Statistics: Posted by Cuchulainn — April 19th, 2019, 1:14 pm

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QED

Statistics: Posted by Cuchulainn — April 19th, 2019, 1:04 pm

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Thank you (both of you).

Now, if I wanted to structure the option in such a way that the notional does decrease every week, I would basically buy a strip of options with the same strike but different expirations. Buying 0.166 for every week up until week #6 (Expiration of the last strip). In this case, this call strip wouldn't be considered a Bermudan option right??

Thank you both for your help!

Andres

With the strip,you can end up with any volume between 0*0.166 and 6*0.166 but with the Bermudan you can only end up with 1 lot, no?Now, if I wanted to structure the option in such a way that the notional does decrease every week, I would basically buy a strip of options with the same strike but different expirations. Buying 0.166 for every week up until week #6 (Expiration of the last strip). In this case, this call strip wouldn't be considered a Bermudan option right??

Thank you both for your help!

Andres

Or am I missing something?

The liquid option contract is most likely an American so the possibility of overhedging is significant. Also only one expiry per futures expiry typically.

Statistics: Posted by tw — April 11th, 2019, 2:57 pm

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Is this right?

Statistics: Posted by billyx524 — April 10th, 2019, 11:45 pm

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The formula is only rigorously true if the discount curve is the same as the forward (projection) curve.

Statistics: Posted by fyvr — April 10th, 2019, 1:49 pm

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For the swap rate formula, it would need a basis adjustment right? But how you apply the basis is a matter of choice?

Statistics: Posted by billyx524 — April 10th, 2019, 1:57 am

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2) don’t make the mistake of getting bogged down by formalism, you need to understand things too. The par swap rate is the fixed rate the market says is economically equivalent to receiving a string of LIBOR fixings. So, you can (should) think of it as just the average (appropriately defined) of the forward LIBORs that span the forward period.

If you understand this, the problem you posted is rather trivial.

Statistics: Posted by fyvr — April 10th, 2019, 1:29 am

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1). I am not sure if I understand why you say the "relevant forward period is identical". For the swaption case, the vol is the forward swap rate in one years time (relative to today) for a future two year period [1, 3]. For the cap case, we have two forward rates, one expiring at one year for the period [1,2], the other expiring in two years for the period [2,3]. Is this right?

2). I can intuitively understand why swap rate is an average of forward libors. However, how can I show this mathematically. I am asking because the swap rate formula is a ratio of zero coupon bond prices:

swap rate = ( P(t, Ta) - P(t, Tb) ) / sum ( tau * P(t, Ti) )

Thanks!

Statistics: Posted by billyx524 — April 10th, 2019, 1:04 am

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\[\frac{\partial v}{\partial t} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 v}{\partial S^2} + \sigma S^2 \frac{\partial^2 V}{\partial S^2}=0\]

So, we indeed need to know gamma in some way. What about about solving simultaneously for [$]V,v[$] as a parabolic PDE system, like with chooser option PDEs?

I have never tried it nor seen it approached this way (on paper) before but with the binomial method (ouch) it can be done by bumping [$]\sigma[$]. And a tree is almost like a PDE, kind of.

At least, the parabolic system's matrix for [$](V,v)[$] is positive definite, so it's kind of hopeful.

Corollary: for [$]\rho[$] we need to know [$]\Delta[$] and [$]V[$]?

Statistics: Posted by Cuchulainn — April 9th, 2019, 3:58 pm

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And if so, what at the BCs? Is vega defined at [$]t = 0[$]?

Statistics: Posted by Cuchulainn — April 9th, 2019, 1:42 pm

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Thanks!

Statistics: Posted by billyx524 — April 9th, 2019, 5:06 am

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