I*M
发帖数: 1533 | 1 做了很久，没有头绪。
请教达人：
Q: For all examples assume a cash dividend paying stock with the following s
.d.e between cash dividend payments.
ds/s = rdt + sigma*dw
where r = riskless rate , sigma = volatility, dw = Brownian motion
1. What is the value today (t) of a contract that at some maturity (T) pays
the inverse of the stock price observed at the maturity?
a) How would this contract be hedged? Explain any drawbacks of the method
you choose.
b) How would you explain your theoretical price to a junior t | I*M
发帖数: 1533 | 2 抛砖引玉
3。Suppose that we believe that there are similarities between the
implementation of a barrier pricing engine and a convertible bond (assume
that the convertible contains early exercise and that the barriers &
convertible barriers are not constant in time):
a) What numerical method would you propose ?
FDM,
b) Give an object orientated overview of how code could be shared between
the models, with some description on the inputs and outputs to the model.
define Asset as a class，apply inheritanc
【在 I*M 的大作中提到】
: 做了很久，没有头绪。
: 请教达人：
: Q: For all examples assume a cash dividend paying stock with the following s
: .d.e between cash dividend payments.
: ds/s = rdt + sigma*dw
: where r = riskless rate , sigma = volatility, dw = Brownian motion
: 1. What is the value today (t) of a contract that at some maturity (T) pays
: the inverse of the stock price observed at the maturity?
: a) How would this contract be hedged? Explain any drawbacks of the method
: you choose.
| I*M
发帖数: 1533 | 3 自己顶一下
1. What is the value today (t) of a contract that at some maturity (T) pays
the inverse of the stock price observed at the maturity?
a) How would this contract be hedged? Explain any drawbacks of the method
you choose.
I am not sure of it.
if u long the contract=> long stocks, have to borrow money
or we define Z=1/S, and define another measure to make discounted Z a
martingale? But Q is current measure is already Risk-neutrual...
s
pays
【在 I*M 的大作中提到】
: 做了很久，没有头绪。
: 请教达人：
: Q: For all examples assume a cash dividend paying stock with the following s
: .d.e between cash dividend payments.
: ds/s = rdt + sigma*dw
: where r = riskless rate , sigma = volatility, dw = Brownian motion
: 1. What is the value today (t) of a contract that at some maturity (T) pays
: the inverse of the stock price observed at the maturity?
: a) How would this contract be hedged? Explain any drawbacks of the method
: you choose.
| c******j
发帖数: 149 | 4 Looks like the paper test from UBS. Are they still hiring? | Q***5
发帖数: 994 | 5 1. What is the value today (t) of a contract that at some maturity (T) pays
the inverse of the stock price observed at the maturity?
Assume no dividend ( the case with fixed dividend rate can be similarily
calcuated)
For simplicity, let t = 0.
V_0 = E(e^{-rT} 1/S_T), where S_T = S_0e^{(r-1/2\sigma^2)T+\sigma W_T}, and
W_T is a Gaussian Random variable with std sqrt(T). Using the fact that E(e
^{-1/2\sigma^2 T+ \sigma W_T}) = 1, V_0 can be easily calcuated.
I got V_0 = 1/S_0 e^{-2rT+\sigma^2 T} | I*M
发帖数: 1533 | 6 Exactly. thanks.
any idea about other Qs?
pays
and
(e
【在 Q***5 的大作中提到】
: 1. What is the value today (t) of a contract that at some maturity (T) pays
: the inverse of the stock price observed at the maturity?
: Assume no dividend ( the case with fixed dividend rate can be similarily
: calcuated)
: For simplicity, let t = 0.
: V_0 = E(e^{-rT} 1/S_T), where S_T = S_0e^{(r-1/2\sigma^2)T+\sigma W_T}, and
: W_T is a Gaussian Random variable with std sqrt(T). Using the fact that E(e
: ^{-1/2\sigma^2 T+ \sigma W_T}) = 1, V_0 can be easily calcuated.
: I got V_0 = 1/S_0 e^{-2rT+\sigma^2 T}
| k***a
发帖数: 22 | 7 LongWayTooGo:
#2 question can be decomposed into a spread option (on two options, which has analytic solution) + an underlying option (which is plain vanilla).
PDE is a bit complicated (because of the correlation between two underlying
options, is differrent from the correlation between two underlying prices themselves). If strike 1 <> strike 2, I think no analytic solution (but I am not so sure). | r**u
发帖数: 69 | 8 not sure if your solution is right.
V_0 = E_{r_free} [ e^{-rT} 1/S_T].
However, under r_free measure, S_T is log-normal and so is 1/S_T.
So the valuation should be simple.
The hedging part is a little complicated. I remember there is something in
this vein in John Hull.
pays
and
(e
【在 Q***5 的大作中提到】
: 1. What is the value today (t) of a contract that at some maturity (T) pays
: the inverse of the stock price observed at the maturity?
: Assume no dividend ( the case with fixed dividend rate can be similarily
: calcuated)
: For simplicity, let t = 0.
: V_0 = E(e^{-rT} 1/S_T), where S_T = S_0e^{(r-1/2\sigma^2)T+\sigma W_T}, and
: W_T is a Gaussian Random variable with std sqrt(T). Using the fact that E(e
: ^{-1/2\sigma^2 T+ \sigma W_T}) = 1, V_0 can be easily calcuated.
: I got V_0 = 1/S_0 e^{-2rT+\sigma^2 T}
| r**u
发帖数: 69 | 9 The underlyings are options, not stocks, hence the prices are not log-normal
model.
i'm not sure if there is analytical solution to the price of spread options
between options. also, the other is compound options (options on options),
which does have analytical solution.
has analytic solution) + an underlying option (which is plain vanilla).
underlying
themselves). If strike 1 <> strike 2, I think no analytic solution (but I am
not so sure).
【在 k***a 的大作中提到】
: LongWayTooGo:
: #2 question can be decomposed into a spread option (on two options, which has analytic solution) + an underlying option (which is plain vanilla).
: PDE is a bit complicated (because of the correlation between two underlying
: options, is differrent from the correlation between two underlying prices themselves). If strike 1 <> strike 2, I think no analytic solution (but I am not so sure).
|
|
