atm, the straddle should
switch. | l*********t
发帖数: 89 | 3 Excellent financial intuition! The conclusions of all the 4 points are right
!
For point 4, you not only solved this problem, but also point out the
drawback of long a straddle when the forward value is close to the strike!
We indeed should switch the position and short the straddle instead!
Thanks a lot, zouzou! I think I need to pick up some financial intuition now
and not always use quant methods :)
should
【在 z****u 的大作中提到】
: think about this way,
: 1. for stock options, if rate increases, call price will increase but put
: price will decrease.
: 2. if the straddle strike is way lower than the forward, the call option
: dominates while put is almost worthless. So if rate increases, straddle
: price should increase.
: 3. if the straddle strike is way higher than the forward, put option
: dominates. So if rate increases, straddle price should decrease.
: 4. somewhere in between, very likely it is close to atm, the straddle should
: switch.
| g*****1
发帖数: 18 | 4 The risk-free rate is used to discount the future payoff. The payoff of the
straddle is always positive, as you are long a call and a put.
Everything being equal, when risk-free rate increases, your straddle value
will decrease, as the future payoff is discounted by a higher rate. It is
assumed that the risk-free rate does not correlate with the stock price
movement. | w*****e
发帖数: 197 | 5 Dude, I thought like so some time ago.
But your words are flawed because stock
has a drift of r in the RN world.
Hence, you can NOT just treat r as a
discount factor.
And this is precisely why calls and puts
behave differently when r changes.
the
【在 g*****1 的大作中提到】
: The risk-free rate is used to discount the future payoff. The payoff of the
: straddle is always positive, as you are long a call and a put.
: Everything being equal, when risk-free rate increases, your straddle value
: will decrease, as the future payoff is discounted by a higher rate. It is
: assumed that the risk-free rate does not correlate with the stock price
: movement.
|
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