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】![](/moin_static193/solenoid/img/up.png) : 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.
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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】![](/moin_static193/solenoid/img/up.png) : 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~
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x**y 发帖数: 10012 | 5 answer?
【在 p****e 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 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.
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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】![](/moin_static193/solenoid/img/up.png) : 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】![](/moin_static193/solenoid/img/up.png) : 基础真烂 : (p*Su+q*Sd)/S0-1就是这期的free rate
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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】![](/moin_static193/solenoid/img/up.png) : 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。
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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】![](/moin_static193/solenoid/img/up.png) : 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! : : })
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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】![](/moin_static193/solenoid/img/up.png) : 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! : : })
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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 |