SERVING THE QUANTITATIVE FINANCE COMMUNITY

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by LocalVolatility
March 17th, 2013, 10:32 am
Forum: Student Forum
Topic: "r" in the 1973 Black Scholes model
Replies: 5
Views: 8320

"r" in the 1973 Black Scholes model

<t>Quotebut should the continuously compounded rate be used within the equation for "r" in d1 and d2 or should they be nominal ratesAre you asking for real vs. nominal? In that case it would be the nominal rate.A rate can be both continuously compounded and nominal - these are not alternatives as yo...
by LocalVolatility
March 13th, 2013, 11:38 pm
Forum: Student Forum
Topic: Geometric Brownian Motion and Independent Increments
Replies: 1
Views: 8065

Geometric Brownian Motion and Independent Increments

<t>QuoteFor any GBM, are the R.V.(s) (X(0), X(1),....X(t) independent or is it that the R.V. increments (X(n)/X(n-1)) for n=0,1,..... are independent?The increments are independent while Cov(X(s), X(t)) = min(s, t).QuoteWhat transformation could I use to transform a GBM to a Standard BM, is it just ...
by LocalVolatility
March 8th, 2013, 11:30 pm
Forum: Student Forum
Topic: Multiplying Two HUGEEE Matrices in Matlab
Replies: 5
Views: 9004

Multiplying Two HUGEEE Matrices in Matlab

What about converting the matrices to single precision first?A = single(rand(5000));B = single(rand(5000));C = A * B;is faster by a factor of 1.87 on my machine.
by LocalVolatility
March 7th, 2013, 3:13 am
Forum: Student Forum
Topic: Why shop loss
Replies: 12
Views: 8578

Why shop loss

Two words: utility theory. As a risk-averse investor, you don't only care about the mean return of your portfolio.
by LocalVolatility
March 6th, 2013, 10:03 pm
Forum: Student Forum
Topic: Expectation Questions
Replies: 3
Views: 8067

Expectation Questions

<t>QuoteE[E^-1/2*sigma^2*t) = ?I don't understand your question? I guess that sigma and t are constants - so there is nothing random here?Quotelet X(t) be the standard brownian motionE[e^sigma*X(t)] = ? I assume you are asking for (please use brackets properly or even better the Latex editor). You s...
by LocalVolatility
March 6th, 2013, 3:38 am
Forum: Student Forum
Topic: Boundary conditions for Black-Scholes-Merton SDE
Replies: 9
Views: 8703

Boundary conditions for Black-Scholes-Merton SDE

<r>QuoteThese BCs can also be 'deduced' mathematically from Fichera theory and that the solution is continuous at S = 0 and at S = SMax.Thank you for pointing that out - very interesting. I just had a look at your paper <URL url="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1552926"><LINK_TEXT...
by LocalVolatility
March 6th, 2013, 2:37 am
Forum: Student Forum
Topic: How to derive drift rate from bond prices for Rendleman Bartter?
Replies: 5
Views: 8253

How to derive drift rate from bond prices for Rendleman Bartter?

<t>I don't know Rendleman Bartter but Wikipedia told me that in this model the short rate follows a geometric Brownian motion. I remember that in these types of models (with geometric diffusion term), the expected value of the money market account is infinite for any time horizon, see e.g. Chapter 3...
by LocalVolatility
March 4th, 2013, 11:54 pm
Forum: Student Forum
Topic: Boundary conditions for Black-Scholes-Merton SDE
Replies: 9
Views: 8703

Boundary conditions for Black-Scholes-Merton SDE

<t>1.a) In any arbitrage free model, the level zero has to be absorbing for the stock price. Thus, if the stock price is ever zero it has to stay there forever with probability one. Consequently, all call options on it expire worthless with probability one.1.b) You might want to replace this with . ...
by LocalVolatility
March 4th, 2013, 11:46 pm
Forum: Student Forum
Topic: Where to get prices for actually traded quanto derivatives from?
Replies: 4
Views: 8483

Where to get prices for actually traded quanto derivatives from?

<t>There is a large number of quanto derivatives in the German exchange traded derivatives market. I am not referring to the listed options exchange Eurex but to the warrants and certificates listed in Frankfurt and Stuttgart. These products include quanto leverage certificates (basically down-and-o...
by LocalVolatility
March 1st, 2013, 5:55 am
Forum: Student Forum
Topic: What is implied volatility really pricing?
Replies: 3
Views: 8935

What is implied volatility really pricing?

Chapter 12 of "Paul Wilmott on Quantitative Finance" should answer most of your questions.
by LocalVolatility
February 21st, 2013, 3:42 am
Forum: Student Forum
Topic: Does the Ornstein?Uhlenbeck using for treat the vol simle?
Replies: 3
Views: 8225

Does the Ornstein?Uhlenbeck using for treat the vol simle?

<t>I can't answer the question if it is often used. However, I saw some empirical tests of the average pricing error of the correlated Stein & Stein / Schoebel & Zhu model (Ornstein-Uhlenbeck stochastic volatility) vs. the Heston model (CIR stochastic variance) and the two performed very sim...
by LocalVolatility
February 19th, 2013, 11:30 pm
Forum: Student Forum
Topic: Conditional Expectation
Replies: 5
Views: 8116

Conditional Expectation

So you are trying to price an option on a asset whose log is driven by a Brownian motion plus a compound Poisson process where the jumps can only take two possible values (like up x+% with probability p and down x-% with probability 1 - p)? Can you be more specific please?
by LocalVolatility
February 19th, 2013, 10:34 pm
Forum: Student Forum
Topic: Conditional Expectation
Replies: 5
Views: 8116

Conditional Expectation

What is X precisely? Do you know its density?
by LocalVolatility
February 18th, 2013, 5:40 am
Forum: Student Forum
Topic: GMM - Optimal Choice of Moment Conditions
Replies: 1
Views: 8056

GMM - Optimal Choice of Moment Conditions

If anyone is interested: I found a reference myself. Chapter 7 in Hall (2005) "Generalized Method of Moments" to discusses exactly this problem of moment selection.
by LocalVolatility
February 16th, 2013, 3:10 am
Forum: Student Forum
Topic: What are the conditions that make it necessary to use the longer form of ito's lemma?
Replies: 3
Views: 8367

What are the conditions that make it necessary to use the longer form of ito's lemma?

<t>These are just two different levels to look at the dynamics of your process Y. The first time, you express Y in term of changes in X (which itself is driven by the B.M.) and the second time you go one level lower and express the dynamics of Y directly in terms of the B.M.. Which of these form you...
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