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by DoubleTrouble
August 7th, 2011, 12:54 pm
Forum: Student Forum
Topic: Pricing Barrier option in BSM model
Replies: 8
Views: 19406

Pricing Barrier option in BSM model

<t>Hi!I'm in need of some guidance. I want to learn how to find the price of a barrier option of European type paying the amount at time T. Where and . This is how I reason:but to get further I need to know the distribution of M(T), which I don't. I know the distribution of maximum of Brownian motio...
by DoubleTrouble
August 2nd, 2011, 7:49 pm
Forum: Student Forum
Topic: Maximum of Brownian Motion
Replies: 5
Views: 18303

Maximum of Brownian Motion

QuoteOriginally posted by: ThinkDifferentwhat you are doing in the second post doesn't seem to lead anywhere. in fact, starting from the second equality sign it becomes nonsense.... Yeah, I see why now! Thanks for your input!
by DoubleTrouble
August 2nd, 2011, 6:37 pm
Forum: Student Forum
Topic: Maximum of Brownian Motion
Replies: 5
Views: 18303

Maximum of Brownian Motion

Perhaps one can find the distribution of easier by reasoning like this:where
by DoubleTrouble
August 2nd, 2011, 6:33 pm
Forum: Student Forum
Topic: Maximum of Brownian Motion
Replies: 5
Views: 18303

Maximum of Brownian Motion

<t>Hi!I would like to present a solution for how to calculate where and I'd really appreciate if you guys would be so kind to pointed out where my reasoning has flaws (if it has any).First of all we need to find the probability density function of . To do this we use the Reflection Principle which t...
by DoubleTrouble
August 2nd, 2011, 11:37 am
Forum: Student Forum
Topic: Put-Call parity and Convexity
Replies: 6
Views: 18948

Put-Call parity and Convexity

The easiest way of proving this inequality ought to be the following: The map is increasing. Therefore if t < T we get:
by DoubleTrouble
August 2nd, 2011, 11:31 am
Forum: Student Forum
Topic: Put-Call parity and Convexity
Replies: 6
Views: 18948

Put-Call parity and Convexity

<t>Thank you for your hints bwarren, that was about all the help I needed! I feel really stupid for not figuring out (2)! I just have one question regarding (1). Is it a reasonable restriction to assume that the Stock is modeled by a GBM with constant rate of return and constant volatility like Guit...
by DoubleTrouble
August 1st, 2011, 9:33 pm
Forum: Student Forum
Topic: Put-Call parity and Convexity
Replies: 6
Views: 18948

Put-Call parity and Convexity

<t>Hello!I've been told that it's possible to show the inequality both using (1) Jensen's inequality (convexity) and using the (2) Put-Call Parity. I would be very grateful to any kind of hint!(1) Regarding the convexity we know that the function is convex so by using Jensen's inequality I can figur...
by DoubleTrouble
April 8th, 2011, 5:04 pm
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

Ok, I figured it out now! It was not as trivial as you made it seem but not very difficult either. Thanks for the tip!
by DoubleTrouble
April 8th, 2011, 4:33 am
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

QuoteOriginally posted by: quantmehQuoteOriginally posted by: DoubleTroubleE[X^2 Y^2] >= E[E^2]E[Y^2] lookup jensen's inequalityI've never used it in 2-dim before. Is that okay? And also, X^2 Y^2 is not convex in R^2!
by DoubleTrouble
April 8th, 2011, 4:32 am
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

<t>QuoteOriginally posted by: bearishLet W and Z be two standard independent normals and write X=aW, Y=b(cW+sqrt(1-c^2)Z); where a and b are the standard deviations of X and Y, and c is the correlation between X and Y. Direct computation then gives E(X^2Y^2)=a^2b^2*(1+2c^2).Thank you for your reply....
by DoubleTrouble
April 7th, 2011, 6:12 pm
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

<t>Another problem that I can't solve. I need to prove that if (X,Y) is a normally distributed random vector and both X and Y have 0 mean but unknown variance (different variance for X and Y of course), then:E[X^2 Y^2] >= E[E^2]E[Y^2] i.e. X^2 and Y^2 are positively correlated.This has bothered me t...
by DoubleTrouble
April 7th, 2011, 5:36 pm
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

I figured out that it must be a misprint in my instructions. I have proved that the variables must be independent or at least uncorrelated for the result to be possible!But thank you very much for taking your time to answer. I will soon have another question in basic probability!/DT
by DoubleTrouble
April 6th, 2011, 5:33 pm
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

QuoteOriginally posted by: ACDAre they from a multivariate normal distribution or are thy just marginally normally distributed?They are not from a multivariate normal distribution. I have X_1, ..., X_n random variables which are all N(0,1).
by DoubleTrouble
April 6th, 2011, 4:10 pm
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

Yes, of course but I was hoping of there being an easier way or some kind of clever trick since the joint density is so messy!
by DoubleTrouble
April 6th, 2011, 3:55 pm
Forum: Student Forum
Topic: Basic Probability
Replies: 15
Views: 21171

Basic Probability

Hi!I'm dealing with a problem in which I have to calculate Cov(X,Y) where X and Y are N(0,1) which is equivalent to calculating E[XY]. X and Y is not necessarily independent. Is there any trick for how to do this?Best regards,DT
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