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by Alan
July 21st, 2003, 2:46 pm
Forum: Technical Forum
Topic: Option Pricing and NonCentral Chi-Square Distribution
Replies: 4
Views: 190044

Option Pricing and NonCentral Chi-Square Distribution

<t>This should be do-able. Since f(x) can be put in the form C x^p e^(-x), then yourintegrand produces two terms with this same form (with p+1 in one case). Since it's a definite integral from K to infinity, it can be written in terms of a known function, namely the incomplete gamma function.Regards...
by Alan
July 14th, 2003, 3:37 pm
Forum: Technical Forum
Topic: Simulating reflected Brownian motion
Replies: 9
Views: 191157

Simulating reflected Brownian motion

<t>QuoteOriginally posted by: adriHi,but nowhere I was able do find a description "how to do it"...Try this: suppose the variable being simulated is X(t), which follows some 1-D diffusion with reflecting boundaries dX(t) = b dt + a dB(t),where B(t) is a Brownian motion and b = b(X(t),t) and a = a(X(...
by Alan
July 11th, 2003, 4:06 pm
Forum: Technical Forum
Topic: Change of Measure
Replies: 33
Views: 192236

Change of Measure

<t>Thanks, Anton, I stand corrected.I should have realized this from the case of stochastic volatility models, where Iknow that stationary models can become non-stationary by the risk-adjustment.A follow up on this. Sato defines a class of "additive processes", which apparently haveindependent incre...
by Alan
July 10th, 2003, 3:47 pm
Forum: Technical Forum
Topic: Change of Measure
Replies: 33
Views: 192236

Change of Measure

<t>QuoteOriginally posted by: Anton<i>so if I understand unlike the diffusion case where only some parameters are shifted here there is a much more general change and the distribution type itself might change</i>exactly. the type of the new process strongly depends on the measure change (i.e. its de...
by Alan
July 9th, 2003, 3:44 pm
Forum: Technical Forum
Topic: Change of Measure
Replies: 33
Views: 192236

Change of Measure

<t>Also Sato's "Levy Processes ... " has a nice discussion in section 33.If I am reading it correctly, the most general transform for a 1D-Levy process(i) keeps the Brownwian motion vol. the same, (ii) multiplies the Levy measure bya pretty general function, with some integrability conditions, and (...
by Alan
July 3rd, 2003, 2:42 pm
Forum: Student Forum
Topic: Zhang Analitical Asian Options
Replies: 3
Views: 189915

Zhang Analitical Asian Options

If you think Mathematica has done a symbolic integral incorrectly, (which is known to happen),re-do it numerically with NIntegrate and compare vs. your first result with specific parameters.Also if you have specific questions, the Mathematica newsgroup is very helpful.Regards,alan
by Alan
June 25th, 2003, 2:31 pm
Forum: Technical Forum
Topic: Stocastic Vol in the Heston Model
Replies: 14
Views: 191451

Stocastic Vol in the Heston Model

<t>QuoteOriginally posted by: mayaroThanks Rez. I scanned through Bakshi's papers listed on his website, but did not find what I was looking for. Perhaps I should clarify a bit. The Heston model is defined by the pair S_t, sigma_t and evolve according to the SDE (in the risk-neutral measure):d ln(S_...
by Alan
June 18th, 2003, 1:33 pm
Forum: Student Forum
Topic: Merton's Lifetime Portfolio Selection
Replies: 7
Views: 189506

Merton's Lifetime Portfolio Selection

<t>It represents the effective utility [derived utility J(W) ] for everything that happensbeyond your time horizon T. If you die at T, it's the utility you associate with thewealth you give your heirs. But you could be analyzing a long-lived project, let's say withprojections for events up to T = 5 ...
by Alan
June 16th, 2003, 3:16 pm
Forum: General Forum
Topic: Parity, Duality, or Supersymmetry in Merton's Jump Diffusion Model
Replies: 9
Views: 190250

Parity, Duality, or Supersymmetry in Merton's Jump Diffusion Model

<t>QuoteOriginally posted by: MikeMI just started playing around with Merton's jump diffusion model as presented in Hull. From what I've heard about this model in general, I assume that put-call parity does not necessarily apply. Does duality, supersymetry, antimatter, or whatever apply to this mode...
by Alan
June 12th, 2003, 12:51 pm
Forum: Technical Forum
Topic: Option expected return
Replies: 7
Views: 189929

Option expected return

For the instantaneous option expected return, apply Ito's formula (see FAQ) tothe option price formula C(S,t). For dS, substitute the real-world (objective) processdS = a S dt + sigma S dB(t). To simplify the other terms, use theBlack-Scholes PDE. Take the expectation. Regards,alan
by Alan
May 30th, 2003, 9:01 pm
Forum: General Forum
Topic: Risk free investment vs stock market
Replies: 14
Views: 190376

Risk free investment vs stock market

Good. Or to supplement Johnny's suggestion, trythe first (or more) of the articles here:http://faculty.london.edu/edimson/articles.htm
by Alan
May 30th, 2003, 5:24 pm
Forum: General Forum
Topic: Risk free investment vs stock market
Replies: 14
Views: 190376

Risk free investment vs stock market

<t>QuoteOriginally posted by: MarsdenThinking about it, I think there actually is a thought experiment that one could do in order to decide which position is most reasonable.To me, it's slam-dunk obvious that you should expect, over the long run, more than riskless rate from the stock market.Apart f...
by Alan
May 29th, 2003, 1:57 am
Forum: General Forum
Topic: Risk free investment vs stock market
Replies: 14
Views: 190376

Risk free investment vs stock market

<t>Your friend is right. When the outcome is say 50/50, most people hate to lose what they have, more than they like to win an equal amount -- tilting the odds so they earn the risk-free rate (almost zeroin the U.S.) still won't get them to take the bet. Most people need significantly more; this is ...
by Alan
May 23rd, 2003, 11:36 pm
Forum: Technical Forum
Topic: Heston's new model
Replies: 5
Views: 190250

Heston's new model

reza, it sounds interesting. Can you try to get permission fromSteve H. to post a copy, or failing that, post a link?
by Alan
May 22nd, 2003, 7:19 pm
Forum: Student Forum
Topic: When does risk neutral valuation work?
Replies: 3
Views: 189645

When does risk neutral valuation work?

<t>The only implicit condition is that there be no arbitrage opportunities. In practice, blatantarbitrage opportunities are rare, so you don't need to worry too much about that. Whatyou do need to worry about is that there is really no such thing as "the" risk neutral measure.Even with a (real-world...