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Nov
20
comment How to price an European call on zero-coupon from the yield curve?
@That Thanks for your comment. I know that. My question is all about how to calculate it just raving the Yield Curve as input and nothing else.
Nov
15
comment Help with integrating stochastic calculus expression from yield curve model
You're welcome. You are right, you can translate that formally by $z(t) \overset{\mathcal L}{=} \int_0^t e^{-2k(t-s)}~ds \frac{1}{\sqrt{t}} W_t$. I added that to the answer
Nov
3
comment Why is OU process stationary?
Solving the recurrence $m_i+\beta(t_i-t_{i-1})m_{i-1}= \alpha(t_i-t_{i-1})$ where $m_i:=\mathbb E[r_{t_i}]$ you may find the right answer
Oct
31
comment (Beginer on bond market) References on callable bond's pricing
Also could you write mathematically what you said. My question was indirectly how to right mathematically the payoff of a callable bond in a continuous framework. Then I will be interested in credit risk indeed. But first things first... All equivalences you mentioned interest me even more. So if could please right it down it would be very kind of you. Many thanks
Oct
31
comment (Beginer on bond market) References on callable bond's pricing
Hi Mark, thanks for your answer. You are talking about the following paper of yours right ? "Vega Control" papers.ssrn.com/sol3/papers.cfm?abstract_id=1398523
Oct
30
comment (Beginer on bond market) References on callable bond's pricing
Not necessarily.
Oct
30
comment (Beginer on bond market) References on callable bond's pricing
thanks a lot for your answer! What about continuous models ? Do you know any reference ? I admit I am more interested in continuous models.
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.