HULL qestion 17.14

[sarita]

Hi David,

how are you doing? with respect to question 17.14 of Hull options and derivatives.

Few questions:

1) when the questions states: a European call option on Japanese yet, is this implying that this is a futures call option? and that is why we are using the exp?
2) how do you come up to delta of 0.5249 - i am using n(1)exp -(r-rf)*t = 0.5405* exp -0.03*.5833 = 0.531124; slightly different from what you have
3)can't quite understand how you are calculating gamma. i know the formula for gamma is N(d1)e-rt/s*sigma*square root of t.

Are we responsible to know the calculation of gama, vega and theta as stated in this questions?

many thanks,
S

 

[David Harper CFA FRM]

Hi saray,

(I moved this to Market Risk)

Did you see the forum thread @ http://forum.bionicturtle.com/viewthread/1955/
.. And the spreadsheet @ http://public.sheet.zoho.com/public/btzoho/hull-15-14

1) No, this question is not a futures option (option to enter into a futures contract). This is "merely" a currency option. The valuation and Greeks are just like a regular option, with the difference that the underlying is a unit of foreign currency and the key adjustment is to treat the foreign interest rate like the dividend.

2) delta = EXP(-Rfx*T)*N(d1), where Rfx = foreign riskfree rate. Note that is the same as delta = EXP(-q*T)*N(d1), but replace dividend (q) with foreign riskfree rate

3) Gamma: same idea

Re: Are we responsible to know the calculation of gama, vega and theta as stated in this questions?
It is hard to answer, honestly, because technically the AIM says yes you should know; i.e.,
"Define, compute and describe theta, gamma, vega, and rho for option positions."
... as noted this question applies the regular Greek calcs

But at the same time, this question is difficult and (in practical terms) is highly unlikely to be asked. Delta is more likely. Vega less likely (I am not sure it has ever been quizzed?). Rho is extremely unlikely (the calc of rho, i am confident, has never been asked).

Hope this helps,
David

 

[sarita]

Thanks for getting back to me. No, i did not see the link you had posted before. many thanks. s

 

[Kerene]

Dear David

Please help me with the following queries

1) With reference to the spreadsheet answer for John Hull Chap 17.14, please guide us on how to manually calculate the N'(d1) value of 0.3696?

2) The gamma formula in above-mentioned spreadsheet seems complicated. Would you have a breakdown of the gamma formula as we could not understand how the value of 4.2059 was derived?

3) In order to derive the option delta, we should always present value back the N(d1). True or False?

Many thanks.

 

[David Harper CFA FRM]

Hi Kerene,

1. N'(d1) is the standard normal probability density function. See http://en.wikipedia.org/wiki/Normal_distribution
... as we want a standard normal, replace mu (u) with 0 and sigma with (1) and you get the formula used in the XLS
The standard normal pdf is the first derivative of the cumulative standard normal CDF
... I like this http://demonstrations.wolfram.com/ConnectingTheCDFAndThePDF/

2. Gamma is a 2nd partial derivative (or first derivative of delta: change in option value with respect to change in delta). I don't know of, nor have ever seen, an intuitive breakdown. It it best understood via calculus.

3. delta is already a PV concept; i.e., change in current call value, c(0), with respect to change in current asset price, S(0).

Hope that helps, David

 

[Kerene]

Dear David

1) Looking at the alternative source pages, the graphs allow me to understand better.

2) Since no intuitive breakdown is given, can i assume that we are not required to memorize the formula for calculating gamma in level 1 exam? and the same applies for theta, rho & vega?

3) If N(d1) (or delta) is already a PV concept, why is the calculation for delta taking in e^-5%*0.5833 mutiply by N(d1) which is denoted by =EXP(-riskfree_foreign*T)*N_d1?. I'm confused.

* please refer to http://public.sheet.zoho.com/public/btzoho/hull-15-14

Many thanks.

 

[David Harper CFA FRM]

Hi Kerene,

1) Terrific!

2) These formulas (non delta Greeks) clearly have what i call "low testability;" i.e., given their relative lack of appearance in the past, most likely is they will not be tested. Personally, I would not bother to memorize them. But to be completely accurate, this is the AIM:
"Define, compute and describe theta, gamma, vega, and rho for option positions."

3) The apparent discounting is not discounting: the foreign interest rate is economically equivalent to a DIVIDEND YIELD. (Please note the XLS input is where the dividend yield would be). This because the asset is a foreign currency, so their interest rate is economically like a dividend on the asset. As such (as economically serving as a dividend), its function is to reduce the asset price not PV the delta (i.e., the holder of the option forgoes the interim benefit of the dividend yield).

I hope that is helpful. Good luck this week! David

 

[[email protected]]

Hi Kerene,

1. N'(d1) is the standard normal probability density function. See http://en.wikipedia.org/wiki/Normal_distribution
... as we want a standard normal, replace mu (u) with 0 and sigma with (1) and you get the formula used in the XLS
The standard normal pdf is the first derivative of the cumulative standard normal CDF
... I like this http://demonstrations.wolfram.com/ConnectingTheCDFAndThePDF/

Hope that helps, David​

Hi David,
Regarding calculation of N'(D1), I follow your example above of chaning mu to 0 and SD to 1 which converts the formula to something like ths :

1/Sqrt (Pi*2) * Exp(-0.5*D1^2)

which gives me answer of 0.3969 same as your excel sheet cell G9.

What i dont follow here is how Normsdist() function in excel calculates standard normal cumulative distrtibution.
When i checked help section of excel it gives me the same formula as one i mentioned above (0.3969).

So how is the value of N(D1) (0.5405) is arrived in cell G5 of your excel .

Thanks