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Sep
30
comment Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)
@James: Thanks for your comment. That is not the case. However I just found a mistake in the transcription of the closed formula my code. I've written $\left(\frac{B}{X0} \right)^{2 \bar{\mu}}$ instead of $\left(\frac{B}{X0} \right)^{2 {\lambda}}$ which explain the scaling difference. Now the match is perfect!
Sep
30
comment Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)
@YuliaV: You are absolutly right ! Of course I'm going to post it as soon as I have time to prepare it (change a little bit the notation for clarity sake). Anyway what about the formula ? Is there any mistake ? I think it's fundamental to check it also. And it's much quicker than check, run and eventually debug a code.
Sep
30
comment Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)
@YuliaV: If I am underestimating it reducing $\delta t $ would just increase the difference between the values computed by the closed formula and those via Monte Carlo. I don't see how it could help. I'm running the simulation with a $\delta t $ 10 times smaller anyway. I am pretty much convinced that if there is a mistake of my part (and it's clearly the case) it is almost surely in the closed formula. So you you guys could check it would be great. I've done that uncountable times and after so many tries our looking on it is so biased that it's too hard to detect a simple mistake.
Sep
30
comment Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation)
@YuliaV: Thanks a lot for your hint. You suppose you meant $X_{n\delta t}> B$ and $X_{(n+1) \delta t}> B$, right? In this case I would be underestimating the probability of hitting the barrier before $T$ instead of overestimating it since I'm excluding a lot of paths in with the condition is satisfied. Am I right ?
Sep
17
comment Pricing a bond contract from the yield curve
Thanks! I just realize that alone today then I came back to check your answer.
Sep
15
comment Pricing a bond contract from the yield curve
I don't have any information about the face value so I supposed that by default if nothing is mentioned about the face value we should consider it 1 and calculate the rate to multiply to the face value. Am I right? For the moment I am getting 0.19 which is not a coherent price at all.It should be at least higher than 1 obviously. Any guesses about a possible mistake I am doing? Maybe the spot rate are in % and should be divided by 100 what do you think ? That should make it bigger.
Sep
15
comment Pricing a bond contract from the yield curve
Also why the 0.5 in the formula?
Sep
15
comment Pricing a bond contract from the yield curve
Thank you very much for your answer. I sill have a question. As you can see I don't have all necessary spot rates of the term structure. Check it for example for the 15 March 2017. We could approximate it very roughly for the closest rate available. Although as I said it sounds too rough. There is another way to do it or am I misunderstanding something maybe ?
Mar
30
comment Gamma vs. Volatility Risk
That's perfect for B&S model. But how to relate Vega and gamma a in more general context like local and stochastic vol. models ?
Jun
7
comment Change option B&S pricing
@Imorin: It's not a homework question, even if it's a basic question. I've just got stuck and so I'd like some help. This question interest me as a inspiration for an bigger problem.
Apr
12
comment Ito's Lemma - Integrand depends on upper limit of integration
Of course not. It's a typo, I forgott the terms. Thank you for note that
Apr
9
comment Foward-start option pricing
@BrianB : No, it was a problem wich was proposed in a old exam.
Apr
9
comment Non-arbitrage theory and existence of a risk premium
@quasi: I forgot this condition on $\sigma_t$ while typing. See edition.
Apr
9
comment Non-arbitrage theory and existence of a risk premium
@quasi: You are totally right! Thank you for the correction.
Apr
8
comment Non-arbitrage theory and existence of a risk premium
@AlexeyKalmykov: I really don't know, but I'd like too if it makes part of a book. It was part of an exam question that I couldn't answer. If you find it somewher, please let me know.
Feb
25
comment Upper bound concerning Snell envelope
Sorry everybody, spetially Christian Fries, I totaly misunderstood the procedure to start a bounty and all. I'm ashamed guys.
Feb
23
comment Upper bound concerning Snell envelope
I can't give you a bounty, because firt of all your answer is not suffitiently complete and also I've already obtained very complete answers in math.stackexchange.com/questions/302466/ and mathoverflow.net/questions/121744/… many days before you give yours. So it semms not so ethic of your part start a bounty just to obtain an arbitrage of points. It's the kind of thing I see just in a forum of finance, never in science one.