Financial Risk Manager

Comparision between binomial and BSM model

2008-11-25T05:07:43-08:00

Dear David

I have created one spreadsheet where I am valuing put and call option with undernoted assumption.
( please see uploaded excel spreadsheet as well)stock 150
Strike 100
Volatility 5%
Rf 5%
T 1
With the above assumption, I am getting call price of Rs.54.88 with both binomial and BSM method, but when I am increasing the volatility, I am getting a slight price differencial (i.e. when volatility is 20%, price of call becomes 54.97.

My question: But when the same volatility jump is applied over to put valuation using binomial and BSM, I am getting a huge price difference. i.e. at
stock 75
Strike 100
Volatility 5%
Rf 5%
T 1

above assumption, I am getting same value for put option using binomial and BSM model, but when I am rasing the volatility to 20%, I am getting a huge price differential with Binomial it is 21.07 and with BSM it is 14.39.

1. What is the causative factor for such a huge difference?
2. Which model is optimum to use in real market situation?
3.When Stock=strike why put option have zero value but call option still positive through BSM model. even when I am having strike price of 100 and stock price of 75, I am getting a positive call value call=max(s-x,0).
4. Is option value and option premium different?
5.Which model the market participants are using mostly?

Regards,
Harish

Metallgeschaft - Contango / Backwardation

2008-11-18T20:33:01-08:00

I think I got the MG question right in the 2008 FRM exam, but I confuse myself when thinking about why positions lose value in contango or backwardation.

For the short position in long-term forward contracts during backwardation, these gain value because it locks in a higher price in the future for the seller? During backwardation, the forward price will be lower compared to the agreed price in the forward contract, creating profits?

For the long position in short-term futures contracts during contango, these lose value because it locks in a higher price in the future for the buyer? Each rolling hedge will require MG to buy at a higher price?

Base currency Vs foreign currency

2007-11-09T02:24:19-08:00

David

Always had this confusion on interpreting the BC and FC.

The current exchange rate between Japanese yen and US dollar is 134 yen/dollar. The one-year
interest rate in USA is 1.95 percent and the one-year interest rate in Japan is 0.65 percent.
According to interest rate parity the one-year forward yen/dollar exchange rate should be
CLOSEST to:

A. 130.59.
B. 131.73.
C. 132.29.
D. 133.50.

The question is simple; the answer being Spot * (1+ domestic)/(1+foreign)

The question is how do you interpret which is domestic and which is foreign? Also is there is a rough cut way of double checking with respect to interest rates. (if domestic interest rates < foreign interest rates) then ..... and vice versa

Grateful for a quick reply… as I am not able to get a fix on this

Thanks as always

PS: while you have pointed out that Interest rate parity is not included in the LOs, the sample FRM questions 2007 has a similar question as above, and in any case these kind of questions is an appln of the forward price determination.

Liquidity cost

2008-11-14T05:38:25-08:00

hi,

simple quick question

why is liquidity cost low when the asset is fungible

could you explain it ?

if the asset that i want to liquidate is fungible, the buyer of this asset can choose another asset which is a substitution of mine
therefore, isn’t it hard to liquidate? then it costs more, doesn’t it?

i think im wrong, but i can not understand in the opposite way

suk

zero cpn bond

2008-11-13T18:56:38-08:00

Hi, I was trying to find the calculator tutorial on here but having some trouble

I was hoping someone could help me price a zero cpn bond using the financial calculator. I am not sure what the various inputs should be. Unfortunately i dont have an example right now but i guess my biggest question is what should be input as PMT and N?

Thaks

practice exam

2008-11-11T13:39:09-08:00

Hi David,

List of questions where “I don’t get it” is growing as exam approaches .( A bit disappointed about the Flash Quiz because there are no reliable set of questions to practice on which cover all the AIMS and since you are best teacher I have come across your questions would have really helped practice better .)
Anyway will attempt some of your 2007 questions. I did not understand this question in 2007 FRM practice exam .It’s from Hull and i am supposed to know it and i don’t .I understand it is a Var calculation and the square root rule has been used but why duration?

Hong Kong Shanghi Bank has entered into a repurchase agreement with a client where
the client will sell a 10-year US treasury bond to the bank and repurchase it in 10 days.
The bond has a notional value of USD 10m, trades at par with the yield volatility for a 10-
year US treasury 0.074%. The swap’s maximum potential exposure at a 99% confidence
level is closest to:
a. USD 320,000
b. USD 380,000
c. USD 550,000
d. USD 1,200,000
CORRECT: B
The approximate duration for a 10 year bond is 7.0. The volatility of the swap value over
10 years is calculated as follows:
σ(V) = [market_value * duration * yield volatility *(10)0.5]
= 10,000,000 * 7.0 * 0.00074 * 3.16 = 163,806.
To get the 99% confidence interval, we multiply σ(V) by 2.33, which gives approximately
$380,000.

Reference: John Hull, Options, Futures, and Other Derivatives, 6th ed. Chapter 7.

Regards
Ravi

Merton Model, and risk capital

2008-11-12T18:57:43-08:00

hi,

in 06 practice exam part II, no.82

82. Consider a risky zero-coupon bond maturing in one year. At that time the issuer owes
USD 100 million. The issuer has no other debt and the bond can be priced using Merton’s model.
The bond is the only asset of a bank. Which of the following statements is correct?

a. The amount of risk capital required for this bond by the bank necessarily increases if
the volatility of the assets of the issuer increases

b. The amount of risk capital required for this bond exhibits a hump shape - it first
increases with asset volatility and then falls

c. The shape of the relation between the amount of risk capital and asset volatility
cannot be determined without knowing the bank’s RAROC hurdle rate

d. The shape of the relation between the amount of risk capital and asset volatility
cannot be determined without knowing the confidence level at which the bank’s
credit-VaR is calculated

ANSWER: B

A risky bond can be decomposed into a risk-free bond and a put option. The price of
the bond equals the price of the default free bond minus the put option premium. As
the asset volatility increases, the put premium will increase and the price of the risky
bond will fall. Thus, a bond issued by a firm with extremely high asset volatility will be
almost worthless, so that it requires little capital.
------------------------------------------------------------------------------------------------------------

i think the explanation at bottom does not match the answer b.
could you help me to understand?

inverse floater hedging

2008-11-12T19:21:37-08:00

hi,

A reverse floater hedges against falling benchmark yields

could you explain how it works?

thanks

suk

contango and backwardation of commodity

2008-11-12T11:46:08-08:00

Hi,

question 27, in 08 practice exam part III

27. Which of the following best describes what we would normally expect to see in a seasonal agricultural
market like wheat? Assume “the harvest” is normal and not unusually big or unusually small. Now
consider the following statements about the market.

I. Prices fall at the harvest and rise after the harvest.
II. Prices are constant on average across the year regardless of seasonality.
III. Prices rise at the harvest and fall afterwards.
IV. The market is in contango when the harvest comes in.
V. The market is in backwardation when the harvest comes in.
VI. If the market goes into contango, it is most likely to do so right before a new harvest.
VII. If the market goes into backwardation, it is most likely to do so right before a new harvest.

Now choose the letter that best describes which of the above statements is true.

could you explain how the price changes according to harvest?

downward sloping before harvest and then upward after harvest , is it right??
that is, backwardation before harvest and contango after harvest
so confused,,
both IV and VII are true but aren’t they clashed each other?
“when the harvest comes in” means.. approaching to harvest ? or exactly at the harvest?
i need to improve my english first of all,,

thanks!

suk

question from 06 practice exam

2008-11-12T18:05:35-08:00

hi,

06 practice exam part II

no.61

61. What is the best estimate of the market value of a portfolio of USD 100 million invested in
recently issued 6% 10-year bonds and USD 100 million of long 10-year zero coupon bond if
interest rates decline by 0.50%:
a. USD 219 million
b. USD 195 million
c. USD 209 million
d. USD 206 million
ANSWER: C

To calculate the best estimate of the market value of the portfolio if interest
rates decline 0.5%, one needs to calculate the change in the market value of
each bond using duration. The duration of the 10-year zero coupon bond is
10. Thus, the change in value of this bond equals 10x0.005x100,000,000,
which equals 5 million dollars.
The duration of the newly issued 6% bond is 7.802 assuming that the price of
the bond is par. Given a duration of 7.802, the change in the value of the
bond equals 7.802x0.005x100,000,000 which equals 3.91 million.
Thus, the best estimate of the market value of the portfolio if interest rates
decline by 0.5% is 200 million + 5 million + 3.91 million which equals 208.91
million.
Thus, the correct answer is ‘C’.
--------------------------------------------------------------------------------------------------

i feel so strange,
market value of zero bond is notional / (1+r)^10 , right?
but here, maculay duration is being used, not modified duration to estimate change in value
is this bad question to be ignored?

suk