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by tw
August 13th, 2002, 1:41 pm
Forum: Student Forum
Topic: Hull on futures options
Replies: 1
Views: 189084

Hull on futures options

<t>From Hull, fourth edition, section 12.9 (p.295):"Traded futures options are, in practice usually American. Assuming that the risk-freerate of interest, r, is positive, there is always some chance that it will be optimal to exercise an American futures option early."On the facing page, he quotes B...
by tw
August 12th, 2002, 7:32 am
Forum: Student Forum
Topic: stationary distributions problem
Replies: 1
Views: 188917

stationary distributions problem

<t>Before anyone spends any time on this (and I hope nobody already has)it was an error of schoolboy proportionsThe stochastic integral in question should be resolved as\int_{0}^{t} \sigma(t') dW(t') = W(t) [\int_{0}^{t} \sigma^{2}(t') dt']/tIn order to get to the variance of the Schwartz/Ornstein-U...
by tw
August 9th, 2002, 1:15 pm
Forum: Student Forum
Topic: stationary distributions problem
Replies: 1
Views: 188917

stationary distributions problem

<t>Here's yet another Ito-type problem that's been puzzling me [& thanks forall the hints given for previous problems!].I would be grateful if anyone can see the inconsistency in the followingtwo arguments:consider a simple one factor Schwartz type modelds/s=k ln(sbar/s)dt+sigma.dWk's the mean r...
by tw
August 7th, 2002, 2:22 pm
Forum: General Forum
Topic: Natural gas storage valuation
Replies: 11
Views: 190526

Natural gas storage valuation

<r>QuoteOriginally posted by: gammasharkHesabu,To compliment MPs thoughts, you can find packages which specialise in finding the value of storage. It is a problem I have looked at a bit, and have discussed with others when valuing a project earlier this year. Anyway Caminus have a software package, ...
by tw
August 4th, 2002, 9:46 am
Forum: Student Forum
Topic: stochastic calculus/Ito question
Replies: 4
Views: 189288

stochastic calculus/Ito question

<t>QuoteOriginally posted by: rezasorry for being slow, but my question is can you solve the ODEdx=m(x,s) dtto getx=f(s,t) ?Sorry, it's me that's being slow.This is exactly the part of the problem that confuses me. I don't currently have an explicit form for m, but imagine that there are no complexi...
by tw
August 3rd, 2002, 9:13 pm
Forum: Student Forum
Topic: stochastic calculus/Ito question
Replies: 4
Views: 189288

stochastic calculus/Ito question

<t>QuoteOriginally posted by: rezanot sure if I understand wellif x=M(s,t)dx = [ dM/dt + dM/ds f(s) + 1/2 d2M/ds2 g2(s) ] dt + dM/ds g(s) dW so I guess we need to get fromdx=m(s,x) dtsomething likedx = h(s,t) dt + n(s,t) dWand identify the two equations above ...do you have the actual expression for...
by tw
August 3rd, 2002, 7:22 pm
Forum: Student Forum
Topic: stochastic calculus/Ito question
Replies: 4
Views: 189288

stochastic calculus/Ito question

<t>Hi,I'm puzzled by a feature of a model I've been working on. Wouldbe very grateful if any one had any pointers about a way to proceed.I'm not even sure if the description is well enough posed, buthere goes...Basically, a quantity S satisfies a stochastic process of the formds= f(s) dt + g(s) dWAn...
by tw
July 19th, 2002, 9:47 am
Forum: Student Forum
Topic: simple stochastic integral
Replies: 1
Views: 189252

simple stochastic integral

<r>I was recently evaulating the following elementary stochastic integral:I=\int_{t=0}^{t=T} \sigma(t) dW_{t} with W(t) a Wiener process. <I><s>[I hope latex notation is a suitable lingua francafor the formulae]</s>.Usually I take a fairly rough and ready approach to evaluating this kind of objectbu...
by tw
July 16th, 2002, 8:35 am
Forum: General Forum
Topic: hedging option-on-future with restricted liquidity
Replies: 4
Views: 189296

hedging option-on-future with restricted liquidity

<t>The situation you posit appears unrealistic to me. You have a simple price process for a non-storable commodity, you can trade at t0 and from t1 to t2, but not from t0 to t1, and the possibility of trading does not affect the process. You know the volatility, spot price and times for certain........
by tw
July 13th, 2002, 5:37 pm
Forum: Book And Research Paper Forum
Topic: Copula books
Replies: 9
Views: 191256

Copula books

<r>Does anyone out there have any recommendations forbooks about Copulas?A trawl of amazon came up with <URL url="http://www.amazon.co.uk/exec/obidos/ASIN/0387986235/qid%3D1026585187/026-2643450-7070829Has"><LINK_TEXT text="http://www.amazon.co.uk/exec/obidos/ASI ... 7070829Has">http://www.amazon.co...
by tw
July 12th, 2002, 11:34 am
Forum: General Forum
Topic: hedging option-on-future with restricted liquidity
Replies: 4
Views: 189296

hedging option-on-future with restricted liquidity

<t>I was recently thinking the following situation, which valuersof real options in the power markets may find familiar.It's concerned with a finite time period of futures liquidityand the related risk issues (is there any literature on this subject?)Suppose I have a call option, for the physical de...
by tw
June 14th, 2002, 3:16 pm
Forum: Student Forum
Topic: ratio of two variables undergoing GBM
Replies: 2
Views: 189069

ratio of two variables undergoing GBM

<t>The derivation looks fine to me... although you can make it simpler by just writing that:S1,t =S1,0 * exp{(mu1-0.5*sigma1^2)*t + sigma1*W1,t}S2,t =S2,0 * exp{(mu2-0.5*sigma2^2)*t + sigma2*W2,t}hence S2,t/S1,t = S2,0/S1,0 * exp{(mu2-mu1-0.5*sigma2^2+0.5*sigma1^2)*t+ sqrt(sigma1^2+sigma2^2)*Wt}-> (...
by tw
June 14th, 2002, 1:02 pm
Forum: Student Forum
Topic: ratio of two variables undergoing GBM
Replies: 2
Views: 189069

ratio of two variables undergoing GBM

<t>Ok, it's friday, and my brain is not working particularly well, but,here's something that doesn't seem to be working out for me.I had always imagined the ratio of two independent variables undergoing geometric brownian motion also undergoes geometric Brownian motion.The reason for this was I had ...
by tw
May 18th, 2002, 8:22 am
Forum: Technical Forum
Topic: Asymptotic VAR?
Replies: 5
Views: 189519

Asymptotic VAR?

<t>Aaron,Thanks for the reply. The nature of asymptotic approximation I had in mind was something along the lines of the following:Suppose you have a portfolio consisting of several underlyingsand derivatives priced off of those underlyings, the change in P&L would be something likeD(P&L) = ...
by tw
May 17th, 2002, 1:03 pm
Forum: Technical Forum
Topic: Asymptotic VAR?
Replies: 5
Views: 189519

Asymptotic VAR?

<t>[I'm caveating this by stating that I'm not a risk manager: myinterest in the calculation of VAR is mostly academic]I was playing around with formulae for VAR recently and wonderedif it was either an accomplished calculation or an area of active researchto calculate an approximate Value at Risk u...
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