y********l
发帖数: 11 | 1 自己碰到过，面经里也经常出现的，最经典的binomial pricing：
At-the-money call/put, current price S, goes up to S_u with probability p,
goes down to S_d with probability (1-p). Without any knowledge on the
risk-free rate, what is the price of the call/put today?
有些印象好像解的时候会假设 r=0 ？还是有其他的什么方法吗？请不吝赐教，谢谢~ |
g*****1
发帖数: 18 | 2 This method is called risk-neutral pricing.
S = (Su*P + Sd*(1-p))*exp(-r*T)
r can be solved.
Then you can get the option price by discounting the option average payoff
with the risk-neutral rate. |
a**a
发帖数: 32 | 3
payoff
How can you solve the risk free interest rate and risk neutral prob
with one equation?
【在 g*****1 的大作中提到】
: This method is called risk-neutral pricing.
: S = (Su*P + Sd*(1-p))*exp(-r*T)
: r can be solved.
: Then you can get the option price by discounting the option average payoff
: with the risk-neutral rate.
|
p****e
发帖数: 1028 | 4 just assume r = 0.
if you were asked this question, obviously the assumption is that you wo
uld get the same answer no matter what r you would use.
same spirit as how risk-neutral valuation is derived.
【在 y********l 的大作中提到】
: 自己碰到过，面经里也经常出现的，最经典的binomial pricing：
: At-the-money call/put, current price S, goes up to S_u with probability p,
: goes down to S_d with probability (1-p). Without any knowledge on the
: risk-free rate, what is the price of the call/put today?
: 有些印象好像解的时候会假设 r=0 ？还是有其他的什么方法吗？请不吝赐教，谢谢~
|
x**y
发帖数: 10012 | 5 answer?
【在 p****e 的大作中提到】
: just assume r = 0.
: if you were asked this question, obviously the assumption is that you wo
: uld get the same answer no matter what r you would use.
: same spirit as how risk-neutral valuation is derived.
|
l****d
发帖数: 55 | 6 I think this might be about real world, not the risk-neutral world since the
probability p is given. P is unlikely same as the risk-neutral work
probability.
In that case, why not just
(S_u-S)*p for call option
(S-S_d)*(1-p) for put option
Any opinion?
【在 y********l 的大作中提到】
: 自己碰到过，面经里也经常出现的，最经典的binomial pricing：
: At-the-money call/put, current price S, goes up to S_u with probability p,
: goes down to S_d with probability (1-p). Without any knowledge on the
: risk-free rate, what is the price of the call/put today?
: 有些印象好像解的时候会假设 r=0 ？还是有其他的什么方法吗？请不吝赐教，谢谢~
|
m******2
发帖数: 564 | 7 基础真烂
(p*Su+q*Sd)/S0-1就是这期的free rate |
y********l
发帖数: 11 | 8 但是你所用的 p 和 q 一定都要是risk-neutral probability (\tilde{p},\tilde{q})
这
个关系才成立的，而risk-neutral measure 下：
\tilde{p}=(1+r-d)/(u-d) （1）
\tilde{q}=1-\tilde{p}=(u-1-r)/(u-d)
事实上（1）和你想求risk-free rate的公式是等价的...
另外，risk-neutral prob. 是 r 的函数，所以r=0 或其他值会影响\tilde{p}的取值
，从而也
影响option 的price。
【在 m******2 的大作中提到】
: 基础真烂
: (p*Su+q*Sd)/S0-1就是这期的free rate
|
z****s
发帖数: 532 | 9 我觉得可以用real prob 来做
assume 1 step time =1, only p,S,S_u,S_d are known.
S*exp(mu*1）=p*S_u+(1-p)*S_d
where mu is the return rate, therefore we can have a discount factor
exp(-mu*1)=...f(S,S_u,S_d,p) noted as DF
then the call=DF*(p*(S_u-S)+（1-p)*0)
real prob expected return then discounted by real return rate |
m******2
发帖数: 564 | 10 如果那个p是现实probability
此题无解
直接告诉他必须用这个假设
你可以侮辱我的智商
不要侮辱quant这门学科!
})
【在 y********l 的大作中提到】
: 但是你所用的 p 和 q 一定都要是risk-neutral probability (\tilde{p},\tilde{q})
: 这
: 个关系才成立的，而risk-neutral measure 下：
: \tilde{p}=(1+r-d)/(u-d) （1）
: \tilde{q}=1-\tilde{p}=(u-1-r)/(u-d)
: 事实上（1）和你想求risk-free rate的公式是等价的...
: 另外，risk-neutral prob. 是 r 的函数，所以r=0 或其他值会影响\tilde{p}的取值
: ，从而也
: 影响option 的price。
|
m********a
发帖数: 12601 | 11 不太明白你的意思
这个题和TOMAS BJOERK的书中的BINOMIAL PRICING有什么不一样的么？
【在 m******2 的大作中提到】
: 如果那个p是现实probability
: 此题无解
: 直接告诉他必须用这个假设
: 你可以侮辱我的智商
: 不要侮辱quant这门学科!
:
: })
|
z****s
发帖数: 532 | 12 为什么给你现实prob你说无解？
管他怎么来的？
【在 m******2 的大作中提到】
: 如果那个p是现实probability
: 此题无解
: 直接告诉他必须用这个假设
: 你可以侮辱我的智商
: 不要侮辱quant这门学科!
:
: })
|
w******i
发帖数: 503 | 13 have to assume p is risk-neutral prob.
then u can compute risk free rate. |
f**x
发帖数: 4325 | 14 这是基础中的基础。假设r=0，用S0,Su,Sd算risk-neutral probability。
题目给的p没用，直接无视 |
