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by pcaspers
April 30th, 2016, 6:18 pm
Forum: Technical Forum
Topic: Choice of LMM skew function
Replies: 1
Views: 1115

Choice of LMM skew function

<t>You want to multiply [$]\sigma(t)[$] with a mixture of a constant and [$]L(t)[$] to produce something between a flat smile and a skew. Since the scale does not matter, [$]\alpha L(0) + (1-\alpha) L(t)[$] is a clever choice because this factor is always in the order of magnitude of the Libor rate ...
by pcaspers
April 17th, 2016, 2:58 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 1169
Views: 151633

Breakthrough in the theory of stochastic differential equations and their simulation

<t>QuoteOriginally posted by: CuchulainnQuoteperfect precision There is no such thing as perfect precision in (numerical) mathematics. Accuracy is a polynomial function of dt based on continuity of the unknown exact solution. Which is what @list has also said, when I look at it. Is convergence monot...
by pcaspers
April 9th, 2016, 3:24 pm
Forum: General Forum
Topic: Vol used in interest rate cap pricing
Replies: 8
Views: 2185

Vol used in interest rate cap pricing

<t>at least for the major currencies there are quotes for fixed strikes like 1%, 2%, ... (or nowadays -1%, -0.5%, 0%, 0.5% ...), which can be used for bootstrapping; you can then place the atm caplets in between those fixed strikes and interpolate in strike direction for bootstrapping from the atm f...
by pcaspers
April 4th, 2016, 12:04 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

that's great, thanks Billy7, I will look at it when there is some free time again for it
by pcaspers
April 4th, 2016, 6:41 am
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

<r>Yes, thanks a lot again. I can rerun with more paths, Sobol sequences + Brownian bridges, a richer basis, but as you say, it won't be very insightful. Concerning the regression I am even thinking if it might be useful to have two regions with a separate calibration. But for the time being the glo...
by pcaspers
April 3rd, 2016, 6:58 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

<t>Actually I did not really notice up to ten minutes ago, but from the plain pricing I had the condition in my code that only ITM paths are taken into account in the regression. This seems to break the new call pricing, in cases where the new call is deep ITM, the put OTM, and the put continuation ...
by pcaspers
April 3rd, 2016, 6:50 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

<t>Here are my updated results (16384 calibration paths, 65536 pricing paths, both MT, basis 1,x,x^2), they look better.Dividend = 0.06 Put = 0.371782 NewCall = 0.369788Dividend = 0.05 Put = 0.35782 NewCall = 0.356191Dividend = 0.04 Put = 0.344102 NewCall = 0.343301Dividend = 0.03 Put = 0.330794 New...
by pcaspers
April 3rd, 2016, 6:09 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

no, it's still on my side, the newcall prices for negative q are way to low, let me check the code again ... sorry ...
by pcaspers
April 3rd, 2016, 3:24 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

<t>What I seem to observe -- for an american "newcall" [$]c(q)[$] and an american put [$]p(q)[$] -- is that [$]c(q) > p(q)[$] for all [$]q[$] and [$]c(q) \rightarrow p(q)[$] for [$]q \rightarrow \infty[$], if the exercise grid is a continuum.If the newcall would be exercisable at [$]t=0[$] (it is ac...
by pcaspers
April 3rd, 2016, 9:57 am
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

in any case, thanks a lot for your input, in particular Billy7 for pointing out the bug in my scheme
by pcaspers
April 3rd, 2016, 9:00 am
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

<t>Yes, it's dependent on the drift, here are my results for the equity case (5 years, 52 steps / year, Variant B), r = 2%, S_0 = K = 1, BS-vol = 0.4Dividend = 0.06 Put = 0.371687 NewCall = 0.381258 NewCall - Put = 0.00957093Dividend = 0.05 Put = 0.357894 NewCall = 0.36837 NewCall - Put = 0.0104756D...
by pcaspers
April 2nd, 2016, 6:05 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

That's for a bermudan new call generating a bermudan put with full two-phase regression as you mentioned.You did that for a bermudan call, but the generating put being european (with exercise at maturity ?). Is it obvious that the qualitative behavior is similar to a generated bermudan put?
by pcaspers
April 2nd, 2016, 6:03 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

<t>ok, I fixed the code for the IR model first (because that's what I am actually interested in) and here I getput = 0.0124168new call = 0.0476237where before (with peeking into the future)new call = 0.086853so it got down, but not to the plain bermudan put. I will next adapt the equity code as well...
by pcaspers
April 2nd, 2016, 5:46 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

yes exactly, currently I have a higher value, now the question is, does it go down to the put or some value in between ... :-)
by pcaspers
April 2nd, 2016, 5:15 pm
Forum: Technical Forum
Topic: Put-Call-Bermudan
Replies: 79
Views: 8531

Put-Call-Bermudan

ok, Variant B or A does not really matter for the time being... You are right, my update scheme takes an illegal shortcut at the moment by directly using "newcall" instead of a regression value to take the exercise decision. Let me update this and see what happens ...
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