One of the great things about maths is how one so often comes up against obstacles requiring taking a different route. And if pupils don't learn this early on then they are doomed to suffering from fear of maths later on. A teacher can demonstrate this by getting things wrong, often and in public!!! That's my excuse!

(But I don't approve of total neglect of a syllabus. Go off piste often by all means though.)

Indeed! Mathematicians love when a theory goes wrong, it gives new insights. Engineers go berzerk when their examples don't generalise 1:1 to higher spaces.

Actually, I think mathematics is one of the few disciplines that encouraged inductive thinking (maybe philosophy and history as well?).

I like these quotes by the brilliant Paul Halmos

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case.

And if it's not fun, don't do maths. I go off piste when someone asks a question. I try to answer for about 3-5 minutes and then return the normal slopes.It's taboo to say IMO "we'll discus it in 124 slides from now.."

Statistics: Posted by Cuchulainn — Yesterday, 6:31 pm

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(But I don't approve of total neglect of a syllabus. Go off piste often by all means though.)

Statistics: Posted by Paul — Yesterday, 5:39 pm

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Another approach is to take a scoped down case and try to solve it on the fly. And never say "let's talk about after the coffee break". Many speakers are scared of interacting with their audience.

These day I try to use graded example and even quizzies. Like in judo.

Statistics: Posted by Cuchulainn — Yesterday, 2:47 pm

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Are you still teaching so badly, Stuart?

Statistics: Posted by DavidJN — Yesterday, 1:32 pm

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1. Available space. Adding something probably means something else has to go.

2. How easy or standard is the step?

3. How much spoon feeding do you want?

And to say something is easy or obvious (I prefer "trivial" whenever possible) can be helpful for the student lacking confidence. And a nice slap on the wrist for the lazy.

You are getting soft in your old age, Cuch!

Statistics: Posted by Paul — July 23rd, 2017, 4:00 pm

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Looks like the text in book is incomplete; stating that something is 'easy' or 'is obvious' is a bit irresponsible. In Maths theses, the examiners get very annoyed.

Either in book include what ppauper has done or give a reference (possibly once-off in an appendix).

An interesting twist is to find the transformation from first principles to arrive at the desired form.

Statistics: Posted by Cuchulainn — July 23rd, 2017, 9:39 am

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∂V∂t = ∂V∂F∂F∂t + ∂V∂t∂t∂t

Statistics: Posted by VinayDvd08 — July 23rd, 2017, 3:23 am

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[$]\frac{\partial V}{\partial S}\left.\right|_{t}=\frac{\partial V}{\partial F}\left.\right|_{t}\frac{\partial F}{\partial S}=e^{r(T_{f}-t)}\frac{\partial V}{\partial F}\left.\right|_{t}[$]

[$]\frac{\partial^{2} V}{\partial S^{2}}\left.\right|_{t}=e^{2r(T_{f}-t)}\frac{\partial^{2}V}{\partial F^{2}}\left.\right|_{t}[$]

[$]\frac{\partial V}{\partial t}\left.\right|_{S}=\frac{\partial V}{\partial t}\left.\right|_{F}+\frac{\partial V}{\partial F}\left.\right|_{t}\frac{\partial F}{\partial t}=\frac{\partial V}{\partial t}\left.\right|_{F}-rF\frac{\partial V}{\partial F}\left.\right|_{t}[$]

assuming I've done the math right, if you put all that in Black Scholes, you get the simpler equation

Statistics: Posted by ppauper — July 22nd, 2017, 2:37 pm

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Question: Can't understand derivation of Black Eqn for Option on Futures. please help!

e.g.

from

Statistics: Posted by VinayDvd08 — July 22nd, 2017, 1:33 pm

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The fund would expect to have realizations starting in year 3 or 4 and would use some of the proceeds of the realizations to pay for subsequent management fees.

Statistics: Posted by bcreilly2 — July 21st, 2017, 6:10 pm

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First one technicality: Shouldn't dS^2 = S^2 * sigma^2 * dz [and not dt] - I guess what you did is assuming no drift rate?

I am aware that this is a henn-egg problem. We are solving for something that we used as input. Still, this seems to be an at least "rough" approximation (although it might not be fully correct academically)?

The interest rates I have obviously neglected. I am reading more about jump diffusion as well, so I hope I am getting closer. Do you have any other keywords so I'd have a starting point where to look to find non misspecified models?

Thank you in advance. Really appreciate your help!!

Statistics: Posted by jonasre — July 20th, 2017, 10:23 pm

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Your initial portfolio is then

[$] \Pi = C - \Delta S + (\Delta S - C) = 0 [$]

If you only delta hedge and keep other variables/parameters constant, then the change in your portfolio value (marked-to-model) after a time dt is

[$] d \Pi = \Theta dt + \frac{1}{2} \Gamma dS^2 + r (\Delta S - C)dt [$]

Assuming you canwrite [$] dS^2 = \sigma^2 S^2 dt [$] (no jumps_, then the break-even move is that value of [$] dS^2 [$] such that [$] d\Pi =0 [$]. In other words when

[$] \Theta = - \frac{1}{2} \Gamma \sigma^2 S^2 - r (\Delta S - C) [$]

Lo and behold, this is the Black-Scholes equation... But not really, since the BS equation tells you, assuming you know the vol to start with, how to solve for your option price and greeks, and this equation tells you if you know your gamma and delta and theta (from a mis-speicfied Black Scholes model) what should be the vol / daily spot move to balance - which is obviously the vol you used initially for solving Black-Scholes. The next question should be so what happens if my daily move is not my implied volatility.

Anyway, I hope you're really confused now and decide to explore further what happens if you hedge with a mis-specified model.

To summarize, assumptions to arrive at the expression in the link (which oversimplifies things):

- you're only letting [$]S[$] vary and (hence) only delta hedging

- r = 0

Statistics: Posted by frolloos — July 20th, 2017, 3:34 pm

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